LMFDB - Embedded newform 50.3.f.b.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	50.13
Dual form			50.3.f.b.27.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39680 - 0.221232i) q^{2} +(1.54417 - 3.03060i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-4.51960 + 2.13851i) q^{5} +(1.48643 - 4.57476i) q^{6} +(-2.71827 + 2.71827i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.51000 - 2.07833i) q^{9} +O(q^{10})$	\(q+(1.39680 - 0.221232i) q^{2} +(1.54417 - 3.03060i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-4.51960 + 2.13851i) q^{5} +(1.48643 - 4.57476i) q^{6} +(-2.71827 + 2.71827i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.51000 - 2.07833i) q^{9} +(-5.83988 + 3.98695i) q^{10} +(13.9453 + 10.1318i) q^{11} +(1.06417 - 6.71888i) q^{12} +(-8.27725 - 1.31099i) q^{13} +(-3.19552 + 4.39825i) q^{14} +(-0.498051 + 16.9993i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-4.91940 - 9.65487i) q^{17} +(-2.56896 - 2.56896i) q^{18} +(-31.3075 - 10.1724i) q^{19} +(-7.27512 + 6.86095i) q^{20} +(4.04052 + 12.4354i) q^{21} +(21.7203 + 11.0670i) q^{22} +(-1.39020 - 8.77738i) q^{23} -9.62038i q^{24} +(15.8536 - 19.3304i) q^{25} -11.8517 q^{26} +(21.6047 - 3.42185i) q^{27} +(-3.49047 + 6.85044i) q^{28} +(-2.63851 + 0.857304i) q^{29} +(3.06510 + 23.8548i) q^{30} +(-14.1220 + 43.4631i) q^{31} +(4.00000 - 4.00000i) q^{32} +(52.2394 - 26.6173i) q^{33} +(-9.00739 - 12.3976i) q^{34} +(6.47244 - 18.0985i) q^{35} +(-4.15667 - 3.02000i) q^{36} +(8.87405 - 56.0286i) q^{37} +(-45.9809 - 7.28265i) q^{38} +(-16.7545 + 23.0606i) q^{39} +(-8.64404 + 11.1929i) q^{40} +(46.2281 - 33.5867i) q^{41} +(8.39492 + 16.4760i) q^{42} +(-6.00015 - 6.00015i) q^{43} +(32.7873 + 10.6533i) q^{44} +(11.2691 + 6.16409i) q^{45} +(-3.88367 - 11.9527i) q^{46} +(22.4520 + 11.4399i) q^{47} +(-2.12833 - 13.4378i) q^{48} +34.2220i q^{49} +(17.8678 - 30.5081i) q^{50} -36.8564 q^{51} +(-16.5545 + 2.62197i) q^{52} +(-13.6421 + 26.7742i) q^{53} +(29.4205 - 9.55929i) q^{54} +(-84.6942 - 15.9697i) q^{55} +(-3.35997 + 10.3409i) q^{56} +(-79.1725 + 79.1725i) q^{57} +(-3.49581 + 1.78121i) q^{58} +(38.3329 + 52.7607i) q^{59} +(9.55879 + 32.6424i) q^{60} +(-68.2457 - 49.5834i) q^{61} +(-10.1102 + 63.8336i) q^{62} +(9.75405 + 1.54489i) q^{63} +(4.70228 - 6.47214i) q^{64} +(40.2134 - 11.7758i) q^{65} +(67.0795 - 48.7361i) q^{66} +(-17.3215 - 33.9954i) q^{67} +(-15.3243 - 15.3243i) q^{68} +(-28.7474 - 9.34060i) q^{69} +(5.03675 - 26.7120i) q^{70} +(33.5080 + 103.127i) q^{71} +(-6.47416 - 3.29875i) q^{72} +(12.6356 + 79.7780i) q^{73} -80.2240i q^{74} +(-34.1022 - 77.8951i) q^{75} -65.8373 q^{76} +(-65.4481 + 10.3660i) q^{77} +(-18.3010 + 35.9177i) q^{78} +(39.1289 - 12.7138i) q^{79} +(-9.59779 + 17.5466i) q^{80} +(30.1357 - 92.7481i) q^{81} +(57.1411 - 57.1411i) q^{82} +(32.1640 - 16.3884i) q^{83} +(15.3710 + 21.1564i) q^{84} +(42.8808 + 33.1159i) q^{85} +(-9.70844 - 7.05360i) q^{86} +(-1.47615 + 9.32008i) q^{87} +(48.1543 + 7.62689i) q^{88} +(57.7869 - 79.5368i) q^{89} +(17.1044 + 6.11693i) q^{90} +(26.0634 - 18.9362i) q^{91} +(-8.06904 - 15.8364i) q^{92} +(109.912 + 109.912i) q^{93} +(33.8919 + 11.0121i) q^{94} +(163.251 - 20.9761i) q^{95} +(-5.94572 - 18.2990i) q^{96} +(-72.8156 - 37.1014i) q^{97} +(7.57100 + 47.8014i) q^{98} -44.2820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

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 $

$2$	1.39680	−	0.221232i	0.698401	−	0.110616i
$2$	1.39680	−	0.221232i	0.698401	−	0.110616i
$3$	1.54417	−	3.03060i	0.514722	−	1.01020i	−0.476647	−	0.879095i	$-0.658148\pi$
$3$	1.54417	−	3.03060i	0.514722	−	1.01020i	0.991369	−	0.131104i	$-0.0418521\pi$
$4$	1.90211	−	0.618034i	0.475528	−	0.154508i
$5$	−4.51960	+	2.13851i	−0.903920	+	0.427702i
$5$	−4.51960	+	2.13851i	−0.903920	+	0.427702i
$6$	1.48643	−	4.57476i	0.247738	−	0.762460i
$7$	−2.71827	+	2.71827i	−0.388324	+	0.388324i	−0.874089	−	0.485765i	$-0.838541\pi$
$7$	−2.71827	+	2.71827i	−0.388324	+	0.388324i	0.485765	+	0.874089i	$0.338541\pi$
$8$	2.52015	−	1.28408i	0.315018	−	0.160510i
$9$	−1.51000	−	2.07833i	−0.167778	−	0.230926i
$10$	−5.83988	+	3.98695i	−0.583988	+	0.398695i
$11$	13.9453	+	10.1318i	1.26775	+	0.921077i	0.999111	−	0.0421629i	$-0.0134249\pi$
$11$	13.9453	+	10.1318i	1.26775	+	0.921077i	0.268643	+	0.963240i	$0.413425\pi$
$12$	1.06417	−	6.71888i	0.0886806	−	0.559907i
$13$	−8.27725	−	1.31099i	−0.636711	−	0.100845i	−0.170270	−	0.985397i	$-0.554464\pi$
$13$	−8.27725	−	1.31099i	−0.636711	−	0.100845i	−0.466441	+	0.884552i	$0.654464\pi$
$14$	−3.19552	+	4.39825i	−0.228251	+	0.314161i
$15$	−0.498051	+	16.9993i	−0.0332034	+	1.13329i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	−4.91940	−	9.65487i	−0.289377	−	0.567933i	0.699856	−	0.714284i	$-0.253247\pi$
$17$	−4.91940	−	9.65487i	−0.289377	−	0.567933i	−0.989233	+	0.146350i	$0.953247\pi$
$18$	−2.56896	−	2.56896i	−0.142720	−	0.142720i
$19$	−31.3075	−	10.1724i	−1.64776	−	0.535391i	−0.669510	−	0.742803i	$-0.733496\pi$
$19$	−31.3075	−	10.1724i	−1.64776	−	0.535391i	−0.978254	+	0.207412i	$0.933496\pi$
$20$	−7.27512	+	6.86095i	−0.363756	+	0.343048i
$21$	4.04052	+	12.4354i	0.192406	+	0.592164i
$22$	21.7203	+	11.0670i	0.987286	+	0.503047i
$23$	−1.39020	−	8.77738i	−0.0604435	−	0.381625i	−0.999303	−	0.0373252i	$-0.988116\pi$
$23$	−1.39020	−	8.77738i	−0.0604435	−	0.381625i	0.938860	−	0.344300i	$-0.111884\pi$
$24$		−	9.62038i		−	0.400849i
$25$	15.8536	−	19.3304i	0.634142	−	0.773217i
$26$	−11.8517			−0.455835
$27$	21.6047	−	3.42185i	0.800174	−	0.126735i
$28$	−3.49047	+	6.85044i	−0.124660	+	0.244659i
$29$	−2.63851	+	0.857304i	−0.0909831	+	0.0295622i	−0.354155	−	0.935187i	$-0.615231\pi$
$29$	−2.63851	+	0.857304i	−0.0909831	+	0.0295622i	0.263172	+	0.964749i	$0.415231\pi$
$30$	3.06510	+	23.8548i	0.102170	+	0.795161i
$31$	−14.1220	+	43.4631i	−0.455549	+	1.40204i	0.414941	+	0.909848i	$0.363802\pi$
$31$	−14.1220	+	43.4631i	−0.455549	+	1.40204i	−0.870490	+	0.492187i	$0.836198\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	52.2394	−	26.6173i	1.58301	−	0.806585i
$34$	−9.00739	−	12.3976i	−0.264923	−	0.364636i
$35$	6.47244	−	18.0985i	0.184927	−	0.517101i
$36$	−4.15667	−	3.02000i	−0.115463	−	0.0838888i
$37$	8.87405	−	56.0286i	0.239839	−	1.51429i	−0.514323	−	0.857597i	$-0.671957\pi$
$37$	8.87405	−	56.0286i	0.239839	−	1.51429i	0.754162	−	0.656689i	$-0.228043\pi$
$38$	−45.9809	−	7.28265i	−1.21002	−	0.191649i
$39$	−16.7545	+	23.0606i	−0.429603	+	0.591298i
$40$	−8.64404	+	11.1929i	−0.216101	+	0.279822i
$41$	46.2281	−	33.5867i	1.12752	−	0.819188i	0.142184	−	0.989840i	$-0.454587\pi$
$41$	46.2281	−	33.5867i	1.12752	−	0.819188i	0.985331	+	0.170652i	$0.0545874\pi$
$42$	8.39492	+	16.4760i	0.199879	+	0.392285i
$43$	−6.00015	−	6.00015i	−0.139538	−	0.139538i	0.633887	−	0.773426i	$-0.281458\pi$
$43$	−6.00015	−	6.00015i	−0.139538	−	0.139538i	−0.773426	+	0.633887i	$0.781458\pi$
$44$	32.7873	+	10.6533i	0.745167	+	0.242119i
$45$	11.2691	+	6.16409i	0.250425	+	0.136980i
$46$	−3.88367	−	11.9527i	−0.0844276	−	0.259842i
$47$	22.4520	+	11.4399i	0.477702	+	0.243401i	0.676225	−	0.736695i	$-0.263615\pi$
$47$	22.4520	+	11.4399i	0.477702	+	0.243401i	−0.198523	+	0.980096i	$0.563615\pi$
$48$	−2.12833	−	13.4378i	−0.0443403	−	0.279953i
$49$			34.2220i			0.698409i
$50$	17.8678	−	30.5081i	0.357355	−	0.610161i
$51$	−36.8564			−0.722674
$52$	−16.5545	+	2.62197i	−0.318356	+	0.0504226i
$53$	−13.6421	+	26.7742i	−0.257399	+	0.505174i	−0.983154	−	0.182779i	$-0.941491\pi$
$53$	−13.6421	+	26.7742i	−0.257399	+	0.505174i	0.725755	+	0.687953i	$0.241491\pi$
$54$	29.4205	−	9.55929i	0.544824	−	0.177024i
$55$	−84.6942	−	15.9697i	−1.53989	−	0.290359i
$56$	−3.35997	+	10.3409i	−0.0599994	+	0.184659i
$57$	−79.1725	+	79.1725i	−1.38899	+	1.38899i
$58$	−3.49581	+	1.78121i	−0.0602726	+	0.0307104i
$59$	38.3329	+	52.7607i	0.649710	+	0.894249i	0.999087	−	0.0427332i	$-0.0136065\pi$
$59$	38.3329	+	52.7607i	0.649710	+	0.894249i	−0.349376	+	0.936982i	$0.613607\pi$
$60$	9.55879	+	32.6424i	0.159313	+	0.544040i
$61$	−68.2457	−	49.5834i	−1.11878	−	0.812842i	−0.134758	−	0.990879i	$-0.543026\pi$
$61$	−68.2457	−	49.5834i	−1.11878	−	0.812842i	−0.984024	+	0.178036i	$0.943026\pi$
$62$	−10.1102	+	63.8336i	−0.163069	+	1.02957i
$63$	9.75405	+	1.54489i	0.154826	+	0.0245221i
$64$	4.70228	−	6.47214i	0.0734732	−	0.101127i
$65$	40.2134	−	11.7758i	0.618668	−	0.181167i
$66$	67.0795	−	48.7361i	1.01636	−	0.738426i
$67$	−17.3215	−	33.9954i	−0.258530	−	0.507394i	0.724861	−	0.688896i	$-0.241904\pi$
$67$	−17.3215	−	33.9954i	−0.258530	−	0.507394i	−0.983391	+	0.181502i	$0.941904\pi$
$68$	−15.3243	−	15.3243i	−0.225357	−	0.225357i
$69$	−28.7474	−	9.34060i	−0.416629	−	0.135371i
$70$	5.03675	−	26.7120i	0.0719536	−	0.381600i
$71$	33.5080	+	103.127i	0.471943	+	1.45249i	0.850036	+	0.526725i	$0.176580\pi$
$71$	33.5080	+	103.127i	0.471943	+	1.45249i	−0.378093	+	0.925768i	$0.623420\pi$
$72$	−6.47416	−	3.29875i	−0.0899189	−	0.0458160i
$73$	12.6356	+	79.7780i	0.173090	+	1.09285i	0.909314	+	0.416111i	$0.136607\pi$
$73$	12.6356	+	79.7780i	0.173090	+	1.09285i	−0.736223	+	0.676739i	$0.763393\pi$
$74$		−	80.2240i		−	1.08411i
$75$	−34.1022	−	77.8951i	−0.454696	−	1.03860i
$76$	−65.8373			−0.866281
$77$	−65.4481	+	10.3660i	−0.849976	+	0.134623i
