LMFDB - Embedded newform 425.3.u.e.401.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.1
Character	$\chi$	$=$	425.401
Dual form			425.3.u.e.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35804 + 3.27860i) q^{2} +(-2.09388 - 1.39909i) q^{3} +(-6.07650 - 6.07650i) q^{4} +(7.43063 - 4.96499i) q^{6} +(3.01835 + 0.600386i) q^{7} +(15.0602 - 6.23812i) q^{8} +(-1.01725 - 2.45586i) q^{9} +(9.22089 + 13.8000i) q^{11} +(4.22193 + 21.2251i) q^{12} +(-2.30659 + 2.30659i) q^{13} +(-6.06746 + 9.08060i) q^{14} +23.4739i q^{16} +(4.41170 - 16.4176i) q^{17} +9.43323 q^{18} +(-11.1013 + 26.8010i) q^{19} +(-5.48007 - 5.48007i) q^{21} +(-57.7671 + 11.4906i) q^{22} +(-10.8556 + 7.25351i) q^{23} +(-40.2619 - 8.00859i) q^{24} +(-4.42995 - 10.6948i) q^{26} +(-5.72761 + 28.7946i) q^{27} +(-14.6927 - 21.9892i) q^{28} +(-4.03821 - 20.3015i) q^{29} +(7.76376 - 11.6193i) q^{31} +(-16.7209 - 6.92600i) q^{32} -41.7965i q^{33} +(47.8354 + 36.7599i) q^{34} +(-8.74171 + 21.1043i) q^{36} +(-31.0567 - 20.7514i) q^{37} +(-72.7936 - 72.7936i) q^{38} +(8.05687 - 1.60261i) q^{39} +(-70.6653 - 14.0562i) q^{41} +(25.4091 - 10.5248i) q^{42} +(6.10068 + 14.7283i) q^{43} +(27.8252 - 139.887i) q^{44} +(-9.03894 - 45.4418i) q^{46} +(41.1986 - 41.1986i) q^{47} +(32.8421 - 49.1516i) q^{48} +(-36.5201 - 15.1271i) q^{49} +(-32.2072 + 28.2041i) q^{51} +28.0320 q^{52} +(-33.6831 + 81.3182i) q^{53} +(-86.6277 - 57.8828i) q^{54} +(49.2020 - 9.78689i) q^{56} +(60.7419 - 40.5864i) q^{57} +(72.0444 + 14.3305i) q^{58} +(29.0766 - 12.0439i) q^{59} +(-20.7793 + 104.464i) q^{61} +(27.5515 + 41.2337i) q^{62} +(-1.59595 - 8.02337i) q^{63} +(-20.9790 + 20.9790i) q^{64} +(137.034 + 56.7613i) q^{66} +16.8254i q^{67} +(-126.569 + 72.9537i) q^{68} +32.8787 q^{69} +(-71.4772 - 47.7595i) q^{71} +(-30.6399 - 30.6399i) q^{72} +(-11.7471 + 2.33665i) q^{73} +(110.212 - 73.6411i) q^{74} +(230.314 - 95.3990i) q^{76} +(19.5465 + 47.1894i) q^{77} +(-5.68723 + 28.5916i) q^{78} +(-14.9438 - 22.3650i) q^{79} +(35.3625 - 35.3625i) q^{81} +(142.051 - 212.594i) q^{82} +(-97.0588 - 40.2031i) q^{83} +66.5994i q^{84} -56.5732 q^{86} +(-19.9480 + 48.1587i) q^{87} +(224.954 + 150.310i) q^{88} +(-64.1441 - 64.1441i) q^{89} +(-8.34694 + 5.57725i) q^{91} +(110.040 + 21.8884i) q^{92} +(-32.5128 + 13.4673i) q^{93} +(79.1242 + 191.023i) q^{94} +(25.3214 + 37.8962i) q^{96} +(18.6933 + 93.9775i) q^{97} +(99.1916 - 99.1916i) q^{98} +(24.5110 - 36.6833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) $ 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	−1.35804	+	3.27860i	−0.679020	+	1.63930i	0.0867861	+	0.996227i	$0.472340\pi$
$2$	−1.35804	+	3.27860i	−0.679020	+	1.63930i	−0.765806	+	0.643072i	$0.777660\pi$
$3$	−2.09388	−	1.39909i	−0.697961	−	0.466363i	0.155286	−	0.987870i	$-0.450370\pi$
$3$	−2.09388	−	1.39909i	−0.697961	−	0.466363i	−0.853247	+	0.521507i	$0.825370\pi$
$4$	−6.07650	−	6.07650i	−1.51913	−	1.51913i
$5$		0			0
$5$		0			0
$6$	7.43063	−	4.96499i	1.23844	−	0.827498i
$7$	3.01835	+	0.600386i	0.431192	+	0.0857695i	0.405915	−	0.913911i	$-0.366953\pi$
$7$	3.01835	+	0.600386i	0.431192	+	0.0857695i	0.0252777	+	0.999680i	$0.491953\pi$
$8$	15.0602	−	6.23812i	1.88252	−	0.779765i
$9$	−1.01725	−	2.45586i	−0.113028	−	0.272873i
$10$		0			0
$11$	9.22089	+	13.8000i	0.838263	+	1.25455i	0.964905	+	0.262600i	$0.0845800\pi$
$11$	9.22089	+	13.8000i	0.838263	+	1.25455i	−0.126642	+	0.991948i	$0.540420\pi$
$12$	4.22193	+	21.2251i	0.351827	+	1.76876i
$13$	−2.30659	+	2.30659i	−0.177430	+	0.177430i	−0.790235	−	0.612804i	$-0.790041\pi$
$13$	−2.30659	+	2.30659i	−0.177430	+	0.177430i	0.612804	+	0.790235i	$0.290041\pi$
$14$	−6.06746	+	9.08060i	−0.433390	+	0.648614i
$15$		0			0
$16$			23.4739i			1.46712i
$17$	4.41170	−	16.4176i	0.259512	−	0.965740i
$17$	4.41170	−	16.4176i	0.259512	−	0.965740i
$18$	9.43323			0.524069
$19$	−11.1013	+	26.8010i	−0.584281	+	1.41058i	0.304618	+	0.952475i	$0.401471\pi$
$19$	−11.1013	+	26.8010i	−0.584281	+	1.41058i	−0.888899	+	0.458104i	$0.848529\pi$
$20$		0			0
$21$	−5.48007	−	5.48007i	−0.260956	−	0.260956i
$22$	−57.7671	+	11.4906i	−2.62578	+	0.522300i
$23$	−10.8556	+	7.25351i	−0.471984	+	0.315370i	−0.768715	−	0.639591i	$-0.779104\pi$
$23$	−10.8556	+	7.25351i	−0.471984	+	0.315370i	0.296731	+	0.954961i	$0.404104\pi$
$24$	−40.2619	−	8.00859i	−1.67758	−	0.333691i
$25$		0			0
$26$	−4.42995	−	10.6948i	−0.170383	−	0.411340i
$27$	−5.72761	+	28.7946i	−0.212134	+	1.06647i
$28$	−14.6927	−	21.9892i	−0.524741	−	0.785330i
$29$	−4.03821	−	20.3015i	−0.139249	−	0.700051i	−0.985824	−	0.167782i	$-0.946340\pi$
$29$	−4.03821	−	20.3015i	−0.139249	−	0.700051i	0.846575	−	0.532269i	$-0.178660\pi$
$30$		0			0
$31$	7.76376	−	11.6193i	0.250444	−	0.374816i	−0.684852	−	0.728682i	$-0.740133\pi$
$31$	7.76376	−	11.6193i	0.250444	−	0.374816i	0.935296	+	0.353866i	$0.115133\pi$
$32$	−16.7209	−	6.92600i	−0.522527	−	0.216438i
$33$		−	41.7965i		−	1.26656i
$34$	47.8354	+	36.7599i	1.40692	+	1.08117i
$35$		0			0
$36$	−8.74171	+	21.1043i	−0.242825	+	0.586232i
$37$	−31.0567	−	20.7514i	−0.839369	−	0.560848i	0.0599201	−	0.998203i	$-0.480915\pi$
$37$	−31.0567	−	20.7514i	−0.839369	−	0.560848i	−0.899289	+	0.437355i	$0.855915\pi$
$38$	−72.7936	−	72.7936i	−1.91562	−	1.91562i
$39$	8.05687	−	1.60261i	0.206586	−	0.0410926i
$40$		0			0
$41$	−70.6653	−	14.0562i	−1.72354	−	0.342834i	−0.768624	−	0.639700i	$-0.779058\pi$
$41$	−70.6653	−	14.0562i	−1.72354	−	0.342834i	−0.954919	+	0.296866i	$0.904058\pi$
$42$	25.4091	−	10.5248i	0.604979	−	0.250590i
$43$	6.10068	+	14.7283i	0.141876	+	0.342519i	0.978806	−	0.204791i	$-0.0656516\pi$
$43$	6.10068	+	14.7283i	0.141876	+	0.342519i	−0.836929	+	0.547311i	$0.815652\pi$
$44$	27.8252	−	139.887i	0.632391	−	3.17924i
$45$		0			0
$46$	−9.03894	−	45.4418i	−0.196499	−	0.987866i
$47$	41.1986	−	41.1986i	0.876565	−	0.876565i	−0.116612	−	0.993178i	$-0.537203\pi$
$47$	41.1986	−	41.1986i	0.876565	−	0.876565i	0.993178	+	0.116612i	$0.0372035\pi$
$48$	32.8421	−	49.1516i	0.684210	−	1.02399i
$49$	−36.5201	−	15.1271i	−0.745309	−	0.308717i
$50$		0			0
$51$	−32.2072	+	28.2041i	−0.631515	+	0.553022i
$52$	28.0320			0.539078
$53$	−33.6831	+	81.3182i	−0.635530	+	1.53431i	0.197045	+	0.980394i	$0.436865\pi$
$53$	−33.6831	+	81.3182i	−0.635530	+	1.53431i	−0.832575	+	0.553912i	$0.813135\pi$
$54$	−86.6277	−	57.8828i	−1.60422	−	1.07190i
$55$		0			0
$56$	49.2020	−	9.78689i	0.878608	−	0.174766i
$57$	60.7419	−	40.5864i	1.06565	−	0.712042i
$58$	72.0444	+	14.3305i	1.24214	+	0.247078i
$59$	29.0766	−	12.0439i	0.492824	−	0.204134i	−0.122409	−	0.992480i	$-0.539062\pi$
$59$	29.0766	−	12.0439i	0.492824	−	0.204134i	0.615233	+	0.788346i	$0.289062\pi$
$60$		0			0
$61$	−20.7793	+	104.464i	−0.340644	+	1.71253i	0.307956	+	0.951401i	$0.400355\pi$
$61$	−20.7793	+	104.464i	−0.340644	+	1.71253i	−0.648599	+	0.761130i	$0.724645\pi$
$62$	27.5515	+	41.2337i	0.444379	+	0.665060i
$63$	−1.59595	−	8.02337i	−0.0253325	−	0.127355i
$64$	−20.9790	+	20.9790i	−0.327798	+	0.327798i
$65$		0			0
$66$	137.034	+	56.7613i	2.07627	+	0.860020i
$67$			16.8254i			0.251125i	0.992086	+	0.125563i	$0.0400736\pi$
$67$			16.8254i			0.251125i	−0.992086	+	0.125563i	$0.959926\pi$
$68$	−126.569	+	72.9537i	−1.86131	+	1.07285i
$69$	32.8787			0.476504
$70$		0			0
$71$	−71.4772	−	47.7595i	−1.00672	−	0.672670i	−0.0611646	−	0.998128i	$-0.519481\pi$
$71$	−71.4772	−	47.7595i	−1.00672	−	0.672670i	−0.945556	+	0.325458i	$0.894481\pi$
$72$	−30.6399	−	30.6399i	−0.425554	−	0.425554i
$73$	−11.7471	+	2.33665i	−0.160920	+	0.0320089i	−0.274893	−	0.961475i	$-0.588642\pi$
$73$	−11.7471	+	2.33665i	−0.160920	+	0.0320089i	0.113973	+	0.993484i	$0.463642\pi$
$74$	110.212	−	73.6411i	1.48935	−	0.995149i
$75$		0			0
$76$	230.314	−	95.3990i	3.03044	−	1.25525i
$77$	19.5465	+	47.1894i	0.253850	+	0.612849i
$78$	−5.68723	+	28.5916i	−0.0729132	+	0.366559i
$79$	−14.9438	−	22.3650i	−0.189162	−	0.283102i	0.724751	−	0.689011i	$-0.241955\pi$
$79$	−14.9438	−	22.3650i	−0.189162	−	0.283102i	−0.913913	+	0.405909i	$0.866955\pi$
$80$		0			0
$81$	35.3625	−	35.3625i	0.436574	−	0.436574i