$78$	−18.3010	+	35.9177i	−0.234628	+	0.460484i
$79$	39.1289	−	12.7138i	0.495303	−	0.160934i	−0.0507051	−	0.998714i	$-0.516147\pi$
$79$	39.1289	−	12.7138i	0.495303	−	0.160934i	0.546008	+	0.837780i	$0.316147\pi$
$80$	−9.59779	+	17.5466i	−0.119972	+	0.219332i
$81$	30.1357	−	92.7481i	0.372045	−	1.14504i
$82$	57.1411	−	57.1411i	0.696843	−	0.696843i
$83$	32.1640	−	16.3884i	0.387518	−	0.197451i	−0.249367	−	0.968409i	$-0.580222\pi$
$83$	32.1640	−	16.3884i	0.387518	−	0.197451i	0.636885	+	0.770959i	$0.280222\pi$
$84$	15.3710	+	21.1564i	0.182989	+	0.251862i
$85$	42.8808	+	33.1159i	0.504479	+	0.389599i
$86$	−9.70844	−	7.05360i	−0.112889	−	0.0820186i
$87$	−1.47615	+	9.32008i	−0.0169673	+	0.107127i
$88$	48.1543	+	7.62689i	0.547208	+	0.0866692i
$89$	57.7869	−	79.5368i	0.649291	−	0.893672i	−0.349777	−	0.936833i	$-0.613743\pi$
$89$	57.7869	−	79.5368i	0.649291	−	0.893672i	0.999068	+	0.0431607i	$0.0137427\pi$
$90$	17.1044	+	6.11693i	0.190049	+	0.0679658i
$91$	26.0634	−	18.9362i	0.286411	−	0.208090i
$92$	−8.06904	−	15.8364i	−0.0877069	−	0.172135i
$93$	109.912	+	109.912i	1.18185	+	1.18185i
$94$	33.8919	+	11.0121i	0.360552	+	0.117150i
$95$	163.251	−	20.9761i	1.71843	−	0.220801i
$96$	−5.94572	−	18.2990i	−0.0619346	−	0.190615i
$97$	−72.8156	−	37.1014i	−0.750677	−	0.382489i	0.0364055	−	0.999337i	$-0.488409\pi$
$97$	−72.8156	−	37.1014i	−0.750677	−	0.382489i	−0.787082	+	0.616848i	$0.788409\pi$
$98$	7.57100	+	47.8014i	0.0772551	+	0.487769i
$99$		−	44.2820i		−	0.447293i
$100$	18.2084	−	46.5667i	0.182084	−	0.465667i
$101$	−24.9483			−0.247013			−0.123506	−	0.992344i	$-0.539414\pi$
$101$	−24.9483			−0.247013			−0.123506	+	0.992344i	$0.539414\pi$
$102$	−51.4811	+	8.15380i	−0.504716	+	0.0799392i
$103$	−45.5971	+	89.4893i	−0.442690	+	0.868828i	0.556586	+	0.830790i	$0.312111\pi$
$103$	−45.5971	+	89.4893i	−0.442690	+	0.868828i	−0.999276	+	0.0380385i	$0.987889\pi$
$104$	−22.5433	+	7.32476i	−0.216762	+	0.0704304i
$105$	−44.8548	−	47.5625i	−0.427189	−	0.452976i
$106$	−13.1321	+	40.4164i	−0.123887	+	0.381286i
$107$	22.8729	−	22.8729i	0.213765	−	0.213765i	−0.592100	−	0.805865i	$-0.701701\pi$
$107$	22.8729	−	22.8729i	0.213765	−	0.213765i	0.805865	+	0.592100i	$0.201701\pi$
$108$	38.9798	−	19.8612i	0.360924	−	0.183900i
$109$	−8.46118	−	11.6458i	−0.0776255	−	0.106842i	0.768439	−	0.639924i	$-0.221034\pi$
$109$	−8.46118	−	11.6458i	−0.0776255	−	0.106842i	−0.846064	+	0.533081i	$0.821034\pi$
$110$	−121.834	−	3.56953i	−1.10758	−	0.0324503i
$111$	−156.097	−	113.411i	−1.40628	−	1.02172i
$112$	−2.40547	+	15.1875i	−0.0214774	+	0.135603i
$113$	−204.622	−	32.4090i	−1.81082	−	0.286805i	−0.842900	−	0.538070i	$-0.819154\pi$
$113$	−204.622	−	32.4090i	−1.81082	−	0.286805i	−0.967918	+	0.251265i	$0.919154\pi$
$114$	−93.0729	+	128.104i	−0.816429	+	1.12372i
$115$	25.0537	+	36.6973i	0.217858	+	0.319107i
$116$	−4.48890	+	3.26138i	−0.0386974	+	0.0281153i
$117$	9.77395	+	19.1825i	0.0835381	+	0.163953i
$118$	65.2158	+	65.2158i	0.552676	+	0.552676i
$119$	39.6168	+	12.8723i	0.332914	+	0.108170i
$120$	20.5733	+	43.4803i	0.171444	+	0.362335i
$121$	54.4257	+	167.505i	0.449800	+	1.38434i
$122$	−106.295	−	54.1601i	−0.871271	−	0.443935i
$123$	−30.4038	−	191.962i	−0.247186	−	1.56067i
$124$			91.3996i			0.737094i
$125$	−30.3134	+	121.269i	−0.242507	+	0.970150i
$126$	13.9663			0.110843
$127$	168.207	−	26.6413i	1.32446	−	0.209774i	0.546169	−	0.837675i	$-0.316086\pi$
$127$	168.207	−	26.6413i	1.32446	−	0.209774i	0.778293	+	0.627901i	$0.216086\pi$
$128$	5.13632	−	10.0806i	0.0401275	−	0.0787546i
$129$	−27.4492	+	8.91880i	−0.212785	+	0.0691380i
$130$	53.5650	−	25.3450i	0.412038	−	0.194961i
$131$	−1.22385	+	3.76662i	−0.00934236	+	0.0287528i	−0.955619	−	0.294605i	$-0.904812\pi$
$131$	−1.22385	+	3.76662i	−0.00934236	+	0.0287528i	0.946277	+	0.323358i	$0.104812\pi$
$132$	82.9148	−	82.9148i	0.628142	−	0.628142i
$133$	112.754	−	57.4508i	0.847772	−	0.431961i
$134$	−31.7156	−	43.6528i	−0.236683	−	0.325767i
$135$	−90.3269	+	61.6672i	−0.669088	+	0.456794i
$136$	−24.7952	−	18.0148i	−0.182318	−	0.132462i
$137$	−33.2579	+	209.982i	−0.242758	+	1.53272i	0.501697	+	0.865043i	$0.332709\pi$
$137$	−33.2579	+	209.982i	−0.242758	+	1.53272i	−0.744456	+	0.667672i	$0.767291\pi$
$138$	−42.2209	−	6.68713i	−0.305948	−	0.0484575i
$139$	18.0245	−	24.8086i	0.129672	−	0.178479i	−0.739244	−	0.673438i	$-0.764817\pi$
$139$	18.0245	−	24.8086i	0.129672	−	0.178479i	0.868916	+	0.494959i	$0.164817\pi$
$140$	1.12581	−	38.4256i	0.00804148	−	0.274469i
$141$	69.3392	−	50.3779i	0.491768	−	0.357290i
$142$	69.6190	+	136.635i	0.490275	+	0.962218i
$143$	−102.146	−	102.146i	−0.714307	−	0.714307i
$144$	−9.77291	−	3.17541i	−0.0678674	−	0.0220515i
$145$	10.0917	−	9.51715i	0.0695976	−	0.0656355i
$146$	35.2989	+	108.639i	0.241773	+	0.744101i
$147$	103.713	+	52.8445i	0.705532	+	0.359486i
$148$	−17.7481	−	112.057i	−0.119920	−	0.757143i
$149$		−	17.7382i		−	0.119048i	−0.998227	−	0.0595242i	$-0.981042\pi$
$149$		−	17.7382i		−	0.119048i	0.998227	−	0.0595242i	$-0.0189584\pi$
$150$	−64.8668	−	101.260i	−0.432446	−	0.675064i
$151$	82.5008			0.546363			0.273181	−	0.961963i	$-0.411924\pi$
$151$	82.5008			0.546363			0.273181	+	0.961963i	$0.411924\pi$
$152$	−91.9617	+	14.5653i	−0.605011	+	0.0958244i
$153$	−12.6378	+	24.8030i	−0.0825997	+	0.162111i
$154$	−89.1248	+	28.9584i	−0.578733	+	0.188042i
$155$	−29.1204	−	226.636i	−0.187874	−	1.46217i
$156$	−17.6167	+	54.2187i	−0.112928	+	0.347556i
$157$	49.4887	−	49.4887i	0.315215	−	0.315215i	−0.531711	−	0.846926i	$-0.678451\pi$
$157$	49.4887	−	49.4887i	0.315215	−	0.315215i	0.846926	+	0.531711i	$0.178451\pi$
$158$	51.8427	−	26.4152i	0.328118	−	0.167185i
$159$	60.0761	+	82.6877i	0.377837	+	0.520048i
$160$	−9.52436	+	26.6324i	−0.0595272	+	0.166453i
$161$	27.6382	+	20.0803i	0.171666	+	0.124723i
$162$	21.5748	−	136.218i	0.133178	−	0.840850i
$163$	−72.4915	−	11.4815i	−0.444733	−	0.0704388i	−0.0699483	−	0.997551i	$-0.522283\pi$
$163$	−72.4915	−	11.4815i	−0.444733	−	0.0704388i	−0.374785	+	0.927112i	$0.622283\pi$
$164$	67.1734	−	92.4563i	0.409594	−	0.563758i
$165$	−179.180	+	232.014i	−1.08594	+	1.40614i
$166$	41.3012	−	30.0071i	0.248802	−	0.180765i
$167$	2.01337	+	3.95145i	0.0120561	+	0.0236614i	0.896956	−	0.442120i	$-0.145773\pi$
$167$	2.01337	+	3.95145i	0.0120561	+	0.0236614i	−0.884900	+	0.465781i	$0.845773\pi$
$168$	26.1508	+	26.1508i	0.155659	+	0.155659i
$169$	−93.9344	−	30.5212i	−0.555825	−	0.180599i
$170$	67.2222	+	36.7698i	0.395425	+	0.216293i
$171$	26.1326	+	80.4278i	0.152822	+	0.470338i
$172$	−15.1213	−	7.70466i	−0.0879143	−	0.0447946i
$173$	−48.0579	−	303.425i	−0.277791	−	1.75390i	−0.593300	−	0.804981i	$-0.702175\pi$
$173$	−48.0579	−	303.425i	−0.277791	−	1.75390i	0.315509	−	0.948923i	$-0.397825\pi$
$174$			13.3449i			0.0766947i
$175$	9.45105	+	95.6395i	0.0540060	+	0.546511i
$176$	68.9493			0.391757
$177$	219.089	−	34.7002i	1.23779	−	0.196047i
$178$	63.1208	−	123.882i	0.354611	−	0.695964i
$179$	−41.8910	+	13.6112i	−0.234028	+	0.0760402i	−0.423683	−	0.905811i	$-0.639263\pi$
$179$	−41.8910	+	13.6112i	−0.234028	+	0.0760402i	0.189655	+	0.981851i	$0.439263\pi$
$180$	25.2448	+	4.76009i	0.140249	+	0.0264450i
$181$	79.7074	−	245.314i	0.440372	−	1.35533i	−0.447107	−	0.894480i	$-0.647546\pi$
$181$	79.7074	−	245.314i	0.440372	−	1.35533i	0.887480	−	0.460847i	$-0.152454\pi$
$182$	32.2161	−	32.2161i	0.177012	−	0.177012i
$183$	−255.650	+	130.260i	−1.39699	+	0.711804i
$184$	−14.7744	−	20.3352i	−0.0802954	−	0.110517i
$185$	79.7105	+	272.204i	0.430867	+	1.47137i
$186$	177.842	+	129.210i	0.956139	+	0.694676i
$187$	29.2192	−	184.483i	0.156252	−	0.986538i
$188$	49.7765	+	7.88382i	0.264769	+	0.0419352i
$189$	−49.4259	+	68.0289i	−0.261513	+	0.359941i
$190$	223.389	−	65.4159i	1.17573	−	0.344294i
$191$	−101.886	+	74.0247i	−0.533436	+	0.387564i	−0.821641	−	0.570005i	$-0.806941\pi$
$191$	−101.886	+	74.0247i	−0.533436	+	0.387564i	0.288206	+	0.957569i	$0.406941\pi$
$192$	−12.3533	−	24.2448i	−0.0643402	−	0.126275i
$193$	159.169	+	159.169i	0.824708	+	0.824708i	0.986779	−	0.162071i	$-0.0518174\pi$
$193$	159.169	+	159.169i	0.824708	+	0.824708i	−0.162071	+	0.986779i	$0.551817\pi$
$194$	−109.917	−	35.7142i	−0.566583	−	0.184094i
$195$	26.4083	−	140.054i	0.135427	−	0.718228i
$196$	21.1504	+	65.0942i	0.107910	+	0.332113i
$197$	55.3779	+	28.2164i	0.281106	+	0.143231i	0.588859	−	0.808235i	$-0.299577\pi$
$197$	55.3779	+	28.2164i	0.281106	+	0.143231i	−0.307753	+	0.951466i	$0.599577\pi$
$198$	−9.79659	−	61.8532i	−0.0494777	−	0.312390i
$199$			137.580i			0.691357i	0.938353	+	0.345679i	$0.112351\pi$
$199$			137.580i			0.691357i	−0.938353	+	0.345679i	$0.887649\pi$
$200$	15.1315	−	69.0727i	0.0756575	−	0.345363i
$201$	−129.774			−0.645640
$202$	−34.8478	+	5.51935i	−0.172514	+	0.0273235i
$203$	4.84180	−	9.50256i	0.0238512	−	0.0468106i
$204$	−70.1050	+	22.7785i	−0.343652	+	0.111659i
$205$	−137.107	+	250.658i	−0.668815	+	1.22272i
$206$	−43.8922	+	135.086i	−0.213069	+	0.655759i
$207$	−16.1431	+	16.1431i	−0.0779861	+	0.0779861i
$208$	−29.8680	+	15.2185i	−0.143596	+	0.0731660i
$209$	−333.527	−	459.060i	−1.59582	−	2.19646i
$210$	−73.1757	−	56.5121i	−0.348455	−	0.269105i
$211$	−149.606	−	108.695i	−0.709033	−	0.515142i	0.173829	−	0.984776i	$-0.444386\pi$
$211$	−149.606	−	108.695i	−0.709033	−	0.515142i	−0.882861	+	0.469634i	$0.844386\pi$
$212$	−9.40152	+	59.3589i	−0.0443468	+	0.279995i
$213$	364.278	+	57.6960i	1.71023	+	0.270873i
$214$	26.8887	−	37.0091i	0.125648	−	0.172940i
$215$	39.9496	+	14.2869i	0.185812	+	0.0664506i
$216$	50.0531	−	36.3657i	0.231727	−	0.168360i
$217$	−79.7570	−	156.532i	−0.367544	−	0.721345i
$218$	−14.3950	−	14.3950i	−0.0660322	−	0.0660322i
$219$	261.286	+	84.8971i	1.19309	+	0.387658i
$220$	−170.968	+	21.9676i	−0.777126	+	0.0998528i
$221$	28.0617	+	86.3650i	0.126976	+	0.390792i
$222$	−243.127	−	123.879i	−1.09517	−	0.558015i
$223$	44.3027	+	279.716i	0.198667	+	1.25433i	0.862348	+	0.506316i	$0.168993\pi$
$223$	44.3027	+	279.716i	0.198667	+	1.25433i	−0.663681	+	0.748016i	$0.731007\pi$
$224$			21.7462i			0.0970810i
$225$	−64.1139	−	3.76009i	−0.284951	−	0.0167115i
$226$	−292.987			−1.29640
$227$	−86.9133	+	13.7657i	−0.382878	+	0.0606419i	−0.344907	−	0.938637i	$-0.612089\pi$
$227$	−86.9133	+	13.7657i	−0.382878	+	0.0606419i	−0.0379711	+	0.999279i	$0.512089\pi$
$228$	−101.664	+	199.526i	−0.445894	+	0.875116i
$229$	−1.53872	+	0.499961i	−0.00671931	+	0.00218324i	−0.312375	−	0.949959i	$-0.601124\pi$
$229$	−1.53872	+	0.499961i	−0.00671931	+	0.00218324i	0.305655	+	0.952142i	$0.401124\pi$
$230$	43.1136	+	45.7162i	0.187451	+	0.198766i
$231$	−69.6477	+	214.354i	−0.301505	+	0.927938i
$232$	−5.54859	+	5.54859i	−0.0239163	+	0.0239163i
$233$	−68.7608	+	35.0354i	−0.295111	+	0.150366i	−0.595277	−	0.803520i	$-0.702958\pi$
$233$	−68.7608	+	35.0354i	−0.295111	+	0.150366i	0.300166	+	0.953887i	$0.402958\pi$
$234$	17.8960	+	24.6318i	0.0764788	+	0.105264i
$235$	−125.938	−	3.68978i	−0.535908	−	0.0157012i
$236$	105.521	+	76.6658i	0.447125	+	0.324855i
$237$	21.8913	−	138.216i	0.0923683	−	0.583190i
$238$	58.1846	+	9.21553i	0.244473	+	0.0387207i
$239$	5.89389	−	8.11224i	0.0246606	−	0.0339424i	−0.796509	−	0.604627i	$-0.793322\pi$
$239$	5.89389	−	8.11224i	0.0246606	−	0.0339424i	0.821169	+	0.570685i	$0.193322\pi$
$240$	38.3560	+	56.1819i	0.159817	+	0.234091i
$241$	172.450	−	125.292i	0.715559	−	0.519884i	−0.169404	−	0.985547i	$-0.554184\pi$
$241$	172.450	−	125.292i	0.715559	−	0.519884i	0.884962	+	0.465663i	$0.154184\pi$
$242$	113.079	+	221.931i	0.467271	+	0.917070i
$243$	−95.3421	−	95.3421i	−0.392355	−	0.392355i
$244$	−160.455	−	52.1351i	−0.657603	−	0.213668i
$245$	−73.1841	−	154.670i	−0.298711	−	0.631305i
$246$	−84.9363	−	261.407i	−0.345270	−	1.06263i
$247$	245.804	+	125.243i	0.995158	+	0.507058i
$248$	20.2205	+	127.667i	0.0815343	+	0.514787i
$249$		−	122.783i		−	0.493103i
$250$	−15.5134	+	176.095i	−0.0620534	+	0.704379i
$251$	350.719			1.39729			0.698643	−	0.715471i	$-0.253788\pi$
$251$	350.719			1.39729			0.698643	+	0.715471i	$0.253788\pi$
$252$	19.5081	−	3.08978i	0.0774131	−	0.0122610i
$253$	69.5443	−	136.488i	0.274879	−	0.539480i
$254$	229.058	−	74.4253i	0.901802	−	0.293013i
$255$	166.576	−	78.8177i	0.653239	−	0.309089i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−351.169	+	351.169i	−1.36642	+	1.36642i	−0.500928	+	0.865489i	$0.667008\pi$
$257$	−351.169	+	351.169i	−1.36642	+	1.36642i	−0.865489	+	0.500928i	$0.832992\pi$
$258$	−36.3680	+	18.5304i	−0.140961	+	0.0718234i
$259$	128.179	+	176.423i	0.494898	+	0.681169i
$260$	69.2125	−	47.2522i	0.266202	−	0.181739i
$261$	5.76591	+	4.18918i	0.0220916	+	0.0160505i
$262$	−0.876179	+	5.53198i	−0.00334420	+	0.0211144i
$263$	−82.1738	−	13.0151i	−0.312448	−	0.0494869i	−0.00175874	−	0.999998i	$-0.500560\pi$
$263$	−82.1738	−	13.0151i	−0.312448	−	0.0494869i	−0.310689	+	0.950512i	$0.600560\pi$
$264$	97.4722	−	134.159i	0.369213	−	0.508178i
$265$	4.40010	−	150.183i	0.0166041	−	0.566727i
$266$	144.785	−	105.192i	0.544303	−	0.395459i
$267$	−151.811	−	297.947i	−0.568582	−	1.11591i
$268$	−53.9578	−	53.9578i	−0.201335	−	0.201335i
$269$	214.251	+	69.6142i	0.796470	+	0.258789i	0.678857	−	0.734271i	$-0.262476\pi$
$269$	214.251	+	69.6142i	0.796470	+	0.258789i	0.117613	+	0.993059i	$0.462476\pi$
$270$	−112.526	+	106.120i	−0.416763	+	0.393038i
$271$	−108.531	−	334.023i	−0.400482	−	1.23256i	−0.924610	−	0.380916i	$-0.875609\pi$
$271$	−108.531	−	334.023i	−0.400482	−	1.23256i	0.524128	−	0.851640i	$-0.324391\pi$
$272$	−38.6195	−	19.6776i	−0.141983	−	0.0723441i
$273$	−17.1417	−	108.228i	−0.0627900	−	0.396440i
$274$			300.661i			1.09730i
$275$	416.935	−	108.942i	1.51613	−	0.396154i
$276$	−60.4536			−0.219035
$277$	−316.145	+	50.0724i	−1.14132	+	0.180767i	−0.698340	−	0.715766i	$-0.746078\pi$
$277$	−316.145	+	50.0724i	−1.14132	+	0.180767i	−0.442977	+	0.896533i	$0.646078\pi$
$278$	19.6882	−	38.6402i	0.0708208	−	0.138994i
$279$	111.655	−	36.2789i	0.400197	−	0.130032i
$280$	−6.92844	−	53.9221i	−0.0247444	−	0.192579i
$281$	28.9023	−	88.9520i	0.102855	−	0.316555i	−0.886366	−	0.462985i	$-0.846778\pi$
$281$	28.9023	−	88.9520i	0.102855	−	0.316555i	0.989221	+	0.146430i	$0.0467783\pi$
$282$	85.7080	−	85.7080i	0.303929	−	0.303929i
$283$	30.4450	−	15.5125i	0.107579	−	0.0548144i	−0.399373	−	0.916789i	$-0.630772\pi$
$283$	30.4450	−	15.5125i	0.107579	−	0.0548144i	0.506952	+	0.861974i	$0.330772\pi$
$284$	127.472	+	175.450i	0.448845	+	0.617782i
$285$	188.517	−	527.139i	0.661462	−	1.84961i
$286$	−165.275	−	120.080i	−0.577886	−	0.419859i
$287$	−34.3628	+	216.958i	−0.119731	+	0.755952i
$288$	−14.3533	−	2.27334i	−0.0498379	−	0.00789355i
$289$	100.854	−	138.814i	0.348976	−	0.480324i
$290$	11.9905	−	15.5262i	0.0413467	−	0.0535385i
$291$	−224.879	+	163.384i	−0.772779	+	0.561457i
$292$	73.3399	+	143.938i	0.251164	+	0.492937i
$293$	115.262	+	115.262i	0.393385	+	0.393385i	0.875892	−	0.482507i	$-0.160274\pi$
$293$	115.262	+	115.262i	0.393385	+	0.393385i	−0.482507	+	0.875892i	$0.660274\pi$
$294$	156.558	+	50.8687i	0.532509	+	0.173023i
$295$	−286.079	−	156.482i	−0.969758	−	0.530447i
$296$	−49.5812	−	152.595i	−0.167504	−	0.515524i
$297$	335.953	+	171.177i	1.13116	+	0.576353i
$298$	−3.92426	−	24.7768i	−0.0131687	−	0.0831436i
$299$			74.4751i			0.249081i
$300$	−113.008	−	127.089i	−0.376693	−	0.423630i
$301$	32.6200			0.108372
$302$	115.237	−	18.2518i	0.381580	−	0.0604364i
$303$	−38.5243	+	75.6082i	−0.127143	+	0.249532i
$304$	−125.230	+	40.6897i	−0.411941	+	0.133848i
$305$	414.478	+	78.1530i	1.35894	+	0.256239i
$306$	−12.1652	+	37.4407i	−0.0397557	+	0.122355i
$307$	−363.925	+	363.925i	−1.18542	+	1.18542i	−0.207103	+	0.978319i	$0.566403\pi$
$307$	−363.925	+	363.925i	−1.18542	+	1.18542i	−0.978319	+	0.207103i	$0.933597\pi$
$308$	−118.083	+	60.1664i	−0.383387	+	0.195346i
$309$	200.797	+	276.373i	0.649827	+	0.894410i
$310$	−90.8145	−	310.123i	−0.292950	−	1.00040i
$311$	−52.7135	−	38.2986i	−0.169497	−	0.123147i	0.499803	−	0.866139i	$-0.333406\pi$
$311$	−52.7135	−	38.2986i	−0.169497	−	0.123147i	−0.669300	+	0.742993i	$0.733406\pi$
$312$	−12.6122	+	79.6302i	−0.0404237	+	0.255225i
$313$	−79.9313	−	12.6599i	−0.255371	−	0.0404469i	0.0274360	−	0.999624i	$-0.491266\pi$
$313$	−79.9313	−	12.6599i	−0.255371	−	0.0404469i	−0.282807	+	0.959177i	$0.591266\pi$
$314$	58.1775	−	80.0745i	0.185279	−	0.255014i
$315$	−47.3882	+	13.8769i	−0.150439	+	0.0440535i
$316$	66.5701	−	48.3660i	0.210665	−	0.153057i
$317$	−123.024	−	241.447i	−0.388087	−	0.761664i	0.611475	−	0.791264i	$-0.290577\pi$
$317$	−123.024	−	241.447i	−0.388087	−	0.761664i	−0.999562	+	0.0296003i	$0.990577\pi$
$318$	102.208	+	102.208i	0.321407	+	0.321407i
$319$	−45.4808	−	14.7776i	−0.142573	−	0.0463248i
$320$	−7.41170	+	39.3073i	−0.0231616	+	0.122835i
$321$	−33.9989	−	104.638i	−0.105916	−	0.325975i
$322$	43.0475	+	21.9338i	0.133688	+	0.0681175i
$323$	55.8008	+	352.312i	0.172758	+	1.09075i
$324$		−	195.042i		−	0.601982i
$325$	−156.566	+	139.219i	−0.481740	+	0.428365i
$326$	−103.796			−0.318394
$327$	−48.3592	+	7.65935i	−0.147888	+	0.0234231i
$328$	73.3737	−	144.004i	0.223700	−	0.439037i
$329$	−92.1273	+	29.9340i	−0.280022	+	0.0909847i
$330$	−198.950	+	363.718i	−0.602878	+	1.10218i
$331$	−112.045	+	344.840i	−0.338506	+	1.04181i	0.626464	+	0.779451i	$0.284502\pi$
$331$	−112.045	+	344.840i	−0.338506	+	1.04181i	−0.964969	+	0.262363i	$0.915498\pi$
$332$	51.0510	−	51.0510i	0.153768	−	0.153768i
$333$	−129.846	+	66.1598i	−0.389927	+	0.198678i
$334$	3.68646	+	5.07398i	0.0110373	+	0.0151916i
$335$	150.986	+	116.603i	0.450704	+	0.348069i
$336$	42.3129	+	30.7421i	0.125931	+	0.0914943i
$337$	27.6755	−	174.736i	0.0821231	−	0.518505i	−0.911995	−	0.410202i	$-0.865458\pi$
$337$	27.6755	−	174.736i	0.0821231	−	0.518505i	0.994118	−	0.108303i	$-0.0345417\pi$
$338$	−137.960	−	21.8507i	−0.408166	−	0.0646471i
$339$	−414.190	+	570.083i	−1.22180	+	1.68166i
$340$	102.031	+	36.4885i	0.300091	+	0.107319i
$341$	−637.297	+	463.023i	−1.86891	+	1.35784i
$342$	54.2952	+	106.560i	0.158758	+	0.311580i
$343$	−226.220	−	226.220i	−0.659533	−	0.659533i
$344$	−22.8259	−	7.41659i	−0.0663544	−	0.0215599i
$345$	149.902	−	19.2608i	0.434498	−	0.0558285i
$346$	−134.255	−	413.193i	−0.388019	−	1.19420i
$347$	−192.498	−	98.0825i	−0.554748	−	0.282658i	0.154058	−	0.988062i	$-0.450766\pi$
$347$	−192.498	−	98.0825i	−0.554748	−	0.282658i	−0.708806	+	0.705403i	$0.750766\pi$
$348$	2.95231	+	18.6402i	0.00848365	+	0.0535637i
$349$		−	182.332i		−	0.522441i	−0.965279	−	0.261220i	$-0.915875\pi$