$82$	142.051	−	212.594i	1.73233	−	2.59261i
$83$	−97.0588	−	40.2031i	−1.16938	−	0.484374i	−0.288394	−	0.957512i	$-0.593121\pi$
$83$	−97.0588	−	40.2031i	−1.16938	−	0.484374i	−0.880989	+	0.473137i	$0.843121\pi$
$84$			66.5994i			0.792850i
$85$		0			0
$86$	−56.5732			−0.657828
$87$	−19.9480	+	48.1587i	−0.229287	+	0.553549i
$88$	224.954	+	150.310i	2.55630	+	1.70806i
$89$	−64.1441	−	64.1441i	−0.720720	−	0.720720i	0.248032	−	0.968752i	$-0.420216\pi$
$89$	−64.1441	−	64.1441i	−0.720720	−	0.720720i	−0.968752	+	0.248032i	$0.920216\pi$
$90$		0			0
$91$	−8.34694	+	5.57725i	−0.0917247	+	0.0612885i
$92$	110.040	+	21.8884i	1.19609	+	0.237917i
$93$	−32.5128	+	13.4673i	−0.349600	+	0.144809i
$94$	79.1242	+	191.023i	0.841747	+	2.03216i
$95$		0			0
$96$	25.3214	+	37.8962i	0.263765	+	0.394752i
$97$	18.6933	+	93.9775i	0.192714	+	0.968840i	0.949162	+	0.314787i	$0.101933\pi$
$97$	18.6933	+	93.9775i	0.192714	+	0.968840i	−0.756448	+	0.654054i	$0.773067\pi$
$98$	99.1916	−	99.1916i	1.01216	−	1.01216i
$99$	24.5110	−	36.6833i	0.247586	−	0.370538i
$100$		0			0
$101$			61.9441i			0.613308i	0.951821	+	0.306654i	$0.0992095\pi$
$101$			61.9441i			0.613308i	−0.951821	+	0.306654i	$0.900791\pi$
$102$	−48.7313	−	143.897i	−0.477758	−	1.41075i
$103$	−113.139			−1.09843			−0.549217	−	0.835680i	$-0.685074\pi$
$103$	−113.139			−1.09843			−0.549217	+	0.835680i	$0.685074\pi$
$104$	−20.3488	+	49.1264i	−0.195662	+	0.472370i
$105$		0			0
$106$	−220.867	−	220.867i	−2.08365	−	2.08365i
$107$	−161.058	+	32.0364i	−1.50521	+	0.299405i	−0.877703	−	0.479204i	$-0.840925\pi$
$107$	−161.058	+	32.0364i	−1.50521	+	0.299405i	−0.627509	+	0.778610i	$0.715925\pi$
$108$	209.775	−	140.167i	1.94236	−	1.29784i
$109$	67.4012	+	13.4069i	0.618359	+	0.122999i	0.494323	−	0.869278i	$-0.335416\pi$
$109$	67.4012	+	13.4069i	0.618359	+	0.122999i	0.124036	+	0.992278i	$0.460416\pi$
$110$		0			0
$111$	35.9960	+	86.9020i	0.324288	+	0.782901i
$112$	−14.0934	+	70.8524i	−0.125834	+	0.632610i
$113$	−32.1670	−	48.1413i	−0.284664	−	0.426030i	0.661388	−	0.750044i	$-0.269968\pi$
$113$	−32.1670	−	48.1413i	−0.284664	−	0.426030i	−0.946052	+	0.324014i	$0.894968\pi$
$114$	50.5767	+	254.266i	0.443655	+	2.23040i
$115$		0			0
$116$	−98.8237	+	147.900i	−0.851929	+	1.27500i
$117$	8.01104	+	3.31828i	0.0684705	+	0.0283614i
$118$			111.687i			0.946496i
$119$	23.1729	−	46.9052i	0.194731	−	0.394161i
$120$		0			0
$121$	−59.1115	+	142.708i	−0.488525	+	1.17940i
$122$	−314.278	−	209.994i	−2.57605	−	1.72126i
$123$	128.299	+	128.299i	1.04308	+	1.04308i
$124$	−117.781	+	23.4281i	−0.949848	+	0.188937i
$125$		0			0
$126$	28.4728	+	5.66359i	0.225974	+	0.0449491i
$127$	−197.044	+	81.6183i	−1.55153	+	0.642664i	−0.983592	−	0.180410i	$-0.942258\pi$
$127$	−197.044	+	81.6183i	−1.55153	+	0.642664i	−0.567935	+	0.823073i	$0.692258\pi$
$128$	−67.9955	−	164.156i	−0.531215	−	1.28247i
$129$	7.83214	−	39.3748i	0.0607142	−	0.305231i
$130$		0			0
$131$	−19.3893	−	97.4764i	−0.148010	−	0.744095i	−0.981485	−	0.191538i	$-0.938652\pi$
$131$	−19.3893	−	97.4764i	−0.148010	−	0.744095i	0.833475	−	0.552557i	$-0.186348\pi$
$132$	−253.977	+	253.977i	−1.92407	+	1.92407i
$133$	−49.5986	+	74.2296i	−0.372922	+	0.558117i
$134$	−55.1637	−	22.8495i	−0.411669	−	0.170519i
$135$		0			0
$136$	−35.9739	−	274.772i	−0.264514	−	2.02038i
$137$	183.661			1.34059			0.670295	−	0.742095i	$-0.266168\pi$
$137$	183.661			1.34059			0.670295	+	0.742095i	$0.266168\pi$
$138$	−44.6506	+	107.796i	−0.323555	+	0.781132i
$139$	72.5126	+	48.4514i	0.521673	+	0.348571i	0.788362	−	0.615212i	$-0.210929\pi$
$139$	72.5126	+	48.4514i	0.521673	+	0.348571i	−0.266688	+	0.963783i	$0.585929\pi$
$140$		0			0
$141$	−143.905	+	28.6246i	−1.02061	+	0.203011i
$142$	253.653	−	169.486i	1.78629	−	1.19356i
$143$	−53.0999	−	10.5622i	−0.371328	−	0.0738617i
$144$	57.6485	−	23.8788i	0.400337	−	0.165825i
$145$		0			0
$146$	8.29214	−	41.6874i	0.0567955	−	0.285530i
$147$	55.3047	+	82.7694i	0.376223	+	0.563057i
$148$	62.6200	+	314.812i	0.423108	+	2.12711i
$149$	−164.741	+	164.741i	−1.10564	+	1.10564i	−0.111925	+	0.993717i	$0.535702\pi$
$149$	−164.741	+	164.741i	−1.10564	+	1.10564i	−0.993717	+	0.111925i	$0.964298\pi$
$150$		0			0
$151$	68.2613	+	28.2748i	0.452062	+	0.187250i	0.597085	−	0.802178i	$-0.296326\pi$
$151$	68.2613	+	28.2748i	0.452062	+	0.187250i	−0.145023	+	0.989428i	$0.546326\pi$
$152$			472.878i			3.11104i
$153$	−44.8070	+	5.86625i	−0.292856	+	0.0383415i
$154$	−181.260			−1.17701
$155$		0			0
$156$	−58.6958	−	39.2193i	−0.376255	−	0.251406i
$157$	−18.7958	−	18.7958i	−0.119719	−	0.119719i	0.644709	−	0.764428i	$-0.276978\pi$
$157$	−18.7958	−	18.7958i	−0.119719	−	0.119719i	−0.764428	+	0.644709i	$0.776978\pi$
$158$	93.6203	−	18.6222i	0.592533	−	0.117862i
$159$	184.300	−	123.145i	1.15912	−	0.774499i
$160$		0			0
$161$	−37.1210	+	15.3760i	−0.230565	+	0.0955032i
$162$	67.9158	+	163.963i	0.419233	+	1.01212i
$163$	23.4970	−	118.127i	0.144153	−	0.724707i	−0.839318	−	0.543641i	$-0.817045\pi$
$163$	23.4970	−	118.127i	0.144153	−	0.724707i	0.983471	−	0.181066i	$-0.0579547\pi$
$164$	343.985	+	514.810i	2.09747	+	3.13909i
$165$		0			0
$166$	263.619	−	263.619i	1.58807	−	1.58807i
$167$	−95.7021	+	143.228i	−0.573067	+	0.857655i	−0.998888	−	0.0471525i	$-0.984985\pi$
$167$	−95.7021	+	143.228i	−0.573067	+	0.857655i	0.425821	+	0.904807i	$0.359985\pi$
$168$	−116.716	−	48.3454i	−0.694739	−	0.287770i
$169$			158.359i			0.937037i
$170$		0			0
$171$	77.1122			0.450949
$172$	52.4260	−	126.568i	0.304802	−	0.735858i
$173$	71.0685	+	47.4864i	0.410800	+	0.274488i	0.743752	−	0.668456i	$-0.233044\pi$
$173$	71.0685	+	47.4864i	0.410800	+	0.274488i	−0.332951	+	0.942944i	$0.608044\pi$
$174$	−130.803	−	130.803i	−0.751741	−	0.751741i
$175$		0			0
$176$	−323.941	+	216.450i	−1.84057	+	1.22983i
$177$	−77.7335	−	15.4622i	−0.439172	−	0.0873568i
$178$	297.413	−	123.192i	1.67086	−	0.692092i
$179$	−87.9680	−	212.374i	−0.491441	−	1.18644i	−0.953987	−	0.299849i	$-0.903064\pi$
$179$	−87.9680	−	212.374i	−0.491441	−	1.18644i	0.462545	−	0.886596i	$-0.346936\pi$
$180$		0			0
$181$	−23.2648	−	34.8182i	−0.128535	−	0.192366i	0.761620	−	0.648023i	$-0.224404\pi$
$181$	−23.2648	−	34.8182i	−0.128535	−	0.192366i	−0.890155	+	0.455658i	$0.849404\pi$
$182$	−6.95008	−	34.9404i	−0.0381872	−	0.191980i
$183$	189.664	−	189.664i	1.03642	−	1.03642i
$184$	−118.239	+	176.958i	−0.642605	+	0.961726i
$185$		0			0
$186$		−	124.886i		−	0.671428i
$187$	267.243	−	90.5030i	1.42911	−	0.483973i
$188$	−500.686			−2.66323
$189$	−34.5758	+	83.4734i	−0.182941	+	0.441658i
$190$		0			0
$191$	33.9712	+	33.9712i	0.177860	+	0.177860i	0.790422	−	0.612563i	$-0.209861\pi$
$191$	33.9712	+	33.9712i	0.177860	+	0.177860i	−0.612563	+	0.790422i	$0.709861\pi$
$192$	73.2792	−	14.5761i	0.381663	−	0.0759174i
$193$	42.5673	−	28.4426i	0.220556	−	0.147371i	−0.440384	−	0.897810i	$-0.645158\pi$
$193$	42.5673	−	28.4426i	0.220556	−	0.147371i	0.660940	+	0.750439i	$0.270158\pi$
$194$	−333.501	−	66.3374i	−1.71908	−	0.341945i
$195$		0			0
$196$	129.995	+	313.835i	0.663238	+	1.60120i
$197$	−14.4570	+	72.6800i	−0.0733855	+	0.368934i	−0.999974	−	0.00714165i	$-0.997727\pi$
$197$	−14.4570	+	72.6800i	−0.0733855	+	0.368934i	0.926589	+	0.376076i	$0.122727\pi$
$198$	86.9828	+	130.179i	0.439307	+	0.657469i
$199$	19.2364	+	96.7081i	0.0966655	+	0.485970i	0.998542	+	0.0539768i	$0.0171897\pi$
$199$	19.2364	+	96.7081i	0.0966655	+	0.485970i	−0.901877	+	0.431994i	$0.857810\pi$
$200$		0			0
$201$	23.5402	−	35.2304i	0.117115	−	0.175276i
$202$	−203.090	−	84.1226i	−1.00540	−	0.416448i
$203$		−	63.7014i		−	0.313800i
$204$	367.090	+	24.3249i	1.79946	+	0.119240i
$205$		0			0
$206$	153.647	−	370.936i	0.745858	−	1.80066i
$207$	28.8565	+	19.2813i	0.139403	+	0.0931463i
$208$	−54.1447	−	54.1447i	−0.260311	−	0.260311i
$209$	−472.219	+	93.9302i	−2.25942	+	0.449427i
$210$		0			0
$211$	247.268	+	49.1846i	1.17188	+	0.233102i	0.742391	−	0.669967i	$-0.233692\pi$
$211$	247.268	+	49.1846i	1.17188	+	0.233102i	0.429494	+	0.903070i	$0.358692\pi$
$212$	698.806	−	289.455i	3.29625	−	1.36535i