$349$		−	182.332i		−	0.522441i	0.965279	−	0.261220i	$-0.0841250\pi$
$350$	34.3597	+	131.499i	0.0981707	+	0.375710i
$351$	−183.313			−0.522260
$352$	96.3085	−	15.2538i	0.273604	−	0.0433346i
$353$	57.6752	−	113.194i	0.163386	−	0.320663i	−0.794769	−	0.606911i	$-0.792408\pi$
$353$	57.6752	−	113.194i	0.163386	−	0.320663i	0.958155	+	0.286248i	$0.0924083\pi$
$354$	298.347	−	96.9388i	0.842788	−	0.273838i
$355$	−371.981	−	394.435i	−1.04783	−	1.11109i
$356$	60.7607	−	187.002i	0.170676	−	0.525287i
$357$	100.186	−	100.186i	0.280632	−	0.280632i
$358$	−55.5022	+	28.2798i	−0.155034	+	0.0789938i
$359$	−138.854	−	191.116i	−0.386780	−	0.532358i	0.570584	−	0.821239i	$-0.306717\pi$
$359$	−138.854	−	191.116i	−0.386780	−	0.532358i	−0.957365	+	0.288881i	$0.906717\pi$
$360$	36.3150	+	1.06397i	0.100875	+	0.00295547i
$361$	584.627	+	424.756i	1.61946	+	1.17661i
$362$	57.0642	−	360.289i	0.157636	−	0.995274i
$363$	591.683	+	93.7134i	1.62998	+	0.258164i
$364$	37.8723	−	52.1268i	0.104045	−	0.143205i
$365$	−227.714	−	333.543i	−0.623874	−	0.913817i
$366$	−328.275	+	238.505i	−0.896925	+	0.651654i
$367$	−58.6290	−	115.066i	−0.159752	−	0.313531i	0.797231	−	0.603674i	$-0.206297\pi$
$367$	−58.6290	−	115.066i	−0.159752	−	0.313531i	−0.956983	+	0.290143i	$0.906297\pi$
$368$	−25.1356	−	25.1356i	−0.0683034	−	0.0683034i
$369$	−139.609	−	45.3616i	−0.378344	−	0.122931i
$370$	171.560	+	362.580i	0.463675	+	0.979947i
$371$	−35.6965	−	109.863i	−0.0962170	−	0.296125i
$372$	276.995	+	141.136i	0.744611	+	0.379398i
$373$	78.9853	+	498.693i	0.211757	+	1.33698i	0.832961	+	0.553331i	$0.186644\pi$
$373$	78.9853	+	498.693i	0.211757	+	1.33698i	−0.621205	+	0.783648i	$0.713356\pi$
$374$		−	264.150i		−	0.706283i
$375$	320.708	+	279.127i	0.855220	+	0.744338i
$376$	71.2721			0.189553
$377$	22.9635	−	3.63706i	0.0609111	−	0.00964738i
$378$	−53.9880	+	105.957i	−0.142825	+	0.280311i
$379$	−89.7830	+	29.1723i	−0.236894	+	0.0769717i	−0.425058	−	0.905166i	$-0.639746\pi$
$379$	−89.7830	+	29.1723i	−0.236894	+	0.0769717i	0.188164	+	0.982138i	$0.439746\pi$
$380$	297.558	−	140.794i	0.783048	−	0.370510i
$381$	179.000	−	550.905i	0.469816	−	1.44595i
$382$	−125.938	+	125.938i	−0.329681	+	0.329681i
$383$	325.615	−	165.909i	0.850171	−	0.433184i	0.0260923	−	0.999660i	$-0.491694\pi$
$383$	325.615	−	165.909i	0.850171	−	0.433184i	0.824078	+	0.566476i	$0.191694\pi$
$384$	−22.6189	−	31.1322i	−0.0589033	−	0.0810734i
$385$	273.632	−	186.812i	0.710732	−	0.485225i
$386$	257.540	+	187.114i	0.667203	+	0.484751i
$387$	−3.41010	+	21.5305i	−0.00881162	+	0.0556344i
$388$	−161.433	−	25.5686i	−0.416066	−	0.0658983i
$389$	−100.649	+	138.531i	−0.258737	+	0.356120i	−0.918547	−	0.395312i	$-0.870637\pi$
$389$	−100.649	+	138.531i	−0.258737	+	0.356120i	0.659810	+	0.751432i	$0.270637\pi$
$390$	5.90275	−	201.471i	0.0151353	−	0.516591i
$391$	−77.9055	+	56.6017i	−0.199247	+	0.144761i
$392$	43.9438	+	86.2445i	0.112101	+	0.220012i
$393$	9.52528	+	9.52528i	0.0242373	+	0.0242373i
$394$	83.5943	+	27.1614i	0.212168	+	0.0689377i
$395$	−149.659	+	141.139i	−0.378882	+	0.357313i
$396$	−27.3678	−	84.2294i	−0.0691106	−	0.212701i
$397$	−170.110	−	86.6754i	−0.428489	−	0.218326i	0.226427	−	0.974028i	$-0.427296\pi$
$397$	−170.110	−	86.6754i	−0.428489	−	0.218326i	−0.654915	+	0.755702i	$0.727296\pi$
$398$	30.4371	+	192.172i	0.0764751	+	0.482845i
$399$		−	430.424i		−	1.07876i
$400$	5.85464	−	99.8285i	0.0146366	−	0.249571i
$401$	81.2535			0.202627			0.101314	−	0.994855i	$-0.467695\pi$
$401$	81.2535			0.202627			0.101314	+	0.994855i	$0.467695\pi$
$402$	−181.268	+	28.7100i	−0.450915	+	0.0714180i
$403$	173.871	−	341.241i	0.431442	−	0.846752i
$404$	−47.4545	+	15.4189i	−0.117462	+	0.0381656i
$405$	62.1415	+	483.630i	0.153436	+	1.19415i
$406$	4.66076	−	14.3444i	0.0114797	−	0.0353309i
$407$	691.424	−	691.424i	1.69883	−	1.69883i
$408$	−92.8835	+	47.3265i	−0.227656	+	0.115996i
$409$	142.583	+	196.249i	0.348614	+	0.479825i	0.946932	−	0.321433i	$-0.104164\pi$
$409$	142.583	+	196.249i	0.348614	+	0.479825i	−0.598319	+	0.801258i	$0.704164\pi$
$410$	−136.058	+	380.452i	−0.331849	+	0.927931i
$411$	585.015	+	425.038i	1.42339	+	1.03416i
$412$	−31.4234	+	198.399i	−0.0762703	+	0.481552i
$413$	−247.617	−	39.2187i	−0.599557	−	0.0949605i
$414$	−18.9774	+	26.1201i	−0.0458391	+	0.0630921i
$415$	−110.322	+	142.852i	−0.265836	+	0.344222i
$416$	−38.3529	+	27.8650i	−0.0921945	+	0.0669833i
$417$	−47.3519	−	92.9334i	−0.113554	−	0.222862i
$418$	−567.430	−	567.430i	−1.35749	−	1.35749i
$419$	−313.535	−	101.874i	−0.748294	−	0.243136i	−0.0900473	−	0.995937i	$-0.528702\pi$
$419$	−313.535	−	101.874i	−0.748294	−	0.243136i	−0.658247	+	0.752802i	$0.728702\pi$
$420$	−114.714	−	62.7474i	−0.273129	−	0.149399i
$421$	−34.6749	−	106.718i	−0.0823633	−	0.253488i	0.901392	−	0.433005i	$-0.142547\pi$
$421$	−34.6749	−	106.718i	−0.0823633	−	0.253488i	−0.983755	+	0.179517i	$0.942547\pi$
$422$	−233.017	−	118.728i	−0.552172	−	0.281346i
$423$	−10.1266	−	63.9369i	−0.0239400	−	0.151151i
$424$			84.9925i			0.200454i
$425$	−264.623	−	57.9699i	−0.622641	−	0.136400i
$426$	521.589			1.22439
$427$	320.291	−	50.7291i	0.750096	−	0.118804i
$428$	29.3706	−	57.6430i	0.0686229	−	0.134680i
$429$	−467.293	+	151.833i	−1.08926	+	0.353922i
$430$	58.9625	+	11.1178i	0.137122	+	0.0258554i
$431$	65.2188	−	200.723i	0.151320	−	0.465714i	−0.846450	−	0.532469i	$-0.821264\pi$
$431$	65.2188	−	200.723i	0.151320	−	0.465714i	0.997769	+	0.0667544i	$0.0212644\pi$
$432$	61.8690	−	61.8690i	0.143215	−	0.143215i
$433$	58.0321	−	29.5688i	0.134023	−	0.0682883i	−0.385693	−	0.922627i	$-0.626038\pi$
$433$	58.0321	−	29.5688i	0.134023	−	0.0682883i	0.519716	+	0.854339i	$0.326038\pi$
$434$	−146.035	−	200.999i	−0.336485	−	0.463132i
$435$	−13.2594	−	45.2798i	−0.0304815	−	0.104091i
$436$	−23.2916	−	16.9224i	−0.0534212	−	0.0388128i
$437$	−45.7635	+	288.940i	−0.104722	+	0.661189i
$438$	383.747	+	60.7796i	0.876136	+	0.138766i
$439$	420.223	−	578.387i	0.957228	−	1.31751i	0.00898677	−	0.999960i	$-0.497139\pi$
$439$	420.223	−	578.387i	0.957228	−	1.31751i	0.948241	−	0.317551i	$-0.102861\pi$
$440$	−233.948	+	68.5079i	−0.531700	+	0.155700i
$441$	71.1248	−	51.6752i	0.161281	−	0.117177i
$442$	58.3033	+	114.427i	0.131908	+	0.258884i
$443$	−398.922	−	398.922i	−0.900500	−	0.900500i	0.0949791	−	0.995479i	$-0.469722\pi$
$443$	−398.922	−	398.922i	−0.900500	−	0.900500i	−0.995479	+	0.0949791i	$0.969722\pi$
$444$	−367.006	−	119.247i	−0.826590	−	0.268575i
$445$	−91.0833	+	483.052i	−0.204682	+	1.08551i
$446$	123.764	+	380.907i	0.277498	+	0.854051i
$447$	−53.7574	−	27.3908i	−0.120263	−	0.0612769i
$448$	4.81094	+	30.3751i	0.0107387	+	0.0678015i
$449$			524.459i			1.16806i	0.811732	+	0.584030i	$0.198525\pi$
$449$			524.459i			1.16806i	−0.811732	+	0.584030i	$0.801475\pi$
$450$	−90.3863	+	8.93193i	−0.200858	+	0.0198487i
$451$	984.960			2.18395
$452$	−409.245	+	64.8180i	−0.905409	+	0.143403i
$453$	127.395	−	250.027i	0.281225	−	0.551935i
$454$	−118.355	+	38.4560i	−0.260694	+	0.0847047i
$455$	−77.3009	+	141.321i	−0.169892	+	0.310595i
$456$	−97.8626	+	301.190i	−0.214611	+	0.660505i
$457$	4.32110	−	4.32110i	0.00945537	−	0.00945537i	−0.702363	−	0.711819i	$-0.747872\pi$
$457$	4.32110	−	4.32110i	0.00945537	−	0.00945537i	0.711819	+	0.702363i	$0.247872\pi$
$458$	−2.03868	+	1.03876i	−0.00445127	+	0.00226804i
$459$	−139.320	−	191.757i	−0.303529	−	0.417771i
$460$	70.3351	+	54.3184i	0.152902	+	0.118083i
$461$	−281.522	−	204.538i	−0.610676	−	0.443682i	0.238976	−	0.971025i	$-0.423188\pi$
$461$	−281.522	−	204.538i	−0.610676	−	0.443682i	−0.849652	+	0.527343i	$0.823188\pi$
$462$	−49.8623	+	314.818i	−0.107927	+	0.681424i
$463$	288.817	+	45.7442i	0.623795	+	0.0987995i	0.460327	−	0.887749i	$-0.347732\pi$
$463$	288.817	+	45.7442i	0.623795	+	0.0987995i	0.163468	+	0.986549i	$0.447732\pi$
$464$	−6.52275	+	8.97780i	−0.0140577	+	0.0193487i
$465$	−731.808	−	261.711i	−1.57378	−	0.562820i
$466$	−88.2943	+	64.1496i	−0.189473	+	0.137660i
$467$	285.147	+	559.633i	0.610594	+	1.19836i	0.964749	+	0.263172i	$0.0847686\pi$
$467$	285.147	+	559.633i	0.610594	+	1.19836i	−0.354155	+	0.935187i	$0.615231\pi$
$468$	30.4466	+	30.4466i	0.0650568	+	0.0650568i
$469$	139.493	+	45.3241i	0.297427	+	0.0966398i
$470$	−176.727	+	22.7077i	−0.376015	+	0.0483142i
$471$	−73.5616	−	226.399i	−0.156182	−	0.480678i
$472$	164.353	+	83.7423i	0.348206	+	0.177420i
$473$	−22.8812	−	144.466i	−0.0483747	−	0.305426i
$474$		−	197.904i		−	0.417518i
$475$	−692.972	+	443.918i	−1.45889	+	0.934564i
$476$	83.3111			0.175023
$477$	76.2454	−	12.0761i	0.159844	−	0.0253167i
$478$	6.43791	−	12.6351i	0.0134684	−	0.0264333i
$479$	402.767	−	130.867i	0.840850	−	0.273209i	0.143241	−	0.989688i	$-0.454248\pi$
$479$	402.767	−	130.867i	0.840850	−	0.273209i	0.697609	+	0.716479i	$0.254248\pi$
$480$	66.0050	+	69.9894i	0.137510	+	0.145811i
$481$	−146.905	+	452.128i	−0.305417	+	0.939976i
$482$	213.159	−	213.159i	0.442240	−	0.442240i
$483$	103.533	−	52.7529i	0.214355	−	0.109219i
$484$	207.048	+	284.977i	0.427785	+	0.588795i
$485$	408.439	+	11.9666i	0.842143	+	0.0246734i
$486$	−154.267	−	112.081i	−0.317421	−	0.230620i
$487$	47.1753	−	297.853i	0.0968692	−	0.611608i	−0.890720	−	0.454551i	$-0.849800\pi$
$487$	47.1753	−	297.853i	0.0968692	−	0.611608i	0.987590	−	0.157056i	$-0.0502004\pi$
$488$	−235.658	−	37.3246i	−0.482906	−	0.0764848i
$489$	−146.735	+	201.963i	−0.300071	+	0.413013i
$490$	−136.442	−	199.853i	−0.278452	−	0.407862i
$491$	−295.498	+	214.692i	−0.601830	+	0.437255i	−0.846528	−	0.532344i	$-0.821311\pi$
$491$	−295.498	+	214.692i	−0.601830	+	0.437255i	0.244698	+	0.969599i	$0.421311\pi$
$492$	−176.471	−	346.343i	−0.358680	−	0.703950i
$493$	21.2570	+	21.2570i	0.0431177	+	0.0431177i
$494$	371.047	+	120.561i	0.751108	+	0.244050i
$495$	94.6975	+	200.137i	0.191308	+	0.404317i
$496$	56.4881	+	173.852i	0.113887	+	0.350509i
$497$	−371.411	−	189.243i	−0.747305	−	0.380771i
$498$	−27.1634	−	171.503i	−0.0545450	−	0.344384i
$499$			94.7720i			0.189924i	0.995481	+	0.0949619i	$0.0302729\pi$
$499$			94.7720i			0.189924i	−0.995481	+	0.0949619i	$0.969727\pi$
$500$	17.2886	+	249.401i	0.0345773	+	0.498803i
$501$	15.0842			0.0301082
$502$	489.885	−	77.5901i	0.975866	−	0.154562i
$503$	−98.1083	+	192.548i	−0.195046	+	0.382800i	−0.967729	−	0.251992i	$-0.918914\pi$
$503$	−98.1083	+	192.548i	−0.195046	+	0.382800i	0.772683	+	0.634792i	$0.218914\pi$
$504$	26.5654	−	8.63162i	0.0527091	−	0.0171262i
$505$	112.756	−	53.3521i	0.223280	−	0.105648i
$506$	66.9441	−	206.033i	0.132301	−	0.407179i
$507$	−237.548	+	237.548i	−0.468536	+	0.468536i
$508$	303.483	−	154.632i	0.597407	−	0.304394i
$509$	83.6706	+	115.163i	0.164382	+	0.226253i	0.883260	−	0.468884i	$-0.155344\pi$
$509$	83.6706	+	115.163i	0.164382	+	0.226253i	−0.718877	+	0.695137i	$0.755344\pi$
$510$	215.237	−	146.945i	0.422033	−	0.288127i
$511$	−251.205	−	182.511i	−0.491595	−	0.357165i
$512$	3.53971	−	22.3488i	0.00691349	−	0.0436501i
$513$	−711.198	−	112.643i	−1.38635	−	0.219576i
$514$	−412.824	+	568.204i	−0.803160	+	1.10545i
$515$	14.7068	−	501.966i	0.0285568	−	0.974691i
$516$	−46.6994	+	33.9291i	−0.0905028	+	0.0657541i
$517$	197.193	+	387.013i	0.381417	+	0.748574i
$518$	218.071	+	218.071i	0.420986	+	0.420986i
$519$	−993.769	−	322.895i	−1.91478	−	0.622149i
$520$	86.2225	−	81.3140i	0.165813	−	0.156373i
$521$	38.0795	+	117.197i	0.0730892	+	0.224945i	0.980927	−	0.194376i	$-0.0622681\pi$
$521$	38.0795	+	117.197i	0.0730892	+	0.224945i	−0.907838	+	0.419321i	$0.862268\pi$
$522$	8.98061	+	4.57585i	0.0172042	+	0.00876599i
$523$	0.194623	+	1.22880i	0.000372128	+	0.00234952i	0.987874	−	0.155260i	$-0.0496214\pi$
$523$	0.194623	+	1.22880i	0.000372128	+	0.00234952i	−0.987502	+	0.157609i	$0.949621\pi$
$524$			7.92092i			0.0151163i
$525$	304.439	+	119.041i	0.579883	+	0.226745i
$526$	−117.660			−0.223688
$527$	489.102	−	77.4662i	0.928088	−	0.146995i
$528$	106.469	−	208.957i	0.201646	−	0.395753i
$529$	427.999	−	139.065i	0.809072	−	0.262883i
$530$	−27.0791	−	210.749i	−0.0510926	−	0.397639i
$531$	51.7718	−	159.337i	0.0974986	−	0.300070i
$532$	178.964	−	178.964i	0.336398	−	0.336398i
$533$	−426.673	+	217.401i	−0.800513	+	0.407882i
$534$	−277.966	−	382.587i	−0.520535	−	0.716455i
$535$	−54.4624	+	152.290i	−0.101799	+	0.284654i
$536$	−87.3055	−	63.4312i	−0.162883	−	0.118342i
$537$	−23.4365	+	147.973i	−0.0436435	+	0.275554i
$538$	314.666	+	49.8383i	0.584882	+	0.0926362i
$539$	−346.732	+	477.236i	−0.643288	+	0.885410i
$540$	−133.700	+	173.123i	−0.247592	+	0.320598i
$541$	−363.946	+	264.422i	−0.672729	+	0.488766i	−0.870938	−	0.491394i	$-0.836488\pi$
$541$	−363.946	+	264.422i	−0.672729	+	0.488766i	0.198209	+	0.980160i	$0.436488\pi$
$542$	−225.492	−	442.553i	−0.416037	−	0.816519i
$543$	−620.367	−	620.367i	−1.14248	−	1.14248i
$544$	−58.2971	−	18.9419i	−0.107164	−	0.0348196i
$545$	63.1458	+	34.5401i	0.115864	+	0.0633763i
$546$	−47.8870	−	147.381i	−0.0877052	−	0.269929i
$547$	−457.733	−	233.226i	−0.836806	−	0.426374i	−0.0175802	−	0.999845i	$-0.505596\pi$
$547$	−457.733	−	233.226i	−0.836806	−	0.426374i	−0.819225	+	0.573472i	$0.805596\pi$
$548$	66.5158	+	419.964i	0.121379	+	0.766358i
$549$			216.708i			0.394732i
$550$	558.274	−	244.410i	1.01504	−	0.444383i
$551$	91.3260			0.165746
$552$	−84.4417	+	13.3743i	−0.152974	+	0.0242287i
$553$	−71.8035	+	140.922i	−0.129844	+	0.254832i
$554$	−430.514	+	139.883i	−0.777102	+	0.252496i
$555$	948.026	+	178.758i	1.70816	+	0.322086i
$556$	18.9520	−	58.3284i	0.0340864	−	0.104907i
$557$	498.053	−	498.053i	0.894171	−	0.894171i	−0.100742	−	0.994913i	$-0.532122\pi$
$557$	498.053	−	498.053i	0.894171	−	0.894171i	0.994913	+	0.100742i	$0.0321215\pi$
$558$	147.934	−	75.3761i	0.265115	−	0.135083i
$559$	41.7986	+	57.5308i	0.0747738	+	0.102917i
$560$	−21.6069	−	73.7857i	−0.0385838	−	0.131760i
$561$	−513.973	−	373.423i	−0.916173	−	0.665638i
$562$	20.6917	−	130.642i	0.0368180	−	0.232460i
$563$	918.854	+	145.532i	1.63207	+	0.258494i	0.904164	−	0.427185i	$-0.140495\pi$
$563$	918.854	+	145.532i	1.63207	+	0.258494i	0.727904	+	0.685679i	$0.240495\pi$
$564$	100.756	−	138.678i	0.178645	−	0.245884i
$565$	994.119	−	291.111i	1.75950	−	0.515241i
$566$	39.0937	−	28.4033i	0.0690702	−	0.0501824i
$567$	170.197	+	334.031i	0.300172	+	0.589120i
$568$	216.868	+	216.868i	0.381810	+	0.381810i
$569$	829.779	+	269.612i	1.45831	+	0.473834i	0.927554	−	0.373690i	$-0.121908\pi$
$569$	829.779	+	269.612i	1.45831	+	0.473834i	0.530757	+	0.847524i	$0.321908\pi$
$570$	146.701	−	778.015i	0.257370	−	1.36494i
$571$	43.0384	+	132.459i	0.0753737	+	0.231977i	0.981644	−	0.190722i	$-0.0610829\pi$
$571$	43.0384	+	132.459i	0.0753737	+	0.231977i	−0.906270	+	0.422699i	$0.861083\pi$
$572$	−257.423	−	131.163i	−0.450040	−	0.229307i
$573$	67.0097	+	423.082i	0.116945	+	0.738364i
$574$			310.650i			0.541202i
$575$	−191.710	−	112.280i	−0.333409	−	0.195269i
$576$	−20.5517			−0.0356800
$577$	454.188	−	71.9363i	0.787154	−	0.124673i	0.250099	−	0.968220i	$-0.419537\pi$
$577$	454.188	−	71.9363i	0.787154	−	0.124673i	0.537055	+	0.843547i	$0.319537\pi$
$578$	110.163	−	216.207i	0.190594	−	0.374061i
$579$	728.159	−	236.593i	1.25761	−	0.408624i
$580$	13.3135	−	24.3397i	0.0229544	−	0.0419650i
$581$	−42.8824	+	131.979i	−0.0738080	+	0.227158i
$582$	−277.965	+	277.965i	−0.477604	+	0.477604i
$583$	−461.516	+	235.154i	−0.791622	+	0.403352i
$584$	134.285	+	184.827i	0.229940	+	0.316485i
$585$	−85.1962	−	65.7953i	−0.145635	−	0.112471i
$586$	186.497	+	135.498i	0.318255	+	0.231226i
$587$	−35.6617	+	225.159i	−0.0607524	+	0.383576i	0.938513	+	0.345245i	$0.112204\pi$
$587$	−35.6617	+	225.159i	−0.0607524	+	0.383576i	−0.999265	+	0.0383309i	$0.987796\pi$
$588$	229.934	+	36.4179i	0.391044	+	0.0619353i
$589$	884.250	−	1217.07i	1.50127	−	2.06633i
$590$	−434.214	−	155.285i	−0.735956	−	0.263194i
$591$	171.025	−	124.257i	0.289383	−	0.210249i
$592$	−103.014	−	202.176i	−0.174010	−	0.341514i
$593$	274.055	+	274.055i	0.462150	+	0.462150i	0.899360	−	0.437210i	$-0.144033\pi$
$593$	274.055	+	274.055i	0.462150	+	0.462150i	−0.437210	+	0.899360i	$0.644033\pi$
$594$	507.130	+	164.777i	0.853755	+	0.277402i
$595$	−206.580	+	26.5434i	−0.347192	+	0.0446107i
$596$	−10.9628	−	33.7401i	−0.0183940	−	0.0566109i
$597$	416.950	+	212.447i	0.698408	+	0.355857i
$598$	16.4763	+	104.027i	0.0275523	+	0.173958i
$599$		−	995.730i		−	1.66232i	−0.556033	−	0.831160i	$-0.687677\pi$
$599$		−	995.730i		−	1.66232i	0.556033	−	0.831160i	$-0.312323\pi$
$600$	−185.966	−	152.517i	−0.309943	−	0.254195i
$601$	−814.641			−1.35548			−0.677738	−	0.735303i	$-0.737040\pi$
$601$	−814.641			−1.35548			−0.677738	+	0.735303i	$0.737040\pi$
$602$	45.5637	−	7.21659i	0.0756873	−	0.0119877i
$603$	−44.4983	+	87.3328i	−0.0737949	+	0.144831i
$604$	156.926	−	50.9883i	0.259811	−	0.0844177i
$605$	−604.194	−	640.666i	−0.998668	−	1.05895i
$606$	−37.0839	+	114.132i	−0.0611945	+	0.188337i
$607$	−767.174	+	767.174i	−1.26388	+	1.26388i	−0.314680	+	0.949198i	$0.601897\pi$
$607$	−767.174	+	767.174i	−1.26388	+	1.26388i	−0.949198	+	0.314680i	$0.898103\pi$
$608$	−165.920	+	84.5403i	−0.272894	+	0.139047i
$609$	−21.3219	−	29.3471i	−0.0350113	−	0.0481889i
$610$	596.233	+	17.4686i	0.977431	+	0.0286371i
$611$	−170.843	−	124.125i	−0.279613	−	0.203150i
$612$	−8.70935	+	54.9886i	−0.0142310	+	0.0898507i
$613$	−1067.95	−	169.147i	−1.74217	−	0.275933i	−0.797349	−	0.603519i	$-0.793765\pi$
$613$	−1067.95	−	169.147i	−1.74217	−	0.275933i	−0.944821	+	0.327587i	$0.893765\pi$
$614$	−427.819	+	588.842i	−0.696774	+	0.959027i
$615$	547.926	+	802.574i	0.890937	+	1.30500i
$616$	−151.628	+	110.164i	−0.246150	+	0.178838i
$617$	241.065	+	473.116i	0.390704	+	0.766800i	0.999651	−	0.0264106i	$-0.00840774\pi$
$617$	241.065	+	473.116i	0.390704	+	0.766800i	−0.608947	+	0.793211i	$0.708408\pi$
$618$	341.615	+	341.615i	0.552776	+	0.552776i
$619$	−694.267	−	225.581i	−1.12159	−	0.364428i	−0.311219	−	0.950338i	$-0.600737\pi$
$619$	−694.267	−	225.581i	−1.12159	−	0.364428i	−0.810376	+	0.585910i	$0.800737\pi$
$620$	−195.459	−	413.090i	−0.315256	−	0.666274i
$621$	−60.0697	−	184.876i	−0.0967307	−	0.297706i
$622$	−82.1031	−	41.8336i	−0.131999	−	0.0672567i
$623$	59.1222	+	373.283i	0.0948992	+	0.599170i
$624$			114.018i			0.182721i
$625$	−122.330	−	612.911i	−0.195728	−	0.980658i
$626$	−114.449			−0.182826
$627$	−1906.25	+	301.920i	−3.04027	+	0.481531i
$628$	63.5475	−	124.719i	0.101190	−	0.198597i
$629$	−584.603	+	189.949i	−0.929417	+	0.301986i
$630$	−63.1219	+	29.8670i	−0.100193	+	0.0474079i
$631$	232.185	−	714.593i	0.367964	−	1.13248i	−0.580140	−	0.814517i	$-0.697002\pi$