$213$	82.8451	+	200.006i	0.388944	+	0.938995i
$214$	113.688	−	571.550i	0.531254	−	2.67079i
$215$		0			0
$216$	93.3657	+	469.381i	0.432249	+	2.17306i
$217$	30.4098	−	30.4098i	0.140137	−	0.140137i
$218$	−135.489	+	202.774i	−0.621511	+	0.930157i
$219$	27.8663	+	11.5426i	0.127244	+	0.0527060i
$220$		0			0
$221$	27.6927	+	48.0447i	0.125306	+	0.217397i
$222$	−333.801			−1.50361
$223$	101.688	−	245.496i	0.455999	−	1.10088i	−0.514004	−	0.857788i	$-0.671838\pi$
$223$	101.688	−	245.496i	0.455999	−	1.10088i	0.970003	−	0.243091i	$-0.0781615\pi$
$224$	−46.3110	−	30.9441i	−0.206746	−	0.138143i
$225$		0			0
$226$	201.520	−	40.0849i	0.891682	−	0.177367i
$227$	108.945	−	72.7947i	0.479934	−	0.320681i	−0.291963	−	0.956430i	$-0.594308\pi$
$227$	108.945	−	72.7947i	0.479934	−	0.320681i	0.771896	+	0.635748i	$0.219308\pi$
$228$	−615.722	−	122.475i	−2.70053	−	0.537170i
$229$	108.516	−	44.9489i	0.473870	−	0.196284i	−0.132950	−	0.991123i	$-0.542445\pi$
$229$	108.516	−	44.9489i	0.473870	−	0.196284i	0.606820	+	0.794839i	$0.292445\pi$
$230$		0			0
$231$	25.0941	−	126.156i	0.108632	−	0.546131i
$232$	−187.459	−	280.552i	−0.808013	−	1.20928i
$233$	62.0785	+	312.090i	0.266431	+	1.33944i	0.849745	+	0.527194i	$0.176756\pi$
$233$	62.0785	+	312.090i	0.266431	+	1.33944i	−0.583314	+	0.812247i	$0.698244\pi$
$234$	−21.7586	+	21.7586i	−0.0929856	+	0.0929856i
$235$		0			0
$236$	−249.869	−	103.499i	−1.05877	−	0.438555i
$237$			67.7375i			0.285812i
$238$	122.314	+	139.674i	0.513922	+	0.586865i
$239$	325.592			1.36231			0.681155	−	0.732139i	$-0.261478\pi$
$239$	325.592			1.36231			0.681155	+	0.732139i	$0.261478\pi$
$240$		0			0
$241$	267.722	+	178.886i	1.11088	+	0.742267i	0.968863	−	0.247598i	$-0.0796411\pi$
$241$	267.722	+	178.886i	1.11088	+	0.742267i	0.142017	+	0.989864i	$0.454641\pi$
$242$	−387.606	−	387.606i	−1.60168	−	1.60168i
$243$	135.631	−	26.9788i	0.558154	−	0.111024i
$244$	761.043	−	508.513i	3.11903	−	2.08407i
$245$		0			0
$246$	−594.876	+	246.406i	−2.41820	+	1.00165i
$247$	−36.2127	−	87.4252i	−0.146610	−	0.353948i
$248$	44.4409	−	223.420i	0.179197	−	0.900885i
$249$	146.982	+	219.974i	0.590290	+	0.883431i
$250$		0			0
$251$	−312.141	+	312.141i	−1.24359	+	1.24359i	−0.285089	+	0.958501i	$0.592023\pi$
$251$	−312.141	+	312.141i	−1.24359	+	1.24359i	−0.958501	+	0.285089i	$0.907977\pi$
$252$	−39.0563	+	58.4518i	−0.154985	+	0.231952i
$253$	−200.197	−	82.9244i	−0.791294	−	0.327765i
$254$		−	756.869i		−	2.97980i
$255$		0			0
$256$	511.865			1.99947
$257$	103.333	−	249.469i	0.402076	−	0.970696i	−0.585086	−	0.810971i	$-0.698939\pi$
$257$	103.333	−	249.469i	0.402076	−	0.970696i	0.987162	−	0.159725i	$-0.0510608\pi$
$258$	118.458	+	79.1510i	0.459139	+	0.306787i
$259$	−81.2809	−	81.2809i	−0.313826	−	0.313826i
$260$		0			0
$261$	−45.7496	+	30.5689i	−0.175286	+	0.117122i
$262$	345.917	+	68.8073i	1.32030	+	0.262623i
$263$	224.407	−	92.9523i	0.853258	−	0.353431i	0.0871908	−	0.996192i	$-0.472211\pi$
$263$	224.407	−	92.9523i	0.853258	−	0.353431i	0.766067	+	0.642761i	$0.222211\pi$
$264$	−260.732	−	629.462i	−0.987620	−	2.38433i
$265$		0			0
$266$	−176.012	−	263.421i	−0.661700	−	0.990303i
$267$	44.5670	+	224.053i	0.166918	+	0.839152i
$268$	102.240	−	102.240i	0.381491	−	0.381491i
$269$	178.212	−	266.713i	0.662498	−	0.991499i	−0.336264	−	0.941768i	$-0.609164\pi$
$269$	178.212	−	266.713i	0.662498	−	0.991499i	0.998763	−	0.0497311i	$-0.0158364\pi$
$270$		0			0
$271$		−	9.30633i		−	0.0343407i	−0.999853	−	0.0171703i	$-0.994534\pi$
$271$		−	9.30633i		−	0.0343407i	0.999853	−	0.0171703i	$-0.00546576\pi$
$272$	385.385	+	103.560i	1.41685	+	0.380735i
$273$	25.2806			0.0926029
$274$	−249.419	+	602.150i	−0.910287	+	2.19763i
$275$		0			0
$276$	−199.788	−	199.788i	−0.723869	−	0.723869i
$277$	−264.142	+	52.5411i	−0.953582	+	0.189679i	−0.647277	−	0.762254i	$-0.724092\pi$
$277$	−264.142	+	52.5411i	−0.953582	+	0.189679i	−0.306304	+	0.951934i	$0.599092\pi$
$278$	−257.328	+	171.941i	−0.925639	+	0.618492i
$279$	−36.4330	−	7.24697i	−0.130584	−	0.0259748i
$280$		0			0
$281$	−71.3107	−	172.159i	−0.253775	−	0.612666i	0.744728	−	0.667368i	$-0.232579\pi$
$281$	−71.3107	−	172.159i	−0.253775	−	0.612666i	−0.998503	+	0.0547017i	$0.982579\pi$
$282$	101.581	−	510.681i	0.360216	−	1.81093i
$283$	64.7275	+	96.8716i	0.228719	+	0.342302i	0.928023	−	0.372522i	$-0.121507\pi$
$283$	64.7275	+	96.8716i	0.228719	+	0.342302i	−0.699304	+	0.714824i	$0.746507\pi$
$284$	144.120	+	724.542i	0.507466	+	2.55121i
$285$		0			0
$286$	106.741	−	159.749i	0.373220	−	0.558564i
$287$	−204.853	−	84.8530i	−0.713774	−	0.295655i
$288$			48.1095i			0.167047i
$289$	−250.074	−	144.859i	−0.865307	−	0.501242i
$290$		0			0
$291$	92.3413	−	222.932i	0.317324	−	0.766088i
$292$	85.5802	+	57.1829i	0.293083	+	0.195832i
$293$	−138.715	−	138.715i	−0.473429	−	0.473429i	0.429593	−	0.903022i	$-0.358657\pi$
$293$	−138.715	−	138.715i	−0.473429	−	0.473429i	−0.903022	+	0.429593i	$0.858657\pi$
$294$	−346.474	+	68.9179i	−1.17848	+	0.234415i
$295$		0			0
$296$	−597.168	−	118.784i	−2.01746	−	0.401297i
$297$	−450.181	+	186.471i	−1.51576	+	0.627848i
$298$	−316.394	−	763.842i	−1.06172	−	2.56323i
$299$	8.30865	−	41.7704i	0.0277881	−	0.139700i
$300$		0			0
$301$	9.57126	+	48.1180i	0.0317982	+	0.159860i
$302$	−185.403	+	185.403i	−0.613918	+	0.613918i
$303$	86.6653	−	129.704i	0.286024	−	0.428065i
$304$	−629.124	−	260.592i	−2.06949	−	0.857209i
$305$		0			0
$306$	41.6166	−	154.871i	0.136002	−	0.506114i
$307$	34.2391			0.111528			0.0557639	−	0.998444i	$-0.482241\pi$
$307$	34.2391			0.111528			0.0557639	+	0.998444i	$0.482241\pi$
$308$	167.972	−	405.521i	0.545364	−	1.31663i
$309$	236.899	+	158.291i	0.766664	+	0.512269i
$310$		0			0
$311$	113.544	−	22.5853i	0.365092	−	0.0726214i	−0.00913523	−	0.999958i	$-0.502908\pi$
$311$	113.544	−	22.5853i	0.365092	−	0.0726214i	0.374228	+	0.927337i	$0.377908\pi$
$312$	111.340	−	74.3952i	0.356860	−	0.238446i
$313$	12.1725	+	2.42127i	0.0388899	+	0.00773568i	0.214497	−	0.976725i	$-0.431189\pi$
$313$	12.1725	+	2.42127i	0.0388899	+	0.00773568i	−0.175607	+	0.984460i	$0.556189\pi$
$314$	87.1495	−	36.0985i	0.277546	−	0.114963i
$315$		0			0
$316$	−45.0949	+	226.707i	−0.142705	+	0.717429i
$317$	46.7826	+	70.0152i	0.147579	+	0.220868i	0.897893	−	0.440214i	$-0.145097\pi$
$317$	46.7826	+	70.0152i	0.147579	+	0.220868i	−0.750314	+	0.661082i	$0.770097\pi$
$318$	153.457	+	771.481i	0.482570	+	2.42604i
$319$	242.925	−	242.925i	0.761520	−	0.761520i
$320$		0			0
$321$	382.058	+	158.254i	1.19021	+	0.493002i
$322$		−	142.586i		−	0.442814i
$323$	391.032	+	300.495i	1.21062	+	0.930325i
$324$	−429.761			−1.32642
$325$		0			0
$326$	355.382	+	237.459i	1.09013	+	0.728401i
$327$	−122.373	−	122.373i	−0.374229	−	0.374229i
$328$	−1151.91	+	229.130i	−3.51193	+	0.698567i
$329$	149.087	−	99.6165i	0.453151	−	0.302786i
$330$		0			0
$331$	59.8241	−	24.7799i	0.180737	−	0.0748639i	−0.290480	−	0.956881i	$-0.593815\pi$
$331$	59.8241	−	24.7799i	0.180737	−	0.0748639i	0.471217	+	0.882017i	$0.343815\pi$
$332$	345.484	+	834.072i	1.04061	+	2.51227i
$333$	−19.3701	+	97.3801i	−0.0581685	+	0.292433i
$334$	−339.621	−	508.279i	−1.01683	−	1.52179i
$335$		0			0
$336$	128.639	−	128.639i	0.382853	−	0.382853i
$337$	−33.6282	+	50.3281i	−0.0997869	+	0.149342i	−0.878003	−	0.478655i	$-0.841125\pi$
$337$	−33.6282	+	50.3281i	−0.0997869	+	0.149342i	0.778216	+	0.627996i	$0.216125\pi$
$338$	−519.196	−	215.058i	−1.53608	−	0.636267i
$339$			145.807i			0.430109i
$340$		0			0
$341$	231.935			0.680162
$342$	−104.721	+	252.820i	−0.306203	+	0.739240i
$343$	−226.531	−	151.363i	−0.660440	−	0.441292i
$344$	183.754	+	183.754i	0.534169	+	0.534169i
$345$		0			0
$346$	−252.203	+	168.516i	−0.728910	+	0.487042i
$347$	218.128	+	43.3885i	0.628612	+	0.125039i	0.499108	−	0.866540i	$-0.333661\pi$
$347$	218.128	+	43.3885i	0.628612	+	0.125039i	0.129505	+	0.991579i	$0.458661\pi$
$348$	413.851	−	171.423i	1.18923	−	0.492594i
$349$	−26.2500	−	63.3730i	−0.0752148	−	0.181585i	0.881800	−	0.471623i	$-0.156332\pi$
$349$	−26.2500	−	63.3730i	−0.0752148	−	0.181585i	−0.957015	+	0.290039i	$0.906332\pi$