$631$	232.185	−	714.593i	0.367964	−	1.13248i	0.948104	−	0.317960i	$-0.102998\pi$
$632$	82.2852	−	82.2852i	0.130198	−	0.130198i
$633$	−560.427	+	285.552i	−0.885351	+	0.451109i
$634$	−225.255	−	310.037i	−0.355292	−	0.489018i
$635$	−703.254	+	480.120i	−1.10749	+	0.756094i
$636$	165.375	+	120.152i	0.260024	+	0.188919i
$637$	44.8646	−	283.264i	0.0704311	−	0.444685i
$638$	−66.7970	−	10.5796i	−0.104698	−	0.0165825i
$639$	163.735	−	225.362i	0.256237	−	0.352680i
$640$	−1.65665	+	56.5443i	−0.00258852	+	0.0883504i
$641$	363.902	−	264.390i	0.567710	−	0.412466i	−0.266563	−	0.963818i	$-0.585888\pi$
$641$	363.902	−	264.390i	0.567710	−	0.412466i	0.834273	+	0.551352i	$0.185888\pi$
$642$	−70.6390	−	138.637i	−0.110030	−	0.215945i
$643$	554.876	+	554.876i	0.862949	+	0.862949i	0.991680	−	0.128731i	$-0.0410903\pi$
$643$	554.876	+	554.876i	0.862949	+	0.862949i	−0.128731	+	0.991680i	$0.541090\pi$
$644$	64.9814	+	21.1137i	0.100903	+	0.0327853i
$645$	104.987	−	99.0099i	0.162770	−	0.153504i
$646$	155.885	+	479.766i	0.241308	+	0.742671i
$647$	207.914	+	105.937i	0.321351	+	0.163736i	0.607223	−	0.794531i	$-0.292283\pi$
$647$	207.914	+	105.937i	0.321351	+	0.163736i	−0.285873	+	0.958268i	$0.592283\pi$
$648$	−43.1495	−	272.435i	−0.0665888	−	0.420425i
$649$			1124.15i			1.73212i
$650$	−187.892	+	229.098i	−0.289064	+	0.352459i
$651$	−597.543			−0.917884
$652$	−144.983	+	22.9631i	−0.222367	+	0.0352194i
$653$	296.217	−	581.359i	0.453625	−	0.890290i	−0.545028	−	0.838418i	$-0.683481\pi$
$653$	296.217	−	581.359i	0.453625	−	0.890290i	0.998654	−	0.0518724i	$-0.0165189\pi$
$654$	−65.8538	+	21.3972i	−0.100694	+	0.0327174i
$655$	−2.52365	−	19.6408i	−0.00385290	−	0.0299860i
$656$	70.6303	−	217.378i	0.107668	−	0.331369i
$657$	146.726	−	146.726i	0.223327	−	0.223327i
$658$	−122.061	+	62.1933i	−0.185503	+	0.0945187i
$659$	652.592	+	898.216i	0.990276	+	1.36300i	0.931105	+	0.364750i	$0.118846\pi$
$659$	652.592	+	898.216i	0.990276	+	1.36300i	0.0591706	+	0.998248i	$0.481154\pi$
$660$	−197.428	+	552.056i	−0.299133	+	0.836448i
$661$	889.686	+	646.395i	1.34597	+	0.977904i	0.999202	+	0.0399532i	$0.0127209\pi$
$661$	889.686	+	646.395i	1.34597	+	0.977904i	0.346768	+	0.937951i	$0.387279\pi$
$662$	−80.2156	+	506.461i	−0.121172	+	0.765048i
$663$	305.069	+	48.3182i	0.460135	+	0.0728782i
$664$	60.0141	−	82.6023i	0.0903827	−	0.124401i
$665$	−386.742	+	500.780i	−0.581567	+	0.753052i
$666$	−166.732	+	121.138i	−0.250349	+	0.181889i
$667$	11.1929	+	21.9674i	0.0167810	+	0.0329346i
$668$	6.27178	+	6.27178i	0.00938890	+	0.00938890i
$669$	916.117	+	297.664i	1.36938	+	0.444939i
$670$	236.694	+	129.469i	0.353274	+	0.193237i
$671$	−449.334	−	1382.91i	−0.669649	−	2.06097i
$672$	65.9038	+	33.5797i	0.0980712	+	0.0499697i
$673$	−90.6315	−	572.224i	−0.134668	−	0.850259i	−0.958846	−	0.283928i	$-0.908362\pi$
$673$	−90.6315	−	572.224i	−0.134668	−	0.850259i	0.824178	−	0.566331i	$-0.191638\pi$
$674$		−	250.194i		−	0.371208i
$675$	276.365	−	471.876i	0.409430	−	0.699076i
$676$	−197.537			−0.292215
$677$	−42.6461	+	6.75448i	−0.0629928	+	0.00997708i	−0.187851	−	0.982197i	$-0.560152\pi$
$677$	−42.6461	+	6.75448i	−0.0629928	+	0.00997708i	0.124858	+	0.992175i	$0.460152\pi$
$678$	−452.421	+	887.925i	−0.667287	+	1.30962i
$679$	298.784	−	97.0808i	0.440035	−	0.142976i
$680$	150.589	+	28.3948i	0.221455	+	0.0417570i
$681$	−92.4902	+	284.656i	−0.135815	+	0.417996i
$682$	−787.742	+	787.742i	−1.15505	+	1.15505i
$683$	831.566	−	423.704i	1.21752	−	0.620357i	0.277253	−	0.960797i	$-0.410576\pi$
$683$	831.566	−	423.704i	1.21752	−	0.620357i	0.940266	+	0.340440i	$0.110576\pi$
$684$	99.4142	+	136.832i	0.145342	+	0.200047i
$685$	−298.736	−	1020.16i	−0.436111	−	1.48928i
$686$	−366.031	−	265.937i	−0.533574	−	0.387664i
$687$	−0.860862	+	5.43527i	−0.00125307	+	0.00791159i
$688$	−33.5241	−	5.30969i	−0.0487269	−	0.00771758i
$689$	148.020	−	203.732i	0.214833	−	0.295692i
$690$	205.122	−	60.0666i	0.297278	−	0.0870531i
$691$	880.749	−	639.902i	1.27460	−	0.926052i	0.275225	−	0.961380i	$-0.411248\pi$
$691$	880.749	−	639.902i	1.27460	−	0.926052i	0.999376	+	0.0353282i	$0.0112476\pi$
$692$	−278.939	−	547.448i	−0.403091	−	0.791110i
$693$	120.370	+	120.370i	0.173695	+	0.173695i
$694$	−290.580	−	94.4152i	−0.418703	−	0.136045i
$695$	−28.4100	+	150.670i	−0.0408777	+	0.216792i
$696$	8.24759	+	25.3835i	0.0118500	+	0.0364705i
$697$	−551.690	−	281.100i	−0.791521	−	0.403300i
$698$	−40.3376	−	254.682i	−0.0577903	−	0.364873i
$699$			262.487i			0.375517i
$700$	77.0854	+	176.076i	0.110122	+	0.251537i
$701$	93.0109			0.132683			0.0663416	−	0.997797i	$-0.478867\pi$
$701$	93.0109			0.132683			0.0663416	+	0.997797i	$0.478867\pi$
$702$	−256.053	+	40.5547i	−0.364747	+	0.0577703i
$703$	−847.771	+	1663.84i	−1.20593	+	2.36678i
$704$	131.149	−	42.6130i	0.186292	−	0.0605298i
$705$	−205.652	+	375.971i	−0.291705	+	0.533292i
$706$	55.5188	−	170.869i	0.0786385	−	0.242024i
$707$	67.8162	−	67.8162i	0.0959210	−	0.0959210i
$708$	395.286	−	201.408i	0.558313	−	0.284475i
$709$	−512.727	−	705.708i	−0.723169	−	0.995357i	−0.999413	−	0.0342694i	$-0.989090\pi$
$709$	−512.727	−	705.708i	−0.723169	−	0.995357i	0.276243	−	0.961088i	$-0.410910\pi$
$710$	−606.845	−	468.654i	−0.854711	−	0.660077i
$711$	−85.5080	−	62.1252i	−0.120264	−	0.0873772i
$712$	43.4999	−	274.647i	0.0610953	−	0.385741i
$713$	401.125	+	63.5319i	0.562587	+	0.0891050i
$714$	117.775	−	162.104i	0.164951	−	0.227036i
$715$	680.098	+	243.218i	0.951186	+	0.340166i
$716$	−71.2692	+	51.7801i	−0.0995379	+	0.0723185i
$717$	−15.4838	−	30.3886i	−0.0215952	−	0.0423831i
$718$	−236.233	−	236.233i	−0.329015	−	0.329015i
$719$	924.330	+	300.333i	1.28558	+	0.417709i	0.870541	−	0.492096i	$-0.163769\pi$
$719$	924.330	+	300.333i	1.28558	+	0.417709i	0.415036	+	0.909805i	$0.363769\pi$
$720$	50.9603	−	6.54788i	0.0707782	−	0.00909428i
$721$	−119.311	−	367.201i	−0.165480	−	0.509294i
$722$	910.577	+	463.962i	1.26119	+	0.642607i
$723$	−113.419	−	716.097i	−0.156872	−	0.990452i
$724$		−	515.877i		−	0.712538i
$725$	−25.2577	+	64.5948i	−0.0348382	+	0.0890963i
$726$	847.197			1.16694
$727$	613.184	−	97.1188i	0.843444	−	0.133588i	0.280264	−	0.959923i	$-0.409578\pi$
$727$	613.184	−	97.1188i	0.843444	−	0.133588i	0.563180	+	0.826334i	$0.309578\pi$
$728$	41.3681	−	81.1894i	0.0568243	−	0.111524i
$729$	398.565	−	129.502i	0.546728	−	0.177643i
$730$	−391.862	−	415.517i	−0.536797	−	0.569201i
$731$	−28.4135	+	87.4478i	−0.0388694	+	0.119628i
$732$	−405.770	+	405.770i	−0.554330	+	0.554330i
$733$	15.0875	−	7.68746i	0.0205832	−	0.0104877i	−0.443669	−	0.896191i	$-0.646323\pi$
$733$	15.0875	−	7.68746i	0.0205832	−	0.0104877i	0.464252	+	0.885703i	$0.346323\pi$
$734$	−107.349	−	147.754i	−0.146252	−	0.201299i
$735$	−581.750	−	17.0443i	−0.791497	−	0.0231895i
$736$	−40.6703	−	29.5487i	−0.0552586	−	0.0401477i
$737$	102.882	−	649.574i	0.139596	−	0.881376i
$738$	−205.041	−	32.4754i	−0.277834	−	0.0440045i
$739$	98.2185	−	135.186i	0.132907	−	0.182931i	−0.737376	−	0.675482i	$-0.763935\pi$
$739$	98.2185	−	135.186i	0.132907	−	0.182931i	0.870284	+	0.492551i	$0.163935\pi$
$740$	319.850	+	468.499i	0.432229	+	0.633106i
$741$	759.124	−	551.536i	1.02446	−	0.744313i
$742$	−74.1660	−	145.559i	−0.0999542	−	0.196171i
$743$	691.071	+	691.071i	0.930108	+	0.930108i	0.997712	−	0.0676038i	$-0.0215354\pi$
$743$	691.071	+	691.071i	0.930108	+	0.930108i	−0.0676038	+	0.997712i	$0.521535\pi$
$744$	418.131	+	135.859i	0.562005	+	0.182606i
$745$	37.9334	+	80.1697i	0.0509173	+	0.107610i
$746$	220.654	+	679.102i	0.295782	+	0.910324i
$747$	−82.6282	−	42.1012i	−0.110613	−	0.0563603i
$748$	−58.4383	−	368.965i	−0.0781261	−	0.493269i
$749$			124.349i			0.166020i
$750$	509.717	+	318.934i	0.679622	+	0.425245i
$751$	−958.191			−1.27589			−0.637944	−	0.770083i	$-0.720215\pi$
$751$	−958.191			−1.27589			−0.637944	+	0.770083i	$0.720215\pi$
$752$	99.5530	−	15.7676i	0.132384	−	0.0209676i
$753$	541.568	−	1062.89i	0.719214	−	1.41154i
$754$	31.2708	−	10.1605i	0.0414733	−	0.0134755i
$755$	−372.870	+	176.429i	−0.493868	+	0.233680i
$756$	−51.9695	+	159.946i	−0.0687427	+	0.211568i
$757$	105.145	−	105.145i	0.138896	−	0.138896i	−0.634240	−	0.773136i	$-0.718687\pi$
$757$	105.145	−	105.145i	0.138896	−	0.138896i	0.773136	+	0.634240i	$0.218687\pi$
$758$	−118.955	+	60.6107i	−0.156933	+	0.0799614i
$759$	−306.253	−	421.522i	−0.403496	−	0.555364i
$760$	384.482	−	262.490i	0.505897	−	0.345382i
$761$	−555.664	−	403.713i	−0.730176	−	0.530504i	0.159443	−	0.987207i	$-0.449030\pi$
$761$	−555.664	−	403.713i	−0.730176	−	0.530504i	−0.889619	+	0.456703i	$0.849030\pi$
$762$	128.150	−	809.106i	0.168176	−	1.06182i
$763$	54.6562	+	8.65670i	0.0716333	+	0.0113456i
$764$	−148.049	+	203.772i	−0.193782	+	0.266718i
$765$	4.07615	−	139.126i	0.00532829	−	0.181863i
$766$	418.116	−	303.779i	0.545843	−	0.396578i
$767$	−248.122	−	486.967i	−0.323497	−	0.634899i
$768$	−38.4815	−	38.4815i	−0.0501061	−	0.0501061i
$769$	−1224.25	−	397.783i	−1.59200	−	0.517273i	−0.626889	−	0.779109i	$-0.715672\pi$
$769$	−1224.25	−	397.783i	−1.59200	−	0.517273i	−0.965112	+	0.261836i	$0.915672\pi$
$770$	340.881	−	321.475i	0.442702	−	0.417500i
$771$	521.988	+	1606.52i	0.677028	+	2.08368i
$772$	401.128	+	204.385i	0.519596	+	0.264748i
$773$	−72.9454	−	460.559i	−0.0943666	−	0.595808i	−0.988874	−	0.148755i	$-0.952474\pi$
$773$	−72.9454	−	460.559i	−0.0943666	−	0.595808i	0.894508	−	0.447053i	$-0.147526\pi$
$774$			30.8283i			0.0398298i
$775$	616.276	+	962.029i	0.795194	+	1.24133i
$776$	−231.147			−0.297870
$777$	732.595	−	116.032i	0.942851	−	0.149333i
$778$	−109.939	+	215.767i	−0.141309	+	0.277335i
$779$	−1788.95	+	581.264i	−2.29647	+	0.746167i
$780$	−36.3267	−	282.721i	−0.0465727	−	0.362462i
$781$	−577.588	+	1777.63i	−0.739549	+	2.27610i
$782$	−96.2965	+	96.2965i	−0.123141	+	0.123141i
$783$	−54.0706	+	27.5504i	−0.0690557	+	0.0351857i
$784$	80.4608	+	110.745i	0.102629	+	0.141256i
$785$	−117.837	+	329.501i	−0.150111	+	0.419747i
$786$	15.4122	+	11.1976i	0.0196084	+	0.0142464i
$787$	22.5670	−	142.483i	0.0286748	−	0.181045i	−0.969194	−	0.246299i	$-0.920786\pi$
$787$	22.5670	−	142.483i	0.0286748	−	0.181045i	0.997869	+	0.0652534i	$0.0207856\pi$
$788$	122.774	+	19.4454i	0.155804	+	0.0246770i
$789$	−166.333	+	228.938i	−0.210815	+	0.290162i
$790$	−177.819	+	230.252i	−0.225087	+	0.291458i
$791$	644.315	−	468.123i	0.814558	−	0.591811i
$792$	−56.8616	−	111.597i	−0.0717950	−	0.140906i
$793$	499.883	+	499.883i	0.630369	+	0.630369i
$794$	−256.785	−	83.4346i	−0.323407	−	0.105081i
$795$	−448.348	−	245.242i	−0.563960	−	0.308480i
$796$	85.0292	+	261.693i	0.106821	+	0.328760i
$797$	1020.72	+	520.082i	1.28070	+	0.652549i	0.956027	−	0.293277i	$-0.0947459\pi$
$797$	1020.72	+	520.082i	1.28070	+	0.652549i	0.324673	+	0.945826i	$0.394746\pi$
$798$	−95.2235	−	601.218i	−0.119328	−	0.753406i
$799$		−	273.049i		−	0.341738i
$800$	−13.9075	−	140.736i	−0.0173843	−	0.175920i
$801$	−252.562			−0.315309
$802$	113.495	−	17.9759i	0.141515	−	0.0224138i
$803$	−632.092	+	1240.55i	−0.787163	+	1.54489i
$804$	−246.844	+	80.2045i	−0.307020	+	0.0997568i
$805$	−167.856	−	31.6505i	−0.208516	−	0.0393174i
$806$	167.370	−	515.112i	0.207655	−	0.639097i
$807$	541.811	−	541.811i	0.671389	−	0.671389i
$808$	−62.8733	+	32.0356i	−0.0778135	+	0.0396480i
$809$	−366.674	−	504.683i	−0.453243	−	0.623836i	0.519847	−	0.854259i	$-0.325989\pi$
$809$	−366.674	−	504.683i	−0.453243	−	0.623836i	−0.973090	+	0.230423i	$0.925989\pi$
$810$	193.794	+	661.787i	0.239251	+	0.817021i
$811$	325.346	+	236.378i	0.401166	+	0.291464i	0.770016	−	0.638025i	$-0.220248\pi$
$811$	325.346	+	236.378i	0.401166	+	0.291464i	−0.368850	+	0.929489i	$0.620248\pi$
$812$	3.33674	−	21.0673i	0.00410928	−	0.0259450i
$813$	−1179.88	−	186.874i	−1.45126	−	0.229857i
$814$	812.818	−	1118.75i	0.998547	−	1.37438i
$815$	352.186	−	103.132i	0.432130	−	0.126542i
$816$	−119.270	+	86.6545i	−0.146164	+	0.106194i
$817$	126.814	+	248.886i	0.155219	+	0.304634i
$818$	242.577	+	242.577i	0.296548	+	0.296548i
$819$	−78.7113	−	25.5749i	−0.0961066	−	0.0312269i
$820$	−105.878	+	561.516i	−0.129120	+	0.684776i
$821$	202.953	+	624.625i	0.247202	+	0.760810i	0.995266	+	0.0971839i	$0.0309835\pi$
$821$	202.953	+	624.625i	0.247202	+	0.760810i	−0.748064	+	0.663626i	$0.769016\pi$
$822$	911.182	+	464.270i	1.10849	+	0.564806i
$823$	−217.260	−	1371.72i	−0.263985	−	1.66674i	−0.662111	−	0.749406i	$-0.730339\pi$
$823$	−217.260	−	1371.72i	−0.263985	−	1.66674i	0.398126	−	0.917331i	$-0.369661\pi$
$824$			284.077i			0.344753i
$825$	313.656	−	1431.79i	0.380190	−	1.73550i
$826$	−354.548			−0.429235
$827$	−788.480	+	124.883i	−0.953423	+	0.151007i	−0.613718	−	0.789525i	$-0.710327\pi$
$827$	−788.480	+	124.883i	−0.953423	+	0.151007i	−0.339704	+	0.940532i	$0.610327\pi$
$828$	−20.7291	+	40.6831i	−0.0250351	+	0.0491341i
$829$	−1412.70	+	459.014i	−1.70410	+	0.553696i	−0.989334	−	0.145667i	$-0.953467\pi$
$829$	−1412.70	+	459.014i	−1.70410	+	0.553696i	−0.714767	+	0.699363i	$0.753467\pi$
$830$	−122.494	+	223.943i	−0.147584	+	0.269811i
$831$	−336.431	+	1035.43i	−0.404851	+	1.24600i
$832$	−47.4068	+	47.4068i	−0.0569794	+	0.0569794i
$833$	330.409	−	168.352i	0.396650	−	0.202103i
$834$	−86.7011	−	119.334i	−0.103958	−	0.143086i
$835$	−17.5498	−	13.5534i	−0.0210178	−	0.0162316i
$836$	−918.121	−	667.054i	−1.09823	−	0.797911i
$837$	−156.378	+	987.331i	−0.186831	+	1.17961i
$838$	−460.485	−	72.9336i	−0.549504	−	0.0870329i
$839$	−720.904	+	992.239i	−0.859241	+	1.18264i	0.122508	+	0.992467i	$0.460906\pi$
$839$	−720.904	+	992.239i	−0.859241	+	1.18264i	−0.981750	+	0.190177i	$0.939094\pi$
$840$	−174.115	−	62.2673i	−0.207279	−	0.0741278i
$841$	−674.157	+	489.803i	−0.801613	+	0.582406i
$842$	−72.0435	−	141.393i	−0.0855624	−	0.167926i
$843$	−224.948	−	224.948i	−0.266842	−	0.266842i
$844$	−351.744	−	114.289i	−0.416759	−	0.135413i
$845$	489.816	−	62.9364i	0.579664	−	0.0744809i
$846$	−28.2898	−	87.0669i	−0.0334394	−	0.102916i
$847$	−603.268	−	307.380i	−0.712241	−	0.362905i
$848$	18.8030	+	118.718i	0.0221734	+	0.139997i
$849$		−	116.220i		−	0.136891i
$850$	−382.450	−	22.4296i	−0.449941	−	0.0263877i
$851$	−504.121			−0.592386
$852$	728.556	−	115.392i	0.855113	−	0.135437i
$853$	437.247	−	858.146i	0.512599	−	1.00603i	−0.479137	−	0.877740i	$-0.659050\pi$
$853$	437.247	−	858.146i	0.512599	−	1.00603i	0.991736	−	0.128292i	$-0.0409496\pi$
$854$	436.160	−	141.717i	0.510727	−	0.165945i
$855$	−290.104	−	307.617i	−0.339303	−	0.359785i
$856$	28.2724	−	87.0136i	0.0330285	−	0.101651i
$857$	827.294	−	827.294i	0.965338	−	0.965338i	−0.0340814	−	0.999419i	$-0.510851\pi$
$857$	827.294	−	827.294i	0.965338	−	0.965338i	0.999419	+	0.0340814i	$0.0108506\pi$
$858$	−619.126	+	315.460i	−0.721592	+	0.367669i
$859$	385.955	+	531.221i	0.449307	+	0.618418i	0.972249	−	0.233950i	$-0.0751653\pi$
$859$	385.955	+	531.221i	0.449307	+	0.618418i	−0.522941	+	0.852369i	$0.675165\pi$
$860$	84.8185	+	2.48504i	0.0986262	+	0.00288958i
$861$	604.451	+	439.159i	0.702034	+	0.510057i
$862$	46.6915	−	294.799i	0.0541665	−	0.341994i
$863$	49.3257	+	7.81243i	0.0571561	+	0.00905264i	0.184947	−	0.982748i	$-0.440789\pi$
$863$	49.3257	+	7.81243i	0.0571561	+	0.00905264i	−0.127791	+	0.991801i	$0.540789\pi$
$864$	72.7314	−	100.106i	0.0841799	−	0.115864i
$865$	866.080	+	1268.59i	1.00125	+	1.46658i
$866$	74.5178	−	54.1403i	0.0860483	−	0.0625177i
$867$	−264.953	−	519.999i	−0.305597	−	0.599768i
$868$	−248.449	−	248.449i	−0.286231	−	0.286231i
$869$	674.478	+	219.151i	0.776154	+	0.252188i
$870$	−28.5381	−	60.3135i	−0.0328025	−	0.0693258i
$871$	98.8069	+	304.096i	0.113441	+	0.349135i
$872$	−36.2776	−	18.4843i	−0.0416027	−	0.0211976i
$873$	32.8423	+	207.358i	0.0376201	+	0.237524i
$874$			413.716i			0.473359i
$875$	−247.241	−	412.041i	−0.282561	−	0.470904i
$876$	549.466			0.627244
$877$	−696.793	+	110.361i	−0.794518	+	0.125839i	−0.540482	−	0.841355i	$-0.681758\pi$
$877$	−696.793	+	110.361i	−0.794518	+	0.125839i	−0.254036	+	0.967195i	$0.581758\pi$
$878$	459.011	−	900.859i	0.522791	−	1.02604i
$879$	527.295	−	171.328i	0.599880	−	0.194913i
$880$	−311.623	+	147.449i	−0.354117	+	0.167555i
$881$	83.4556	−	256.850i	0.0947282	−	0.291544i	−0.892455	−	0.451137i	$-0.851018\pi$
$881$	83.4556	−	256.850i	0.0947282	−	0.291544i	0.987183	+	0.159594i	$0.0510184\pi$
$882$	87.9151	−	87.9151i	0.0996769	−	0.0996769i
$883$	730.774	−	372.348i	0.827603	−	0.421685i	0.0117409	−	0.999931i	$-0.496263\pi$
$883$	730.774	−	372.348i	0.827603	−	0.421685i	0.815862	+	0.578246i	$0.196263\pi$
$884$	106.753	+	146.933i	0.120761	+	0.166214i
$885$	−915.986	+	625.355i	−1.03501	+	0.706615i
$886$	−645.469	−	468.960i	−0.728520	−	0.529301i
$887$	−82.5838	+	521.413i	−0.0931046	+	0.587839i	0.896390	+	0.443267i	$0.146181\pi$
$887$	−82.5838	+	521.413i	−0.0931046	+	0.587839i	−0.989494	+	0.144572i	$0.953819\pi$
$888$	−539.016	−	85.3717i	−0.607000	−	0.0961394i
$889$	−384.813	+	529.649i	−0.432860	+	0.595781i
$890$	−20.3588	+	694.879i	−0.0228751	+	0.780763i
$891$	1359.96	−	988.069i	1.52633	−	1.10894i
$892$	257.143	+	504.671i	0.288277	+	0.565775i
$893$	−586.545	−	586.545i	−0.656826	−	0.656826i
$894$	−81.1482	−	26.3666i	−0.0907698	−	0.0294929i
$895$	160.223	−	151.101i	0.179020	−	0.168828i
$896$	13.4399	+	41.3636i	0.0149998	+	0.0461648i
$897$	225.704	+	115.002i	0.251621	+	0.128207i
$898$	116.027	+	732.565i	0.129206	+	0.815774i
$899$		−	126.785i		−	0.141029i
$900$	−124.276	+	32.4724i	−0.138084	+	0.0360805i
$901$	325.613			0.361390
$902$	1375.79	−	217.904i	1.52527	−	0.241579i
$903$	50.3707	−	98.8581i	0.0557816	−	0.109477i
$904$	−557.295	+	181.076i	−0.616476	+	0.200305i
$905$	164.361	+	1279.18i	0.181615	+	1.41346i
$906$	122.632	−	377.421i	0.135355	−	0.416580i
$907$	−78.0839	+	78.0839i	−0.0860903	+	0.0860903i	−0.748841	−	0.662750i	$-0.769389\pi$
$907$	−78.0839	+	78.0839i	−0.0860903	+	0.0860903i	0.662750	+	0.748841i	$0.269389\pi$
$908$	−156.811	+	79.8993i	−0.172700	+	0.0879948i
$909$	37.6718	+	51.8509i	0.0414432	+	0.0570416i
$910$	−76.7095	+	214.499i	−0.0842961	+	0.235713i
$911$	457.456	+	332.361i	0.502147	+	0.364831i	0.809836	−	0.586656i	$-0.199556\pi$
$911$	457.456	+	332.361i	0.502147	+	0.364831i	−0.307690	+	0.951487i	$0.599556\pi$
$912$	−70.0619	+	442.353i	−0.0768222	+	0.485037i
$913$	614.581	+	97.3401i	0.673145	+	0.106616i
$914$	5.07976	−	6.99169i	0.00555773	−	0.00764956i
$915$	876.872	−	1135.43i	0.958330	−	1.24091i
$916$	−2.61783	+	1.90196i	−0.00285789	+	0.00207638i
$917$	−6.91194	−	13.5654i	−0.00753755	−	0.0147933i
$918$	−237.025	−	237.025i	−0.258197	−	0.258197i