$350$		0			0
$351$	−53.2063	−	79.6288i	−0.151585	−	0.226863i
$352$	−58.6020	−	294.612i	−0.166483	−	0.836967i
$353$	−49.3308	+	49.3308i	−0.139747	+	0.139747i	−0.773520	−	0.633772i	$-0.781506\pi$
$353$	−49.3308	+	49.3308i	−0.139747	+	0.139747i	0.633772	+	0.773520i	$0.281506\pi$
$354$	156.259	−	233.859i	0.441411	−	0.660618i
$355$		0			0
$356$			779.543i			2.18973i
$357$	−114.146	+	65.7931i	−0.319737	+	0.184294i
$358$	815.751			2.27864
$359$	−122.127	+	294.840i	−0.340186	+	0.821282i	0.657510	+	0.753445i	$0.271610\pi$
$359$	−122.127	+	294.840i	−0.340186	+	0.821282i	−0.997696	+	0.0678363i	$0.978390\pi$
$360$		0			0
$361$	−339.788	−	339.788i	−0.941241	−	0.941241i
$362$	145.749	−	28.9913i	0.402623	−	0.0800866i
$363$	323.433	−	216.111i	0.891001	−	0.595348i
$364$	84.6104	+	16.8301i	0.232446	+	0.0462364i
$365$		0			0
$366$	364.261	+	879.404i	0.995249	+	2.40274i
$367$	−6.25833	+	31.4628i	−0.0170527	+	0.0857296i	−0.988374	−	0.152039i	$-0.951416\pi$
$367$	−6.25833	+	31.4628i	−0.0170527	+	0.0857296i	0.971322	+	0.237769i	$0.0764160\pi$
$368$	−170.268	−	254.824i	−0.462685	−	0.692457i
$369$	37.3642	+	187.842i	0.101258	+	0.509058i
$370$		0			0
$371$	−150.490	+	225.224i	−0.405633	+	0.607072i
$372$	279.398	+	115.730i	0.751070	+	0.311103i
$373$			52.8801i			0.141770i	0.997485	+	0.0708849i	$0.0225823\pi$
$373$			52.8801i			0.141770i	−0.997485	+	0.0708849i	$0.977418\pi$
$374$	−66.2037	+	999.089i	−0.177015	+	2.67136i
$375$		0			0
$376$	363.455	−	877.458i	0.966636	−	2.33367i
$377$	56.1417	+	37.5127i	0.148917	+	0.0995032i
$378$	−226.720	−	226.720i	−0.599790	−	0.599790i
$379$	−72.2913	+	14.3796i	−0.190742	+	0.0379410i	−0.289537	−	0.957167i	$-0.593501\pi$
$379$	−72.2913	+	14.3796i	−0.190742	+	0.0379410i	0.0987947	+	0.995108i	$0.468501\pi$
$380$		0			0
$381$	526.778	+	104.783i	1.38262	+	0.275020i
$382$	−157.512	+	65.2436i	−0.412335	+	0.170795i
$383$	−29.7185	−	71.7467i	−0.0775939	−	0.187328i	0.880322	−	0.474376i	$-0.157326\pi$
$383$	−29.7185	−	71.7467i	−0.0775939	−	0.187328i	−0.957916	+	0.287048i	$0.907326\pi$
$384$	−87.2936	+	438.855i	−0.227327	+	1.14285i
$385$		0			0
$386$	35.4437	+	178.187i	0.0918229	+	0.461625i
$387$	29.9648	−	29.9648i	0.0774284	−	0.0774284i
$388$	457.465	−	684.645i	1.17903	−	1.76455i
$389$	−584.790	−	242.228i	−1.50332	−	0.622694i	−0.529150	−	0.848529i	$-0.677489\pi$
$389$	−584.790	−	242.228i	−1.50332	−	0.622694i	−0.974166	+	0.225835i	$0.927489\pi$
$390$		0			0
$391$	71.1931	+	210.224i	0.182080	+	0.537656i
$392$	−644.364			−1.64379
$393$	−95.7793	+	231.232i	−0.243713	+	0.588376i
$394$	−218.655	−	146.101i	−0.554963	−	0.370814i
$395$		0			0
$396$	−371.847	+	73.9650i	−0.939008	+	0.186780i
$397$	−181.151	+	121.041i	−0.456299	+	0.304889i	−0.762396	−	0.647111i	$-0.775977\pi$
$397$	−181.151	+	121.041i	−0.456299	+	0.304889i	0.306097	+	0.952000i	$0.400977\pi$
$398$	−343.191	−	68.2649i	−0.862289	−	0.171520i
$399$	207.708	−	86.0353i	0.520570	−	0.215627i
$400$		0			0
$401$	78.9077	−	396.696i	0.196777	−	0.989267i	−0.748534	−	0.663097i	$-0.769242\pi$
$401$	78.9077	−	396.696i	0.196777	−	0.989267i	0.945311	−	0.326170i	$-0.105758\pi$
$402$	83.5378	+	125.023i	0.207806	+	0.311003i
$403$	8.89313	+	44.7088i	0.0220673	+	0.110940i
$404$	376.404	−	376.404i	0.931692	−	0.931692i
$405$		0			0
$406$	208.851	+	86.5090i	0.514412	+	0.213076i
$407$		−	619.929i		−	1.52317i
$408$	−309.105	+	625.671i	−0.757611	+	1.53351i
$409$	−756.210			−1.84892			−0.924462	−	0.381274i	$-0.875485\pi$
$409$	−756.210			−1.84892			−0.924462	+	0.381274i	$0.875485\pi$
$410$		0			0
$411$	−384.565	−	256.958i	−0.935680	−	0.625201i
$412$	687.488	+	687.488i	1.66866	+	1.66866i
$413$	94.9942	−	18.8955i	0.230010	−	0.0457519i
$414$	−102.404	+	68.4240i	−0.247352	+	0.165275i
$415$		0			0
$416$	54.5437	−	22.5927i	0.131115	−	0.0543094i
$417$	−84.0452	−	202.903i	−0.201547	−	0.486578i
$418$	333.333	−	1675.78i	0.797447	−	4.00903i
$419$	−281.424	−	421.181i	−0.671656	−	1.00520i	−0.998197	−	0.0600212i	$-0.980883\pi$
$419$	−281.424	−	421.181i	−0.671656	−	1.00520i	0.326541	−	0.945183i	$-0.394117\pi$
$420$		0			0
$421$	−173.266	+	173.266i	−0.411558	+	0.411558i	−0.882281	−	0.470723i	$-0.843993\pi$
$421$	−173.266	+	173.266i	−0.411558	+	0.411558i	0.470723	+	0.882281i	$0.343993\pi$
$422$	−497.056	+	743.897i	−1.17786	+	1.76279i
$423$	−143.087	−	59.2686i	−0.338267	−	0.140115i
$424$			1434.78i			3.38392i
$425$		0			0
$426$	−768.246			−1.80339
$427$	−125.438	+	302.834i	−0.293766	+	0.709213i
$428$	1173.34	+	783.998i	2.74144	+	1.83177i
$429$	96.4075	+	96.4075i	0.224726	+	0.224726i
$430$		0			0
$431$	−461.933	+	308.653i	−1.07177	+	0.716133i	−0.960675	−	0.277676i	$-0.910436\pi$
$431$	−461.933	+	308.653i	−1.07177	+	0.716133i	−0.111095	+	0.993810i	$0.535436\pi$
$432$	−675.922	−	134.449i	−1.56464	−	0.311225i
$433$	−372.206	+	154.173i	−0.859598	+	0.356057i	−0.768550	−	0.639789i	$-0.779022\pi$
$433$	−372.206	+	154.173i	−0.859598	+	0.356057i	−0.0910478	+	0.995847i	$0.529022\pi$
$434$	58.4038	+	140.999i	0.134571	+	0.324883i
$435$		0			0
$436$	−328.096	−	491.031i	−0.752514	−	1.12622i
$437$	−73.8891	−	371.466i	−0.169083	−	0.850035i
$438$	−75.6872	+	75.6872i	−0.172802	+	0.172802i
$439$	65.4706	−	97.9837i	0.149136	−	0.223198i	−0.749378	−	0.662142i	$-0.769648\pi$
$439$	65.4706	−	97.9837i	0.149136	−	0.223198i	0.898514	+	0.438944i	$0.144648\pi$
$440$		0			0
$441$			105.076i			0.238268i
$442$	−195.127	+	25.5465i	−0.441464	+	0.0577976i
$443$	−3.48363			−0.00786373			−0.00393186	−	0.999992i	$-0.501252\pi$
$443$	−3.48363			−0.00786373			−0.00393186	+	0.999992i	$0.501252\pi$
$444$	309.331	−	746.790i	0.696691	−	1.68196i
$445$		0			0
$446$	666.787	+	666.787i	1.49504	+	1.49504i
$447$	575.434	−	114.461i	1.28732	−	0.256065i
$448$	−75.9176	+	50.7265i	−0.169459	+	0.113229i
$449$	484.563	+	96.3856i	1.07921	+	0.214667i	0.702513	−	0.711671i	$-0.252061\pi$
$449$	484.563	+	96.3856i	1.07921	+	0.214667i	0.376693	+	0.926338i	$0.377061\pi$
$450$		0			0
$451$	−457.621	−	1104.79i	−1.01468	−	2.44965i
$452$	−97.0681	+	487.994i	−0.214752	+	1.07963i
$453$	−103.372	−	154.708i	−0.228195	−	0.341518i
$454$	90.7129	+	456.045i	0.199808	+	1.00450i
$455$		0			0
$456$	661.599	−	990.153i	1.45087	−	2.17139i
$457$	−37.2066	−	15.4115i	−0.0814149	−	0.0337232i	0.341604	−	0.939844i	$-0.389030\pi$
$457$	−37.2066	−	15.4115i	−0.0814149	−	0.0337232i	−0.423019	+	0.906121i	$0.639030\pi$
$458$			416.824i			0.910096i
$459$	447.470	+	221.067i	0.974880	+	0.481627i
$460$		0			0
$461$	259.577	−	626.675i	0.563075	−	1.35938i	−0.344221	−	0.938889i	$-0.611857\pi$
$461$	259.577	−	626.675i	0.563075	−	1.35938i	0.907296	−	0.420494i	$-0.138143\pi$
$462$	379.537	+	253.599i	0.821509	+	0.548915i
$463$	579.794	+	579.794i	1.25225	+	1.25225i	0.954707	+	0.297547i	$0.0961685\pi$
$463$	579.794	+	579.794i	1.25225	+	1.25225i	0.297547	+	0.954707i	$0.403831\pi$
$464$	476.554	−	94.7926i	1.02706	−	0.204294i
$465$		0			0
$466$	−1107.52	−	220.300i	−2.37666	−	0.472746i
$467$	−46.9412	+	19.4437i	−0.100516	+	0.0416353i	−0.432375	−	0.901694i	$-0.642324\pi$
$467$	−46.9412	+	19.4437i	−0.100516	+	0.0416353i	0.331859	+	0.943329i	$0.392324\pi$
$468$	−28.5156	−	68.8427i	−0.0609307	−	0.147100i
$469$	−10.1017	+	50.7849i	−0.0215389	+	0.108283i
$470$		0			0
$471$	13.0593	+	65.6533i	0.0277267	+	0.139391i
$472$	362.766	−	362.766i	0.768573	−	0.768573i
$473$	−146.998	+	219.998i	−0.310778	+	0.465112i
$474$	−222.084	−	91.9903i	−0.468532	−	0.194072i
$475$		0			0
$476$	−425.830	+	144.209i	−0.894601	+	0.302961i
$477$	233.970			0.490503
$478$	−442.167	+	1067.49i	−0.925035	+	2.23323i
$479$	519.007	+	346.789i	1.08352	+	0.723986i	0.963210	−	0.268750i	$-0.0866105\pi$
$479$	519.007	+	346.789i	1.08352	+	0.723986i	0.120312	+	0.992736i	$0.461610\pi$
$480$		0			0
$481$	119.500	−	23.7700i	0.248441	−	0.0494180i
$482$	−950.073	+	634.819i	−1.97111	+	1.31705i
$483$	99.2395	+	19.7400i	0.205465	+	0.0408695i
$484$	1226.36	−	507.973i	2.53379	−	1.04953i
$485$		0			0
$486$	−95.7404	+	481.319i	−0.196997	+	0.990369i
$487$	−163.370	−	244.500i	−0.335461	−	0.502053i	0.624940	−	0.780672i	$-0.285123\pi$
$487$	−163.370	−	244.500i	−0.335461	−	0.502053i	−0.960402	+	0.278619i	$0.910123\pi$
$488$	338.722	+	1702.87i	0.694103	+	3.48949i
$489$	−214.470	+	214.470i	−0.438590	+	0.438590i
$490$		0			0
$491$	126.942	+	52.5810i	0.258537	+	0.107090i	0.508187	−	0.861246i	$-0.330316\pi$
$491$	126.942	+	52.5810i	0.258537	+	0.107090i	−0.249650	+	0.968336i	$0.580316\pi$
$492$		−	1559.22i		−	3.16914i
$493$	−351.116	−	23.2664i	−0.712203	−	0.0471935i
$494$	335.811			0.679778
$495$		0			0
$496$	272.750	+	182.246i	0.549899	+	0.367431i
$497$	−187.069	−	187.069i	−0.376396	−	0.376396i
$498$	−920.815	+	183.162i	−1.84903	+	0.367794i
$499$	−357.226	+	238.691i	−0.715884	+	0.478338i	−0.859396	−	0.511310i	$-0.829160\pi$
$499$	−357.226	+	238.691i	−0.715884	+	0.478338i	0.143512	+	0.989649i	$0.454160\pi$
$500$		0			0
$501$	400.778	−	166.008i	0.799957	−	0.331353i
$502$	−599.485	−	1447.29i	−1.19419	−	2.88304i
$503$	−26.6908	+	134.184i	−0.0530633	+	0.266767i	−0.998205	−	0.0598942i	$-0.980924\pi$
$503$	−26.6908	+	134.184i	−0.0530633	+	0.266767i	0.945141	+	0.326661i	$0.105924\pi$
$504$	−74.0860	−	110.877i	−0.146996	−	0.219995i
$505$		0			0
$506$	543.752	−	543.752i	1.07461	−	1.07461i
$507$	221.559	−	331.586i	0.436999	−	0.654016i
$508$	1693.29	+	701.384i	3.33325	+	1.38068i
$509$		−	549.679i		−	1.07992i	−0.841691	−	0.539959i	$-0.818440\pi$
$509$		−	549.679i		−	1.07992i	0.841691	−	0.539959i	$-0.181560\pi$
$510$		0			0
$511$	−36.8598			−0.0721327
$512$	−423.152	+	1021.58i	−0.826468	+	1.99527i
$513$	−708.141	−	473.165i	−1.38039	−	0.922348i
$514$	677.577	+	677.577i	1.31824	+	1.31824i
$515$		0			0
$516$	−286.853	+	191.669i	−0.555917	+	0.371452i
$517$	948.429	+	188.654i	1.83449	+	0.364902i
$518$	376.870	−	156.105i	0.727548	−	0.301360i
$519$	−82.3714	−	198.862i	−0.158712	−	0.383164i
$520$		0			0
$521$	101.649	+	152.129i	0.195104	+	0.291993i	0.916103	−	0.400942i	$-0.131317\pi$
$521$	101.649	+	152.129i	0.195104	+	0.291993i	−0.721000	+	0.692935i	$0.756317\pi$
$522$	−38.0934	−	191.508i	−0.0729759	−	0.366874i
$523$	137.945	−	137.945i	0.263757	−	0.263757i	−0.562821	−	0.826579i	$-0.690284\pi$
$523$	137.945	−	137.945i	0.263757	−	0.263757i	0.826579	+	0.562821i	$0.190284\pi$
$524$	−474.497	+	710.135i	−0.905529	+	1.35522i
$525$		0			0
$526$			861.973i			1.63873i
$527$	−156.509	−	178.723i	−0.296981	−	0.339133i
$528$	981.127			1.85820
$529$	−137.208	+	331.249i	−0.259372	+	0.626180i
$530$		0			0
$531$	−59.1563	−	59.1563i	−0.111405	−	0.111405i
$532$	752.443	−	149.670i	1.41437	−	0.281335i
$533$	195.418	−	130.574i	0.366638	−	0.244980i
$534$	−795.105	−	158.156i	−1.48896	−	0.296173i
$535$		0			0
$536$	104.959	+	253.393i	0.195819	+	0.472748i
$537$	−112.935	+	567.761i	−0.210307	+	1.05728i
$538$	632.426	+	946.493i	1.17551	+	1.75928i
$539$	−127.993	−	643.465i	−0.237464	−	1.19381i
$540$		0			0
$541$	−253.891	+	379.975i	−0.469300	+	0.702358i	−0.988318	−	0.152406i	$-0.951298\pi$
$541$	−253.891	+	379.975i	−0.469300	+	0.702358i	0.519018	+	0.854764i	$0.326298\pi$
$542$	30.5117	+	12.6384i	0.0562946	+	0.0233180i
$543$			105.455i			0.194208i
$544$	−187.476	+	243.960i	−0.344624	+	0.448457i
$545$		0			0
$546$	−34.3321	+	82.8849i	−0.0628792	+	0.151804i
$547$	593.369	+	396.477i	1.08477	+	0.724820i	0.963475	−	0.267797i	$-0.0862955\pi$
$547$	593.369	+	396.477i	1.08477	+	0.724820i	0.121294	+	0.992617i	$0.461296\pi$
$548$	−1116.02	−	1116.02i	−2.03653	−	2.03653i
$549$	277.687	−	55.2354i	0.505806	−	0.100611i
$550$		0			0
$551$	588.929	+	117.145i	1.06884	+	0.212605i
$552$	495.159	−	205.102i	0.897027	−	0.371561i
$553$	−31.6780	−	76.4775i	−0.0572839	−	0.138296i
$554$	186.454	−	937.369i	0.336560	−	1.69200i
$555$		0			0
$556$	−146.208	−	735.038i	−0.262964	−	1.32201i
$557$	682.239	−	682.239i	1.22485	−	1.22485i	0.258956	−	0.965889i	$-0.416622\pi$
$557$	682.239	−	682.239i	1.22485	−	1.22485i	0.965889	−	0.258956i	$-0.0833785\pi$
$558$	73.2374	−	109.607i	0.131250	−	0.196429i
$559$	−48.0440	−	19.9005i	−0.0859464	−	0.0356002i
$560$		0			0
$561$	−686.198	−	184.394i	−1.22317	−	0.328688i
$562$	661.284			1.17666
$563$	279.069	−	673.732i	0.495682	−	1.19668i	−0.456106	−	0.889925i	$-0.650756\pi$
$563$	279.069	−	673.732i	0.495682	−	1.19668i	0.951788	−	0.306756i	$-0.0992436\pi$
$564$	1048.38	+	700.505i	1.85883	+	1.24203i
$565$		0			0
$566$	−405.505	+	80.6600i	−0.716441	+	0.142509i
$567$	127.968	−	85.5052i	0.225692	−	0.150803i
$568$	−1374.39	−	273.383i	−2.41970	−	0.481307i
$569$	−393.659	+	163.059i	−0.691844	+	0.286571i	−0.700768	−	0.713389i	$-0.747159\pi$
$569$	−393.659	+	163.059i	−0.691844	+	0.286571i	0.00892410	+	0.999960i	$0.497159\pi$
$570$		0			0
$571$	−89.2030	+	448.454i	−0.156222	+	0.785383i	0.820629	+	0.571462i	$0.193624\pi$
$571$	−89.2030	+	448.454i	−0.156222	+	0.785383i	−0.976851	+	0.213921i	$0.931376\pi$
$572$	258.480	+	386.843i	0.451889	+	0.676299i
$573$	−23.6030	−	118.660i	−0.0411920	−	0.207086i
$574$	556.397	−	556.397i	0.969333	−	0.969333i
$575$		0			0
$576$	72.8625	+	30.1806i	0.126497	+	0.0523969i
$577$		−	560.230i		−	0.970936i	−0.874254	−	0.485468i	$-0.838649\pi$
$577$		−	560.230i		−	0.970936i	0.874254	−	0.485468i	$-0.161351\pi$
$578$	814.544	−	623.167i	1.40925	−	1.07814i
$579$	−128.925			−0.222668
$580$		0			0
$581$	−268.820	−	179.620i	−0.462685	−	0.309156i
$582$	605.500	+	605.500i	1.04038	+	1.04038i
$583$	−1432.78	+	284.998i	−2.45760	+	0.488848i
$584$	−162.337	+	108.470i	−0.277975	+	0.185737i
$585$		0			0
$586$	643.170	−	266.410i	1.09756	−	0.454624i
$587$	−417.924	−	1008.96i	−0.711966	−	1.71884i	−0.695029	−	0.718982i	$-0.744608\pi$
$587$	−417.924	−	1008.96i	−0.711966	−	1.71884i	−0.0169378	−	0.999857i	$-0.505392\pi$
$588$	166.889	−	839.008i	0.283825	−	1.42688i
$589$	225.220	+	337.066i	0.382378	+	0.572268i
$590$		0			0
$591$	131.957	−	131.957i	0.223277	−	0.223277i
$592$	487.116	−	729.021i	0.822831	−	1.23145i
$593$	203.455	+	84.2737i	0.343094	+	0.142114i	0.547575	−	0.836756i	$-0.315551\pi$
$593$	203.455	+	84.2737i	0.343094	+	0.142114i	−0.204482	+	0.978870i	$0.565551\pi$
$594$		−	1729.20i		−	2.91111i
$595$		0			0
$596$	2002.09			3.35922
$597$	95.0243	−	229.409i	0.159170	−	0.384270i
$598$	125.665	+	83.9666i	0.210142	+	0.140412i
$599$	132.139	+	132.139i	0.220599	+	0.220599i	0.808751	−	0.588151i	$-0.200144\pi$
$599$	132.139	+	132.139i	0.220599	+	0.220599i	−0.588151	+	0.808751i	$0.700144\pi$
$600$		0			0
$601$	898.685	−	600.482i	1.49532	−	0.999139i	0.504577	−	0.863367i	$-0.331649\pi$
$601$	898.685	−	600.482i	1.49532	−	0.999139i	0.990740	−	0.135772i	$-0.0433514\pi$
$602$	−170.758	−	33.9658i	−0.283651	−	0.0564216i
$603$	41.3208	−	17.1156i	0.0685253	−	0.0283841i
$604$	−242.978	−	586.602i	−0.402282	−	0.971195i
$605$		0			0
$606$	307.552	+	460.284i	0.507511	+	0.759544i
$607$	116.204	+	584.198i	0.191440	+	0.962435i	0.950337	+	0.311224i	$0.100739\pi$
$607$	116.204	+	584.198i	0.191440	+	0.962435i	−0.758897	+	0.651211i	$0.774261\pi$
$608$	371.248	−	371.248i	0.610605	−	0.610605i
$609$	−89.1238	+	133.383i	−0.146345	+	0.219020i
$610$		0			0
$611$			190.057i			0.311058i
$612$	307.916	+	236.624i	0.503131	+	0.386640i
$613$	−971.365			−1.58461			−0.792304	−	0.610126i	$-0.791119\pi$
$613$	−971.365			−1.58461			−0.792304	+	0.610126i	$0.791119\pi$
$614$	−46.4980	+	112.256i	−0.0757296	+	0.182828i
$615$		0			0
$616$	588.746	+	588.746i	0.955757	+	0.955757i
$617$	−963.388	+	191.630i	−1.56141	+	0.310583i	−0.898791	−	0.438377i	$-0.855554\pi$
$617$	−963.388	+	191.630i	−1.56141	+	0.310583i	−0.662615	+	0.748960i	$0.730554\pi$
$618$	−840.691	+	561.732i	−1.36034	+	0.908951i
$619$	511.747	+	101.793i	0.826732	+	0.164447i	0.590283	−	0.807197i	$-0.299016\pi$
$619$	511.747	+	101.793i	0.826732	+	0.164447i	0.236449	+	0.971644i	$0.424016\pi$
$620$		0			0
$621$	−146.685	−	354.130i	−0.236208	−	0.570257i
$622$	−80.1489	+	402.936i	−0.128857	+	0.647807i
$623$	−155.098	−	232.120i	−0.248953	−	0.372585i
$624$	37.6195	+	189.126i	0.0602877	+	0.303087i
$625$		0			0
$626$	−24.4691	+	36.6206i	−0.0390881	+	0.0584994i
$627$	1120.19	+	463.997i	1.78658	+	0.740027i
$628$			228.426i			0.363736i