$919$	−791.048	−	257.027i	−0.860771	−	0.279681i	−0.154820	−	0.987943i	$-0.549480\pi$
$919$	−791.048	−	257.027i	−0.860771	−	0.279681i	−0.705950	+	0.708261i	$0.749480\pi$
$920$	110.261	+	60.3117i	0.119849	+	0.0655562i
$921$	540.948	+	1664.87i	0.587349	+	1.80767i
$922$	−438.481	−	223.417i	−0.475575	−	0.242318i
$923$	−142.156	−	897.536i	−0.154015	−	0.972411i
$924$			450.770i			0.487846i
$925$	−942.370	−	1059.79i	−1.01878	−	1.14572i
$926$	413.541			0.446588
$927$	254.840	−	40.3627i	0.274908	−	0.0435412i
$928$	−7.12482	+	13.9833i	−0.00767761	+	0.0150682i
$929$	680.836	−	221.217i	0.732869	−	0.238124i	0.0812754	−	0.996692i	$-0.474101\pi$
$929$	680.836	−	221.217i	0.732869	−	0.238124i	0.651594	+	0.758568i	$0.274101\pi$
$930$	−1080.09	−	203.659i	−1.16139	−	0.218989i
$931$	348.121	−	1071.41i	0.373922	−	1.15081i
$932$	−109.138	+	109.138i	−0.117101	+	0.117101i
$933$	−197.466	+	100.614i	−0.211646	+	0.107839i
$934$	522.103	+	718.613i	0.558997	+	0.769393i
$935$	262.459	+	896.273i	0.280705	+	0.958580i
$936$	49.2636	+	35.7921i	0.0526320	+	0.0382394i
$937$	259.512	−	1638.49i	0.276960	−	1.74866i	−0.320949	−	0.947096i	$-0.604002\pi$
$937$	259.512	−	1638.49i	0.276960	−	1.74866i	0.597910	−	0.801563i	$-0.295998\pi$
$938$	204.871	+	32.4485i	0.218413	+	0.0345932i
$939$	−161.794	+	222.690i	−0.172305	+	0.237157i
$940$	−241.829	+	70.8158i	−0.257265	+	0.0753360i
$941$	928.405	−	674.525i	0.986615	−	0.716818i	0.0274377	−	0.999624i	$-0.491265\pi$
$941$	928.405	−	674.525i	0.986615	−	0.716818i	0.959177	+	0.282806i	$0.0912652\pi$
$942$	−152.838	−	299.961i	−0.162248	−	0.318430i
$943$	−359.070	−	359.070i	−0.380774	−	0.380774i
$944$	248.096	+	80.6112i	0.262813	+	0.0853932i
$945$	77.9047	−	413.161i	0.0824389	−	0.437207i
$946$	−63.9211	−	196.729i	−0.0675699	−	0.207959i
$947$	−768.561	−	391.602i	−0.811575	−	0.413518i	−0.00161156	−	0.999999i	$-0.500513\pi$
$947$	−768.561	−	391.602i	−0.811575	−	0.413518i	−0.809963	+	0.586481i	$0.800513\pi$
$948$	−43.7826	−	276.432i	−0.0461841	−	0.291595i
$949$		−	676.907i		−	0.713285i
$950$	−869.737	+	773.373i	−0.915512	+	0.814077i
$951$	−921.698			−0.969188
$952$	116.369	−	18.4311i	0.122237	−	0.0193604i
$953$	−194.635	+	381.992i	−0.204234	+	0.400831i	−0.970291	−	0.241941i	$-0.922216\pi$
$953$	−194.635	+	381.992i	−0.204234	+	0.400831i	0.766057	+	0.642772i	$0.222216\pi$
$954$	103.828	−	33.7358i	0.108834	−	0.0353625i
$955$	302.182	−	552.447i	0.316421	−	0.578478i
$956$	6.19720	−	19.0730i	0.00648243	−	0.0199509i
$957$	−115.015	+	115.015i	−0.120183	+	0.120183i
$958$	533.634	−	271.900i	0.557029	−	0.283821i
$959$	−480.384	−	661.191i	−0.500922	−	0.689459i
$960$	107.680	+	83.1589i	0.112166	+	0.0866239i
$961$	−912.144	−	662.711i	−0.949161	−	0.689606i
$962$	−105.173	+	664.034i	−0.109327	+	0.690264i
$963$	−82.0755	−	12.9995i	−0.0852289	−	0.0134989i
$964$	250.584	−	344.899i	0.259942	−	0.357779i
$965$	−1059.76	−	378.995i	−1.09820	−	0.392741i
$966$	132.945	−	96.5903i	0.137624	−	0.0999899i
$967$	843.184	+	1654.84i	0.871958	+	1.71131i	0.684461	+	0.729049i	$0.260038\pi$
$967$	843.184	+	1654.84i	0.871958	+	1.71131i	0.187497	+	0.982265i	$0.439962\pi$
$968$	352.251	+	352.251i	0.363895	+	0.363895i
$969$	1153.88	+	374.919i	1.19080	+	0.386913i
$970$	573.156	−	73.6448i	0.590883	−	0.0759224i
$971$	173.464	+	533.869i	0.178645	+	0.549813i	0.999781	−	0.0209193i	$-0.00665931\pi$
$971$	173.464	+	533.869i	0.178645	+	0.549813i	−0.821136	+	0.570733i	$0.806659\pi$
$972$	−240.276	−	122.427i	−0.247198	−	0.125954i
$973$	18.4410	+	116.432i	0.0189527	+	0.119663i
$974$		−	426.478i		−	0.437863i
$975$	180.153	+	689.464i	0.184772	+	0.707143i
$976$	−337.425			−0.345722
$977$	−1039.14	+	164.584i	−1.06361	+	0.168459i	−0.663625	−	0.748065i	$-0.730983\pi$
$977$	−1039.14	+	164.584i	−1.06361	+	0.168459i	−0.399981	+	0.916524i	$0.630983\pi$
$978$	−160.279	+	314.565i	−0.163884	+	0.321641i
$979$	1611.71	−	523.676i	1.64628	−	0.534909i
$980$	−234.796	−	248.969i	−0.239587	−	0.254050i
$981$	−11.4275	+	35.1703i	−0.0116489	+	0.0358515i
$982$	−365.256	+	365.256i	−0.371951	+	0.371951i
$983$	949.807	−	483.951i	0.966233	−	0.492321i	0.101656	−	0.994820i	$-0.467586\pi$
$983$	949.807	−	483.951i	0.966233	−	0.492321i	0.864578	+	0.502499i	$0.167586\pi$
$984$	−323.117	−	444.732i	−0.328371	−	0.451964i
$985$	−310.627	−	9.10085i	−0.315357	−	0.00923944i
$986$	34.3946	+	24.9892i	0.0348830	+	0.0253440i
$987$	−51.5420	+	325.423i	−0.0522209	+	0.329710i
$988$	544.952	+	86.3119i	0.551571	+	0.0873602i
$989$	−44.3242	+	61.0070i	−0.0448172	+	0.0616855i
$990$	176.550	+	258.602i	0.178334	+	0.261214i
$991$	9.79794	−	7.11862i	0.00988692	−	0.00718327i	−0.582831	−	0.812594i	$-0.698055\pi$
$991$	9.79794	−	7.11862i	0.00988692	−	0.00718327i	0.592718	+	0.805410i	$0.298055\pi$
$992$	117.364	+	230.340i	0.118311	+	0.232198i
$993$	872.055	+	872.055i	0.878202	+	0.878202i
$994$	−560.654	−	182.167i	−0.564038	−	0.183267i
$995$	−294.216	−	621.807i	−0.295695	−	0.624932i
$996$	−75.8838	−	233.546i	−0.0761886	−	0.234484i
$997$	−872.430	−	444.525i	−0.875055	−	0.445863i	−0.0420419	−	0.999116i	$-0.513386\pi$
$997$	−872.430	−	444.525i	−0.875055	−	0.445863i	−0.833013	+	0.553253i	$0.813386\pi$
$998$	20.9666	+	132.378i	0.0210086	+	0.132643i
$999$		−	1240.85i		−	1.24209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.b.13.3	✓	24
4.3	odd	2		400.3.bg.b.113.1		24
5.2	odd	4		250.3.f.f.207.1		24
5.3	odd	4		250.3.f.d.207.3		24
5.4	even	2		250.3.f.e.43.1		24
25.2	odd	20	inner	50.3.f.b.27.3	yes	24
25.11	even	5		250.3.f.f.93.1		24
25.14	even	10		250.3.f.d.93.3		24
25.23	odd	20		250.3.f.e.157.1		24
100.27	even	20		400.3.bg.b.177.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.13.3	✓	24	1.1	even	1	trivial
50.3.f.b.27.3	yes	24	25.2	odd	20	inner
250.3.f.d.93.3		24	25.14	even	10
250.3.f.d.207.3		24	5.3	odd	4
250.3.f.e.43.1		24	5.4	even	2
250.3.f.e.157.1		24	25.23	odd	20
250.3.f.f.93.1		24	25.11	even	5
250.3.f.f.207.1		24	5.2	odd	4
400.3.bg.b.113.1		24	4.3	odd	2
400.3.bg.b.177.1		24	100.27	even	20

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39680 - 0.221232i) q^{2} +(1.54417 - 3.03060i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-4.51960 + 2.13851i) q^{5} +(1.48643 - 4.57476i) q^{6} +(-2.71827 + 2.71827i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.51000 - 2.07833i) q^{9} +O(q^{10})\)	\(q+(1.39680 - 0.221232i) q^{2} +(1.54417 - 3.03060i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-4.51960 + 2.13851i) q^{5} +(1.48643 - 4.57476i) q^{6} +(-2.71827 + 2.71827i) q^{7} +(2.52015 - 1.28408i) q^{8} +(-1.51000 - 2.07833i) q^{9} +(-5.83988 + 3.98695i) q^{10} +(13.9453 + 10.1318i) q^{11} +(1.06417 - 6.71888i) q^{12} +(-8.27725 - 1.31099i) q^{13} +(-3.19552 + 4.39825i) q^{14} +(-0.498051 + 16.9993i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-4.91940 - 9.65487i) q^{17} +(-2.56896 - 2.56896i) q^{18} +(-31.3075 - 10.1724i) q^{19} +(-7.27512 + 6.86095i) q^{20} +(4.04052 + 12.4354i) q^{21} +(21.7203 + 11.0670i) q^{22} +(-1.39020 - 8.77738i) q^{23} -9.62038i q^{24} +(15.8536 - 19.3304i) q^{25} -11.8517 q^{26} +(21.6047 - 3.42185i) q^{27} +(-3.49047 + 6.85044i) q^{28} +(-2.63851 + 0.857304i) q^{29} +(3.06510 + 23.8548i) q^{30} +(-14.1220 + 43.4631i) q^{31} +(4.00000 - 4.00000i) q^{32} +(52.2394 - 26.6173i) q^{33} +(-9.00739 - 12.3976i) q^{34} +(6.47244 - 18.0985i) q^{35} +(-4.15667 - 3.02000i) q^{36} +(8.87405 - 56.0286i) q^{37} +(-45.9809 - 7.28265i) q^{38} +(-16.7545 + 23.0606i) q^{39} +(-8.64404 + 11.1929i) q^{40} +(46.2281 - 33.5867i) q^{41} +(8.39492 + 16.4760i) q^{42} +(-6.00015 - 6.00015i) q^{43} +(32.7873 + 10.6533i) q^{44} +(11.2691 + 6.16409i) q^{45} +(-3.88367 - 11.9527i) q^{46} +(22.4520 + 11.4399i) q^{47} +(-2.12833 - 13.4378i) q^{48} +34.2220i q^{49} +(17.8678 - 30.5081i) q^{50} -36.8564 q^{51} +(-16.5545 + 2.62197i) q^{52} +(-13.6421 + 26.7742i) q^{53} +(29.4205 - 9.55929i) q^{54} +(-84.6942 - 15.9697i) q^{55} +(-3.35997 + 10.3409i) q^{56} +(-79.1725 + 79.1725i) q^{57} +(-3.49581 + 1.78121i) q^{58} +(38.3329 + 52.7607i) q^{59} +(9.55879 + 32.6424i) q^{60} +(-68.2457 - 49.5834i) q^{61} +(-10.1102 + 63.8336i) q^{62} +(9.75405 + 1.54489i) q^{63} +(4.70228 - 6.47214i) q^{64} +(40.2134 - 11.7758i) q^{65} +(67.0795 - 48.7361i) q^{66} +(-17.3215 - 33.9954i) q^{67} +(-15.3243 - 15.3243i) q^{68} +(-28.7474 - 9.34060i) q^{69} +(5.03675 - 26.7120i) q^{70} +(33.5080 + 103.127i) q^{71} +(-6.47416 - 3.29875i) q^{72} +(12.6356 + 79.7780i) q^{73} -80.2240i q^{74} +(-34.1022 - 77.8951i) q^{75} -65.8373 q^{76} +(-65.4481 + 10.3660i) q^{77} +(-18.3010 + 35.9177i) q^{78} +(39.1289 - 12.7138i) q^{79} +(-9.59779 + 17.5466i) q^{80} +(30.1357 - 92.7481i) q^{81} +(57.1411 - 57.1411i) q^{82} +(32.1640 - 16.3884i) q^{83} +(15.3710 + 21.1564i) q^{84} +(42.8808 + 33.1159i) q^{85} +(-9.70844 - 7.05360i) q^{86} +(-1.47615 + 9.32008i) q^{87} +(48.1543 + 7.62689i) q^{88} +(57.7869 - 79.5368i) q^{89} +(17.1044 + 6.11693i) q^{90} +(26.0634 - 18.9362i) q^{91} +(-8.06904 - 15.8364i) q^{92} +(109.912 + 109.912i) q^{93} +(33.8919 + 11.0121i) q^{94} +(163.251 - 20.9761i) q^{95} +(-5.94572 - 18.2990i) q^{96} +(-72.8156 - 37.1014i) q^{97} +(7.57100 + 47.8014i) q^{98} -44.2820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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