$629$	−477.700	+	418.326i	−0.759460	+	0.665065i
$630$		0			0
$631$	−4.24296	+	10.2434i	−0.00672418	+	0.0162336i	−0.927206	−	0.374552i	$-0.877797\pi$
$631$	−4.24296	+	10.2434i	−0.00672418	+	0.0162336i	0.920482	+	0.390785i	$0.127797\pi$
$632$	−364.572	−	243.599i	−0.576855	−	0.385442i
$633$	−448.936	−	448.936i	−0.709220	−	0.709220i
$634$	−293.084	+	58.2981i	−0.462278	+	0.0919528i
$635$		0			0
$636$	−1868.19	−	371.606i	−2.93741	−	0.584287i
$637$	119.129	−	49.3450i	0.187016	−	0.0774646i
$638$	466.552	+	1126.36i	0.731272	+	1.76545i
$639$	−44.5805	+	224.121i	−0.0697660	+	0.350737i
$640$		0			0
$641$	1.68748	+	8.48355i	0.00263258	+	0.0132349i	0.982079	−	0.188468i	$-0.0603523\pi$
$641$	1.68748	+	8.48355i	0.00263258	+	0.0132349i	−0.979447	+	0.201703i	$0.935352\pi$
$642$	−1037.70	+	1037.70i	−1.61635	+	1.61635i
$643$	−86.6511	+	129.683i	−0.134761	+	0.201684i	−0.892712	−	0.450627i	$-0.851200\pi$
$643$	−86.6511	+	129.683i	−0.134761	+	0.201684i	0.757952	+	0.652311i	$0.226200\pi$
$644$	318.998	+	132.133i	0.495339	+	0.205176i
$645$		0			0
$646$	−1516.24	+	873.951i	−2.34712	+	1.35287i
$647$	−856.541			−1.32387			−0.661933	−	0.749563i	$-0.730263\pi$
$647$	−856.541			−1.32387			−0.661933	+	0.749563i	$0.730263\pi$
$648$	311.969	−	753.161i	0.481434	−	1.16228i
$649$	434.318	+	290.202i	0.669212	+	0.447153i
$650$		0			0
$651$	−106.221	+	21.1286i	−0.163165	+	0.0324556i
$652$	−860.580	+	575.021i	−1.31991	+	0.881934i
$653$	15.0508	+	2.99379i	0.0230487	+	0.00458467i	0.206601	−	0.978425i	$-0.433760\pi$
$653$	15.0508	+	2.99379i	0.0230487	+	0.00458467i	−0.183553	+	0.983010i	$0.558760\pi$
$654$	567.398	−	235.024i	0.867581	−	0.359364i
$655$		0			0
$656$	329.954	−	1658.79i	0.502978	−	2.52864i
$657$	17.6883	+	26.4723i	0.0269228	+	0.0402928i
$658$	124.137	+	624.078i	0.188658	+	0.948447i
$659$	−343.599	+	343.599i	−0.521394	+	0.521394i	−0.917992	−	0.396598i	$-0.870191\pi$
$659$	−343.599	+	343.599i	−0.521394	+	0.521394i	0.396598	+	0.917992i	$0.370191\pi$
$660$		0			0
$661$	−52.7976	−	21.8695i	−0.0798754	−	0.0330855i	0.342388	−	0.939559i	$-0.388764\pi$
$661$	−52.7976	−	21.8695i	−0.0798754	−	0.0330855i	−0.422263	+	0.906473i	$0.638764\pi$
$662$			229.791i			0.347117i
$663$	9.23353	−	139.344i	0.0139269	−	0.210173i
$664$	−1712.51			−2.57908
$665$		0			0
$666$	−292.965	−	195.753i	−0.439887	−	0.293923i
$667$	191.094	+	191.094i	0.286498	+	0.286498i
$668$	1451.86	−	288.793i	2.17345	−	0.432325i
$669$	−556.393	+	371.770i	−0.831679	+	0.555710i
$670$		0			0
$671$	−1633.22	+	676.500i	−2.43400	+	1.00820i
$672$	53.6765	+	129.587i	0.0798757	+	0.192837i
$673$	−151.595	+	762.118i	−0.225252	+	1.13242i	0.688215	+	0.725507i	$0.258394\pi$
$673$	−151.595	+	762.118i	−0.225252	+	1.13242i	−0.913467	+	0.406912i	$0.866606\pi$
$674$	−119.337	−	178.601i	−0.177058	−	0.264986i
$675$		0			0
$676$	962.271	−	962.271i	1.42348	−	1.42348i
$677$	260.970	−	390.569i	0.385480	−	0.576912i	−0.587090	−	0.809522i	$-0.699727\pi$
$677$	260.970	−	390.569i	0.385480	−	0.576912i	0.972570	+	0.232610i	$0.0747266\pi$
$678$	−478.042	−	198.012i	−0.705077	−	0.292052i
$679$			294.880i			0.434286i
$680$		0			0
$681$	−329.964			−0.484529
$682$	−314.977	+	760.423i	−0.461844	+	1.11499i
$683$	730.394	+	488.034i	1.06939	+	0.714544i	0.960154	−	0.279472i	$-0.0901594\pi$
$683$	730.394	+	488.034i	1.06939	+	0.714544i	0.109237	+	0.994016i	$0.465159\pi$
$684$	−468.573	−	468.573i	−0.685048	−	0.685048i
$685$		0			0
$686$	803.897	−	537.147i	1.17186	−	0.783013i
$687$	−290.108	−	57.7061i	−0.422283	−	0.0839972i
$688$	−345.731	+	143.207i	−0.502517	+	0.208149i
$689$	−109.875	−	265.261i	−0.159470	−	0.384995i
$690$		0			0
$691$	155.737	+	233.077i	0.225379	+	0.337304i	0.926875	−	0.375369i	$-0.122484\pi$
$691$	155.737	+	233.077i	0.225379	+	0.337304i	−0.701496	+	0.712673i	$0.747484\pi$
$692$	−143.296	−	720.399i	−0.207076	−	1.04104i
$693$	96.0068	−	96.0068i	0.138538	−	0.138538i
$694$	−438.480	+	656.232i	−0.631816	+	0.945580i
$695$		0			0
$696$			849.716i			1.22086i
$697$	−542.523	+	1098.14i	−0.778369	+	1.57552i
$698$	243.423			0.348744
$699$	306.656	−	740.333i	0.438707	−	1.05913i
$700$		0			0
$701$	−387.183	−	387.183i	−0.552330	−	0.552330i	0.374783	−	0.927113i	$-0.377717\pi$
$701$	−387.183	−	387.183i	−0.552330	−	0.552330i	−0.927113	+	0.374783i	$0.877717\pi$
$702$	333.327	−	66.3029i	0.474825	−	0.0944485i
$703$	900.928	−	601.981i	1.28155	−	0.856303i
$704$	−482.957	−	96.0661i	−0.686019	−	0.136458i
$705$		0			0
$706$	−94.7427	−	228.729i	−0.134196	−	0.323979i
$707$	−37.1904	+	186.969i	−0.0526031	+	0.264454i
$708$	378.392	+	566.304i	0.534452	+	0.799864i
$709$	182.905	+	919.525i	0.257976	+	1.29693i	0.864808	+	0.502102i	$0.167440\pi$
$709$	182.905	+	919.525i	0.257976	+	1.29693i	−0.606832	+	0.794830i	$0.707560\pi$
$710$		0			0
$711$	−39.7237	+	59.4507i	−0.0558702	+	0.0836157i
$712$	−1366.16	−	565.881i	−1.91876	−	0.794777i
$713$			182.449i			0.255890i
$714$	−60.6942	−	463.588i	−0.0850059	−	0.649284i
$715$		0			0
$716$	−755.951	+	1825.03i	−1.05580	+	2.54892i
$717$	−681.752	−	455.532i	−0.950840	−	0.635331i
$718$	−800.809	−	800.809i	−1.11533	−	1.11533i
$719$	1315.87	−	261.743i	1.83014	−	0.364038i	0.844861	−	0.534985i	$-0.179683\pi$
$719$	1315.87	−	261.743i	1.83014	−	0.364038i	0.985280	+	0.170947i	$0.0546828\pi$
$720$		0			0
$721$	−341.492	−	67.9269i	−0.473636	−	0.0942121i
$722$	1575.47	−	652.583i	2.18210	−	0.903854i
$723$	−310.301	−	749.134i	−0.429186	−	1.03615i
$724$	−70.2044	+	352.941i	−0.0969674	+	0.487488i
$725$		0			0
$726$	269.307	+	1353.90i	0.370946	+	1.86487i
$727$	638.490	−	638.490i	0.878253	−	0.878253i	−0.115101	−	0.993354i	$-0.536719\pi$
$727$	638.490	−	638.490i	0.878253	−	0.878253i	0.993354	+	0.115101i	$0.0367191\pi$
$728$	−90.9147	+	136.063i	−0.124883	+	0.186900i
$729$	−737.573	−	305.513i	−1.01176	−	0.419084i
$730$		0			0
$731$	268.718	−	35.1813i	0.367603	−	0.0481276i
$732$	−2304.99			−3.14890
$733$	−117.668	+	284.077i	−0.160530	+	0.387553i	−0.983594	−	0.180395i	$-0.942263\pi$
$733$	−117.668	+	284.077i	−0.160530	+	0.387553i	0.823064	+	0.567948i	$0.192263\pi$
$734$	−94.6547	−	63.2462i	−0.128957	−	0.0861665i
$735$		0			0
$736$	231.753	−	46.0986i	0.314882	−	0.0626340i
$737$	−232.191	+	155.145i	−0.315049	+	0.210509i
$738$	−666.602	−	132.595i	−0.903255	−	0.179669i
$739$	−963.699	+	399.177i	−1.30406	+	0.540159i	−0.923145	−	0.384452i	$-0.874390\pi$
$739$	−963.699	+	399.177i	−1.30406	+	0.540159i	−0.380914	+	0.924611i	$0.624390\pi$
$740$		0			0
$741$	−46.4904	+	233.723i	−0.0627401	+	0.315416i
$742$	−534.047	−	799.258i	−0.719740	−	1.07717i
$743$	−17.3581	−	87.2651i	−0.0233622	−	0.117450i	0.967345	−	0.253465i	$-0.0815703\pi$
$743$	−17.3581	−	87.2651i	−0.0233622	−	0.117450i	−0.990707	+	0.136016i	$0.956570\pi$
$744$	−405.638	+	405.638i	−0.545212	+	0.545212i
$745$		0			0
$746$	−173.373	−	71.8133i	−0.232403	−	0.0962645i
$747$			279.259i			0.373841i
$748$	−2173.84	−	1073.96i	−2.90621	−	1.43578i
$749$	−505.362			−0.674716
$750$		0			0
$751$	−716.987	−	479.076i	−0.954710	−	0.637917i	−0.0224663	−	0.999748i	$-0.507152\pi$
$751$	−716.987	−	479.076i	−0.954710	−	0.637917i	−0.932244	+	0.361831i	$0.882152\pi$
$752$	967.091	+	967.091i	1.28603	+	1.28603i
$753$	1090.30	−	216.874i	1.44794	−	0.288014i
$754$	−199.232	+	133.122i	−0.264233	+	0.176555i
$755$		0			0
$756$	717.327	−	297.126i	0.948845	−	0.393024i
$757$	132.099	+	318.916i	0.174504	+	0.421290i	0.986797	−	0.161959i	$-0.0517813\pi$
$757$	132.099	+	318.916i	0.174504	+	0.421290i	−0.812294	+	0.583249i	$0.801781\pi$
$758$	51.0294	−	256.542i	0.0673211	−	0.338446i
$759$	303.171	+	453.728i	0.399435	+	0.597797i
$760$		0			0
$761$	412.972	−	412.972i	0.542670	−	0.542670i	−0.381640	−	0.924311i	$-0.624641\pi$
$761$	412.972	−	412.972i	0.542670	−	0.542670i	0.924311	+	0.381640i	$0.124641\pi$
$762$	−1058.93	+	1584.80i	−1.38967	+	2.07978i
$763$	195.391	+	80.9335i	0.256082	+	0.106073i
$764$		−	412.852i		−	0.540382i
$765$		0			0
$766$	275.587			0.359775
$767$	−39.2874	+	94.8483i	−0.0512222	+	0.123661i
$768$	−1071.79	−	716.145i	−1.39556	−	0.932481i
$769$	325.724	+	325.724i	0.423568	+	0.423568i	0.886430	−	0.462862i	$-0.153177\pi$
$769$	325.724	+	325.724i	0.423568	+	0.423568i	−0.462862	+	0.886430i	$0.653177\pi$
$770$		0			0
$771$	−565.397	+	377.786i	−0.733330	+	0.489995i
$772$	−431.492	−	85.8291i	−0.558927	−	0.111178i
$773$	−319.078	+	132.166i	−0.412779	+	0.170978i	−0.579402	−	0.815042i	$-0.696714\pi$
$773$	−319.078	+	132.166i	−0.412779	+	0.170978i	0.166623	+	0.986021i	$0.446714\pi$
$774$	57.5491	+	138.936i	0.0743528	+	0.179504i
$775$		0			0
$776$	867.767	+	1298.70i	1.11826	+	1.67359i
$777$	56.4736	+	283.912i	0.0726816	+	0.365395i
$778$	1588.33	−	1588.33i	2.04156	−	2.04156i
$779$	1161.20	−	1737.86i	1.49063	−	2.23088i
$780$		0			0
$781$		−	1426.77i		−	1.82685i
$782$	−785.922	−	52.0784i	−1.00502	−	0.0665964i
$783$	607.703			0.776121
$784$	355.093	−	857.270i	0.452925	−	1.09346i
$785$		0			0
$786$	−628.044	−	628.044i	−0.799038	−	0.799038i
$787$	305.401	−	60.7481i	0.388058	−	0.0771895i	0.00279427	−	0.999996i	$-0.499111\pi$
$787$	305.401	−	60.7481i	0.388058	−	0.0771895i	0.385264	+	0.922807i	$0.374111\pi$
$788$	529.488	−	353.793i	0.671939	−	0.448975i
$789$	−599.930	−	119.334i	−0.760368	−	0.151247i
$790$		0			0
$791$	−68.1878	−	164.620i	−0.0862046	−	0.208116i
$792$	140.304	−	705.358i	0.177152	−	0.890603i
$793$	−193.028	−	288.886i	−0.243414	−	0.364295i
$794$	−150.835	−	758.299i	−0.189969	−	0.955036i
$795$		0			0
$796$	470.757	−	704.537i	0.591403	−	0.885097i
$797$	1030.53	+	426.860i	1.29301	+	0.535583i	0.919882	−	0.392196i	$-0.128284\pi$
$797$	1030.53	+	426.860i	1.29301	+	0.535583i	0.373130	+	0.927779i	$0.378284\pi$
$798$			797.829i			0.999786i
$799$	−494.625	−	858.137i	−0.619055	−	1.07401i
$800$		0			0
$801$	−92.2782	+	222.779i	−0.115204	+	0.278126i
$802$	1193.45	+	797.436i	1.48809	+	0.994309i
$803$	−140.565	−	140.565i	−0.175050	−	0.175050i
$804$	−357.120	+	71.0356i	−0.444179	+	0.0883527i
$805$		0			0
$806$	−158.659	−	31.5593i	−0.196848	−	0.0391555i
$807$	−746.311	+	309.132i	−0.924796	+	0.383063i
$808$	386.415	+	932.888i	0.478236	+	1.15456i
$809$	−124.788	+	627.352i	−0.154250	+	0.775467i	0.823765	+	0.566931i	$0.191870\pi$
$809$	−124.788	+	627.352i	−0.154250	+	0.775467i	−0.978015	+	0.208535i	$0.933130\pi$
$810$		0			0
$811$	239.294	+	1203.01i	0.295060	+	1.48337i	0.789281	+	0.614032i	$0.210453\pi$
$811$	239.294	+	1203.01i	0.295060	+	1.48337i	−0.494221	+	0.869336i	$0.664547\pi$
$812$	−387.081	+	387.081i	−0.476701	+	0.476701i
$813$	−13.0204	+	19.4864i	−0.0160152	+	0.0239685i
$814$	2032.50	+	841.888i	2.49693	+	1.03426i
$815$		0			0
$816$	−662.061	−	756.029i	−0.811349	−	0.926507i
$817$	−462.460			−0.566046
$818$	1026.96	−	2479.31i	1.25546	−	3.03094i
$819$	22.1879	+	14.8255i	0.0270914	+	0.0181019i
$820$		0			0
$821$	1032.55	−	205.386i	1.25767	−	0.250166i	0.479119	−	0.877750i	$-0.340956\pi$
$821$	1032.55	−	205.386i	1.25767	−	0.250166i	0.778549	+	0.627584i	$0.215956\pi$
$822$	1364.72	−	911.873i	1.66024	−	1.10934i
$823$	−700.457	−	139.330i	−0.851102	−	0.169295i	−0.249781	−	0.968302i	$-0.580359\pi$
$823$	−700.457	−	139.330i	−0.851102	−	0.169295i	−0.601321	+	0.799008i	$0.705359\pi$
$824$	−1703.89	+	705.773i	−2.06782	+	0.856520i
$825$		0			0
$826$	−67.0551	+	337.109i	−0.0811805	+	0.408122i
$827$	−214.883	−	321.595i	−0.259834	−	0.388870i	0.678499	−	0.734601i	$-0.262631\pi$
$827$	−214.883	−	321.595i	−0.259834	−	0.388870i	−0.938333	+	0.345732i	$0.887631\pi$
$828$	−58.1837	−	292.509i	−0.0702702	−	0.353272i
$829$	453.378	−	453.378i	0.546897	−	0.546897i	−0.378645	−	0.925542i	$-0.623610\pi$
$829$	453.378	−	453.378i	0.546897	−	0.546897i	0.925542	+	0.378645i	$0.123610\pi$
$830$		0			0
$831$	626.593	+	259.543i	0.754022	+	0.312326i
$832$		−	96.7803i		−	0.116322i
$833$	−409.467	+	532.836i	−0.491557	+	0.639659i
$834$	779.375			0.934502
$835$		0			0
$836$	3440.21	+	2298.67i	4.11508	+	2.74961i
$837$	290.105	+	290.105i	0.346602	+	0.346602i
$838$	1763.07	−	350.696i	2.10390	−	0.418491i
$839$	8.04937	−	5.37841i	0.00959400	−	0.00641051i	−0.550764	−	0.834661i	$-0.685664\pi$
$839$	8.04937	−	5.37841i	0.00959400	−	0.00641051i	0.560358	+	0.828251i	$0.310664\pi$
$840$		0			0
$841$	381.140	−	157.873i	0.453199	−	0.187721i
$842$	−332.767	−	803.371i	−0.395210	−	0.954122i
$843$	−91.5497	+	460.252i	−0.108600	+	0.545969i
$844$	−1203.65	−	1801.39i	−1.42613	−	2.13435i
$845$		0			0
$846$	388.636	−	388.636i	0.459380	−	0.459380i
$847$	−264.099	+	395.252i	−0.311805	+	0.466649i
$848$	−1908.86	−	790.674i	−2.25101	−	0.932398i
$849$		−	293.397i		−	0.345580i
$850$		0			0
$851$	487.660			0.573044
$852$	711.928	−	1718.75i	0.835596	−	2.01731i
$853$	685.262	+	457.878i	0.803355	+	0.536785i	0.888118	−	0.459616i	$-0.152013\pi$
$853$	685.262	+	457.878i	0.803355	+	0.536785i	−0.0847622	+	0.996401i	$0.527013\pi$
$854$	−822.521	−	822.521i	−0.963140	−	0.963140i
$855$		0			0
$856$	−2225.71	+	1487.17i	−2.60012	+	1.73735i
$857$	701.467	+	139.530i	0.818515	+	0.162813i	0.586552	−	0.809912i	$-0.300485\pi$
$857$	701.467	+	139.530i	0.818515	+	0.162813i	0.231963	+	0.972725i	$0.425485\pi$
$858$	−447.007	+	185.156i	−0.520987	+	0.215800i
$859$	318.269	+	768.370i	0.370511	+	0.894494i	0.993664	+	0.112393i	$0.0358516\pi$
$859$	318.269	+	768.370i	0.370511	+	0.894494i	−0.623152	+	0.782100i	$0.714148\pi$
$860$		0			0
$861$	310.222	+	464.280i	0.360304	+	0.539233i
$862$	−384.628	−	1933.65i	−0.446204	−	2.24322i
$863$	−938.729	+	938.729i	−1.08775	+	1.08775i	−0.0919915	+	0.995760i	$0.529323\pi$
$863$	−938.729	+	938.729i	−1.08775	+	1.08775i	−0.995760	+	0.0919915i	$0.970677\pi$
$864$	295.202	−	441.802i	0.341669	−	0.511344i
$865$		0			0
$866$		−	1429.69i		−	1.65091i
$867$	320.955	+	653.193i	0.370190	+	0.753395i
$868$	−369.570			−0.425772
$869$	170.843	−	412.451i	0.196597	−	0.474627i
$870$		0			0
$871$	−38.8093	−	38.8093i	−0.0445572	−	0.0445572i
$872$	1098.71	−	218.546i	1.25998	−	0.250626i
$873$	211.780	−	141.507i	0.242588	−	0.162092i
$874$	1318.23	+	262.212i	1.50827	+	0.300014i
$875$		0			0
$876$	−99.1911	−	239.469i	−0.113232	−	0.273366i
$877$	123.536	−	621.056i	0.140862	−	0.708160i	−0.844210	−	0.536013i	$-0.819930\pi$
$877$	123.536	−	621.056i	0.140862	−	0.708160i	0.985071	−	0.172147i	$-0.0550703\pi$
$878$	232.338	+	347.718i	0.264621	+	0.396034i
$879$	96.3784	+	484.527i	0.109645	+	0.551225i
$880$		0			0
$881$	−906.749	+	1357.05i	−1.02923	+	1.54035i	−0.201285	+	0.979533i	$0.564512\pi$
$881$	−906.749	+	1357.05i	−1.02923	+	1.54035i	−0.827942	+	0.560814i	$0.810488\pi$
$882$	−344.503	−	142.698i	−0.390593	−	0.161789i
$883$			601.659i			0.681381i	0.940176	+	0.340690i	$0.110661\pi$
$883$			601.659i			0.681381i	−0.940176	+	0.340690i	$0.889339\pi$
$884$	123.669	−	460.218i	0.139897	−	0.520609i
$885$		0			0
$886$	4.73091	−	11.4214i	0.00533963	−	0.0128910i
$887$	−878.830	−	587.215i	−0.990789	−	0.662024i	−0.0492004	−	0.998789i	$-0.515667\pi$
$887$	−878.830	−	587.215i	−0.990789	−	0.662024i	−0.941589	+	0.336765i	$0.890667\pi$
$888$	1084.21	+	1084.21i	1.22096	+	1.22096i
$889$	−643.749	+	128.050i	−0.724128	+	0.144038i
$890$		0			0
$891$	814.078	+	161.930i	0.913668	+	0.181740i
$892$	−2109.66	+	873.851i	−2.36509	+	0.979654i
$893$	646.803	+	1561.52i	0.724304	+	1.74862i
$894$	−406.191	+	2042.06i	−0.454352	+	2.28418i
$895$		0			0
$896$	−106.677	−	536.302i	−0.119059	−	0.598552i
$897$	−75.8379	+	75.8379i	−0.0845461	+	0.0845461i
$898$	−974.066	+	1457.79i	−1.08471	+	1.62338i
$899$	−267.240	−	110.695i	−0.297264	−	0.123131i
$900$		0			0
$901$	1186.45	+	911.747i	1.31681	+	1.01193i
$902$	4243.64			4.70470
$903$	47.2802	−	114.145i	0.0523590	−	0.126406i
$904$	−784.752	−	524.354i	−0.868088	−	0.580038i
$905$		0			0
$906$	647.608	−	128.817i	0.714799	−	0.142182i
$907$	814.198	−	544.030i	0.897683	−	0.599812i	−0.0188279	−	0.999823i	$-0.505993\pi$
$907$	814.198	−	544.030i	0.897683	−	0.599812i	0.916511	+	0.400010i	$0.130993\pi$
$908$	−1104.34	−	219.667i	−1.21623	−	0.241924i
$909$	152.126	−	63.0126i	0.167355	−	0.0693208i
$910$		0			0
$911$	149.631	−	752.244i	0.164249	−	0.825735i	−0.807527	−	0.589830i	$-0.799195\pi$
$911$	149.631	−	752.244i	0.164249	−	0.825735i	0.971776	−	0.235905i	$-0.0758053\pi$
$912$	952.721	+	1425.85i	1.04465	+	1.56343i
$913$	−340.165	−	1710.12i	−0.372579	−	1.87308i
$914$	101.056	−	101.056i	0.110565	−	0.110565i
$915$		0			0
$916$	−932.532	−	386.267i	−1.01805	−	0.421689i
$917$		−	305.859i		−	0.333543i
$918$	−1332.47	+	1166.86i	−1.45149	+	1.27108i
$919$	729.897			0.794230			0.397115	−	0.917769i	$-0.370011\pi$
$919$	729.897			0.794230			0.397115	+	0.917769i	$0.370011\pi$
$920$		0			0
$921$	−71.6926	−	47.9035i	−0.0778422	−	0.0520125i
$922$	1702.10	+	1702.10i	1.84609	+	1.84609i
$923$	275.031	−	54.7070i	0.297975	−	0.0592708i
$924$	−919.074	+	614.105i	−0.994669	+	0.664616i
$925$		0			0
$926$	−2688.29	+	1113.53i	−2.90312	+	1.20251i
$927$	115.090	+	277.852i	0.124153	+	0.299733i
$928$	−73.0857	+	367.426i	−0.0787561	+	0.395934i
$929$	−18.6465	−	27.9064i	−0.0200716	−	0.0300392i	0.821298	−	0.570499i	$-0.193250\pi$
$929$	−18.6465	−	27.9064i	−0.0200716	−	0.0300392i	−0.841370	+	0.540460i	$0.818250\pi$
$930$		0			0
$931$	810.845	−	810.845i	0.870940	−	0.870940i
$932$	1519.19	−	2273.63i	1.63004	−	2.43952i
$933$	−269.346	−	111.567i	−0.288688	−	0.119579i
$934$		−	180.306i		−	0.193048i
$935$		0			0
$936$	141.347			0.151012
$937$	239.475	−	578.143i	0.255576	−	0.617015i	−0.743060	−	0.669225i	$-0.766626\pi$
$937$	239.475	−	578.143i	0.255576	−	0.617015i	0.998636	+	0.0522094i	$0.0166263\pi$
$938$	−152.785	−	102.087i	−0.162883	−	0.108835i
$939$	−22.1003	−	22.1003i	−0.0235360	−	0.0235360i
$940$		0			0
$941$	1480.41	−	989.179i	1.57323	−	1.05120i	0.606608	−	0.795001i	$-0.292530\pi$
$941$	1480.41	−	989.179i	1.57323	−	1.05120i	0.966624	−	0.256199i	$-0.0824702\pi$
$942$	−232.986	−	46.3438i	−0.247331	−	0.0491972i
$943$	869.073	−	359.982i	0.921605	−	0.381741i
$944$	282.718	+	682.541i	0.299489	+	0.723031i
$945$		0			0
$946$	−521.656	−	780.713i	−0.551433	−	0.825278i
$947$	−121.759	−	612.125i	−0.128574	−	0.646383i	−0.990293	−	0.138998i	$-0.955612\pi$
$947$	−121.759	−	612.125i	−0.128574	−	0.646383i	0.861719	−	0.507386i	$-0.169388\pi$
$948$	411.607	−	411.607i	0.434185	−	0.434185i
$949$	21.7062	−	32.4856i	0.0228727	−	0.0342314i
$950$		0			0
$951$		−	212.057i		−	0.222983i
$952$	56.3878	−	850.955i	0.0592308	−	0.893861i
$953$	1343.90			1.41018			0.705090	−	0.709118i	$-0.250906\pi$
$953$	1343.90			1.41018			0.705090	+	0.709118i	$0.250906\pi$
$954$	−317.741	+	767.094i	−0.333061	+	0.804082i
$955$		0			0
$956$	−1978.46	−	1978.46i	−2.06952	−	2.06952i
$957$	−848.530	+	168.783i	−0.886657	+	0.176367i
$958$	−1841.82	+	1230.66i	−1.92256	+	1.28462i
$959$	554.352	+	110.267i	0.578052	+	0.114982i
$960$		0			0
$961$	293.027	+	707.429i	0.304919	+	0.736139i
$962$	−84.3534	+	424.073i	−0.0876855	+	0.440825i
$963$	242.513	+	362.946i	0.251830	+	0.376891i
$964$	−539.812	−	2713.82i	−0.559971	−	2.81516i
$965$		0			0
$966$	−199.490	+	298.559i	−0.206512	+	0.309067i
$967$	−151.504	−	62.7548i	−0.156674	−	0.0648964i	0.302968	−	0.953001i	$-0.402022\pi$
$967$	−151.504	−	62.7548i	−0.156674	−	0.0648964i	−0.459642	+	0.888104i	$0.652022\pi$
$968$			2517.94i			2.60118i
$969$	−398.356	−	1176.29i	−0.411100	−	1.21392i
$970$		0			0
$971$	300.034	−	724.345i	0.308994	−	0.745978i	−0.690744	−	0.723099i	$-0.742717\pi$
$971$	300.034	−	724.345i	0.308994	−	0.745978i	0.999738	−	0.0228789i	$-0.00728321\pi$
$972$	−988.102	−	660.228i	−1.01657	−	0.679247i
$973$	189.779	+	189.779i	0.195045	+	0.195045i
$974$	1023.48	−	203.583i	1.05080	−	0.209017i
$975$		0			0
$976$	−2452.19	−	487.770i	−2.51249	−	0.499764i
$977$	−1391.58	+	576.412i	−1.42434	+	0.589982i	−0.955948	−	0.293537i	$-0.905168\pi$
$977$	−1391.58	+	576.412i	−1.42434	+	0.589982i	−0.468395	+	0.883519i	$0.655168\pi$
$978$	−411.903	−	994.422i	−0.421169	−	1.01679i
$979$	293.725	−	1476.66i	0.300026	−	1.50833i
$980$		0			0
$981$	−35.6383	−	179.166i	−0.0363285	−	0.182636i
$982$	−344.784	+	344.784i	−0.351104	+	0.351104i
$983$	481.292	−	720.305i	0.489616	−	0.732762i	−0.501588	−	0.865107i	$-0.667251\pi$
$983$	481.292	−	720.305i	0.489616	−	0.732762i	0.991204	+	0.132345i	$0.0422506\pi$
$984$	2732.55	+	1131.86i	2.77698	+	1.15026i
$985$		0			0
$986$	553.111	−	1119.57i	0.560964	−	1.13547i
$987$	−451.542			−0.457490
$988$	−311.193	+	751.287i	−0.314973	+	0.760412i
$989$	−173.059	−	115.634i	−0.174984	−	0.116920i
$990$		0			0
$991$	−134.143	+	26.6827i	−0.135361	+	0.0269250i	−0.262306	−	0.964985i	$-0.584483\pi$
$991$	−134.143	+	26.6827i	−0.135361	+	0.0269250i	0.126945	+	0.991910i	$0.459483\pi$
$992$	−210.292	+	140.513i	−0.211988	+	0.141646i
$993$	−159.934	−	31.8129i	−0.161061	−	0.0320371i
$994$	867.370	−	359.276i	0.872606	−	0.361445i
$995$		0			0
$996$	443.537	−	2229.81i	0.445319	−	2.23877i
$997$	−142.134	−	212.719i	−0.142562	−	0.213359i	0.753317	−	0.657658i	$-0.228453\pi$
$997$	−142.134	−	212.719i	−0.142562	−	0.213359i	−0.895879	+	0.444299i	$0.853453\pi$
$998$	−297.444	−	1495.35i	−0.298040	−	1.49835i
$999$	775.409	−	775.409i	0.776186	−	0.776186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.e.401.1		96
5.2	odd	4		425.3.t.e.299.1		96
5.3	odd	4		425.3.t.h.299.12		96
5.4	even	2		85.3.q.a.61.12	yes	96
17.12	odd	16	inner	425.3.u.e.301.1		96
85.12	even	16		425.3.t.h.199.12		96
85.29	odd	16		85.3.q.a.46.12	✓	96
85.63	even	16		425.3.t.e.199.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.12	✓	96	85.29	odd	16
85.3.q.a.61.12	yes	96	5.4	even	2
425.3.t.e.199.1		96	85.63	even	16
425.3.t.e.299.1		96	5.2	odd	4
425.3.t.h.199.12		96	85.12	even	16
425.3.t.h.299.12		96	5.3	odd	4
425.3.u.e.301.1		96	17.12	odd	16	inner
425.3.u.e.401.1		96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35804 + 3.27860i) q^{2} +(-2.09388 - 1.39909i) q^{3} +(-6.07650 - 6.07650i) q^{4} +(7.43063 - 4.96499i) q^{6} +(3.01835 + 0.600386i) q^{7} +(15.0602 - 6.23812i) q^{8} +(-1.01725 - 2.45586i) q^{9} +(9.22089 + 13.8000i) q^{11} +(4.22193 + 21.2251i) q^{12} +(-2.30659 + 2.30659i) q^{13} +(-6.06746 + 9.08060i) q^{14} +23.4739i q^{16} +(4.41170 - 16.4176i) q^{17} +9.43323 q^{18} +(-11.1013 + 26.8010i) q^{19} +(-5.48007 - 5.48007i) q^{21} +(-57.7671 + 11.4906i) q^{22} +(-10.8556 + 7.25351i) q^{23} +(-40.2619 - 8.00859i) q^{24} +(-4.42995 - 10.6948i) q^{26} +(-5.72761 + 28.7946i) q^{27} +(-14.6927 - 21.9892i) q^{28} +(-4.03821 - 20.3015i) q^{29} +(7.76376 - 11.6193i) q^{31} +(-16.7209 - 6.92600i) q^{32} -41.7965i q^{33} +(47.8354 + 36.7599i) q^{34} +(-8.74171 + 21.1043i) q^{36} +(-31.0567 - 20.7514i) q^{37} +(-72.7936 - 72.7936i) q^{38} +(8.05687 - 1.60261i) q^{39} +(-70.6653 - 14.0562i) q^{41} +(25.4091 - 10.5248i) q^{42} +(6.10068 + 14.7283i) q^{43} +(27.8252 - 139.887i) q^{44} +(-9.03894 - 45.4418i) q^{46} +(41.1986 - 41.1986i) q^{47} +(32.8421 - 49.1516i) q^{48} +(-36.5201 - 15.1271i) q^{49} +(-32.2072 + 28.2041i) q^{51} +28.0320 q^{52} +(-33.6831 + 81.3182i) q^{53} +(-86.6277 - 57.8828i) q^{54} +(49.2020 - 9.78689i) q^{56} +(60.7419 - 40.5864i) q^{57} +(72.0444 + 14.3305i) q^{58} +(29.0766 - 12.0439i) q^{59} +(-20.7793 + 104.464i) q^{61} +(27.5515 + 41.2337i) q^{62} +(-1.59595 - 8.02337i) q^{63} +(-20.9790 + 20.9790i) q^{64} +(137.034 + 56.7613i) q^{66} +16.8254i q^{67} +(-126.569 + 72.9537i) q^{68} +32.8787 q^{69} +(-71.4772 - 47.7595i) q^{71} +(-30.6399 - 30.6399i) q^{72} +(-11.7471 + 2.33665i) q^{73} +(110.212 - 73.6411i) q^{74} +(230.314 - 95.3990i) q^{76} +(19.5465 + 47.1894i) q^{77} +(-5.68723 + 28.5916i) q^{78} +(-14.9438 - 22.3650i) q^{79} +(35.3625 - 35.3625i) q^{81} +(142.051 - 212.594i) q^{82} +(-97.0588 - 40.2031i) q^{83} +66.5994i q^{84} -56.5732 q^{86} +(-19.9480 + 48.1587i) q^{87} +(224.954 + 150.310i) q^{88} +(-64.1441 - 64.1441i) q^{89} +(-8.34694 + 5.57725i) q^{91} +(110.040 + 21.8884i) q^{92} +(-32.5128 + 13.4673i) q^{93} +(79.1242 + 191.023i) q^{94} +(25.3214 + 37.8962i) q^{96} +(18.6933 + 93.9775i) q^{97} +(99.1916 - 99.1916i) q^{98} +(24.5110 - 36.6833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) \) 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Introduction

L-functions

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