LMFDB - Embedded newform 350.2.h.d.281.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 15 x^{18} - 30 x^{17} + 145 x^{16} - 194 x^{15} + 1187 x^{14} - 1490 x^{13} + \cdots + 400 $ x^20 - 3x^19 + 15x^18 - 30x^17 + 145x^16 - 194x^15 + 1187x^14 - 1490x^13 + 10170x^12 - 13920x^11 + 42087x^10 - 591x^9 + 65635x^8 + 120715x^7 + 257180x^6 + 306283x^5 + 246171x^4 + 99850x^3 + 26260x^2 + 4200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			281.5
Root			$2.59536 - 1.88564i$ of defining polynomial
Character	$\chi$	$=$	350.281
Dual form			350.2.h.d.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(2.59536 - 1.88564i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.0648780 - 2.23513i) q^{5} +(-2.59536 - 1.88564i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(2.25320 - 6.93464i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(2.59536 - 1.88564i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.0648780 - 2.23513i) q^{5} +(-2.59536 - 1.88564i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(2.25320 - 6.93464i) q^{9} +(-2.10568 + 0.752395i) q^{10} +(1.17344 + 3.61147i) q^{11} +(-0.991338 + 3.05103i) q^{12} +(-1.68717 + 5.19257i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-4.38302 - 5.67862i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.75753 - 3.45655i) q^{17} -7.29151 q^{18} +(4.35831 + 3.16650i) q^{19} +(1.36626 + 1.77012i) q^{20} +(2.59536 - 1.88564i) q^{21} +(3.07210 - 2.23201i) q^{22} +(0.697091 + 2.14543i) q^{23} +3.20804 q^{24} +(-4.99158 + 0.290021i) q^{25} +5.45979 q^{26} +(-4.25434 - 13.0935i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-3.79378 + 2.75634i) q^{29} +(-4.04626 + 5.92329i) q^{30} +(4.13836 + 3.00669i) q^{31} -1.00000 q^{32} +(9.85542 + 7.16038i) q^{33} +(-1.81722 + 5.59282i) q^{34} +(-0.0648780 - 2.23513i) q^{35} +(2.25320 + 6.93464i) q^{36} +(0.131143 - 0.403617i) q^{37} +(1.66473 - 5.12350i) q^{38} +(5.41250 + 16.6580i) q^{39} +(1.26129 - 1.84639i) q^{40} +(2.25698 - 6.94626i) q^{41} +(-2.59536 - 1.88564i) q^{42} -8.16279 q^{43} +(-3.07210 - 2.23201i) q^{44} +(-15.6460 - 4.58628i) q^{45} +(1.82501 - 1.32595i) q^{46} +(-0.214373 + 0.155751i) q^{47} +(-0.991338 - 3.05103i) q^{48} +1.00000 q^{49} +(1.81831 + 4.65765i) q^{50} -18.8653 q^{51} +(-1.68717 - 5.19257i) q^{52} +(5.20889 - 3.78448i) q^{53} +(-11.1380 + 8.09224i) q^{54} +(7.99596 - 2.85709i) q^{55} +(0.809017 + 0.587785i) q^{56} +17.2822 q^{57} +(3.79378 + 2.75634i) q^{58} +(2.61721 - 8.05495i) q^{59} +(6.88375 + 2.01782i) q^{60} +(1.57501 + 4.84738i) q^{61} +(1.58071 - 4.86493i) q^{62} +(2.25320 - 6.93464i) q^{63} +(0.309017 + 0.951057i) q^{64} +(11.7155 + 3.43415i) q^{65} +(3.76443 - 11.5857i) q^{66} +(-9.86193 - 7.16511i) q^{67} +5.88063 q^{68} +(5.85470 + 4.25369i) q^{69} +(-2.10568 + 0.752395i) q^{70} +(-6.35208 + 4.61506i) q^{71} +(5.89896 - 4.28584i) q^{72} +(2.54602 + 7.83583i) q^{73} -0.424388 q^{74} +(-12.4081 + 10.1650i) q^{75} -5.38717 q^{76} +(1.17344 + 3.61147i) q^{77} +(14.1701 - 10.2952i) q^{78} +(5.00253 - 3.63455i) q^{79} +(-2.14578 - 0.628989i) q^{80} +(-18.0343 - 13.1027i) q^{81} -7.30373 q^{82} +(6.35772 + 4.61915i) q^{83} +(-0.991338 + 3.05103i) q^{84} +(-7.41717 + 10.8579i) q^{85} +(2.52244 + 7.76327i) q^{86} +(-4.64875 + 14.3074i) q^{87} +(-1.17344 + 3.61147i) q^{88} +(0.135057 + 0.415663i) q^{89} +(0.473058 + 16.2975i) q^{90} +(-1.68717 + 5.19257i) q^{91} +(-1.82501 - 1.32595i) q^{92} +16.4100 q^{93} +(0.214373 + 0.155751i) q^{94} +(6.79476 - 9.94681i) q^{95} +(-2.59536 + 1.88564i) q^{96} +(-3.44077 + 2.49987i) q^{97} +(-0.309017 - 0.951057i) q^{98} +27.6882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9} - 9 q^{11} - 2 q^{12} + 5 q^{13} + 5 q^{14} - 5 q^{16} - 12 q^{17} - 34 q^{18} + 2 q^{19} + 5 q^{20} + 3 q^{21} - 6 q^{22} - 5 q^{23} + 2 q^{24} - 35 q^{25} + 20 q^{26} - 6 q^{27} - 5 q^{28} - 22 q^{29} - 25 q^{30} - 7 q^{31} - 20 q^{32} + 25 q^{33} - 18 q^{34} - 5 q^{35} - 6 q^{36} - 3 q^{37} + 8 q^{38} - 22 q^{39} + 19 q^{41} - 3 q^{42} + 2 q^{43} + 6 q^{44} + 45 q^{45} - 10 q^{46} - 14 q^{47} - 2 q^{48} + 20 q^{49} + 10 q^{50} + 38 q^{51} + 5 q^{52} - q^{53} - 19 q^{54} - 20 q^{55} + 5 q^{56} + 116 q^{57} + 22 q^{58} + 17 q^{59} - 5 q^{60} - 38 q^{61} + 7 q^{62} - 6 q^{63} - 5 q^{64} + 15 q^{65} - 16 q^{67} - 12 q^{68} + 35 q^{69} + q^{71} + 11 q^{72} + 19 q^{73} + 18 q^{74} + 35 q^{75} + 12 q^{76} - 9 q^{77} - 18 q^{78} - 64 q^{79} - 40 q^{81} + 26 q^{82} + 57 q^{83} - 2 q^{84} - 40 q^{85} - 2 q^{86} - 78 q^{87} + 9 q^{88} - 6 q^{89} + 10 q^{90} + 5 q^{91} + 10 q^{92} - 22 q^{93} + 14 q^{94} + 60 q^{95} - 3 q^{96} - 18 q^{97} + 5 q^{98} + 112 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9 - 9 * q^11 - 2 * q^12 + 5 * q^13 + 5 * q^14 - 5 * q^16 - 12 * q^17 - 34 * q^18 + 2 * q^19 + 5 * q^20 + 3 * q^21 - 6 * q^22 - 5 * q^23 + 2 * q^24 - 35 * q^25 + 20 * q^26 - 6 * q^27 - 5 * q^28 - 22 * q^29 - 25 * q^30 - 7 * q^31 - 20 * q^32 + 25 * q^33 - 18 * q^34 - 5 * q^35 - 6 * q^36 - 3 * q^37 + 8 * q^38 - 22 * q^39 + 19 * q^41 - 3 * q^42 + 2 * q^43 + 6 * q^44 + 45 * q^45 - 10 * q^46 - 14 * q^47 - 2 * q^48 + 20 * q^49 + 10 * q^50 + 38 * q^51 + 5 * q^52 - q^53 - 19 * q^54 - 20 * q^55 + 5 * q^56 + 116 * q^57 + 22 * q^58 + 17 * q^59 - 5 * q^60 - 38 * q^61 + 7 * q^62 - 6 * q^63 - 5 * q^64 + 15 * q^65 - 16 * q^67 - 12 * q^68 + 35 * q^69 + q^71 + 11 * q^72 + 19 * q^73 + 18 * q^74 + 35 * q^75 + 12 * q^76 - 9 * q^77 - 18 * q^78 - 64 * q^79 - 40 * q^81 + 26 * q^82 + 57 * q^83 - 2 * q^84 - 40 * q^85 - 2 * q^86 - 78 * q^87 + 9 * q^88 - 6 * q^89 + 10 * q^90 + 5 * q^91 + 10 * q^92 - 22 * q^93 + 14 * q^94 + 60 * q^95 - 3 * q^96 - 18 * q^97 + 5 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	2.59536	−	1.88564i	1.49843	−	1.08867i	0.527429	−	0.849599i	$-0.323156\pi$
$3$	2.59536	−	1.88564i	1.49843	−	1.08867i	0.971001	−	0.239075i	$-0.0768440\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.0648780	−	2.23513i	−0.0290143	−	0.999579i
$5$	−0.0648780	−	2.23513i	−0.0290143	−	0.999579i
$6$	−2.59536	−	1.88564i	−1.05955	−	0.769808i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.25320	−	6.93464i	0.751067	−	2.31155i
$10$	−2.10568	+	0.752395i	−0.665876	+	0.237928i
$11$	1.17344	+	3.61147i	0.353805	+	1.08890i	0.956699	+	0.291078i	$0.0940141\pi$
$11$	1.17344	+	3.61147i	0.353805	+	1.08890i	−0.602894	+	0.797821i	$0.705986\pi$
$12$	−0.991338	+	3.05103i	−0.286175	+	0.880755i
$13$	−1.68717	+	5.19257i	−0.467936	+	1.44016i	0.387316	+	0.921947i	$0.373402\pi$
$13$	−1.68717	+	5.19257i	−0.467936	+	1.44016i	−0.855252	+	0.518212i	$0.826598\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−4.38302	−	5.67862i	−1.13169	−	1.46621i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.75753	−	3.45655i	−1.15387	−	0.838337i	−0.164880	−	0.986314i	$-0.552724\pi$
$17$	−4.75753	−	3.45655i	−1.15387	−	0.838337i	−0.988991	+	0.147977i	$0.952724\pi$
$18$	−7.29151			−1.71863
$19$	4.35831	+	3.16650i	0.999865	+	0.726444i	0.962059	−	0.272841i	$-0.0879633\pi$
$19$	4.35831	+	3.16650i	0.999865	+	0.726444i	0.0378055	+	0.999285i	$0.487963\pi$
$20$	1.36626	+	1.77012i	0.305505	+	0.395811i
$21$	2.59536	−	1.88564i	0.566353	−	0.411480i
$22$	3.07210	−	2.23201i	0.654974	−	0.475867i
$23$	0.697091	+	2.14543i	0.145354	+	0.447352i	0.997056	−	0.0766731i	$-0.0244298\pi$
$23$	0.697091	+	2.14543i	0.145354	+	0.447352i	−0.851703	+	0.524025i	$0.824430\pi$
$24$	3.20804			0.654838
$25$	−4.99158	+	0.290021i	−0.998316	+	0.0580042i
$26$	5.45979			1.07075
$27$	−4.25434	−	13.0935i	−0.818748	−	2.51985i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	−3.79378	+	2.75634i	−0.704487	+	0.511840i	−0.881390	−	0.472388i	$-0.843392\pi$
$29$	−3.79378	+	2.75634i	−0.704487	+	0.511840i	0.176904	+	0.984228i	$0.443392\pi$
$30$	−4.04626	+	5.92329i	−0.738742	+	1.08144i
$31$	4.13836	+	3.00669i	0.743271	+	0.540018i	0.893734	−	0.448598i	$-0.148076\pi$
$31$	4.13836	+	3.00669i	0.743271	+	0.540018i	−0.150463	+	0.988616i	$0.548076\pi$
$32$	−1.00000			−0.176777
$33$	9.85542	+	7.16038i	1.71561	+	1.24646i
$34$	−1.81722	+	5.59282i	−0.311650	+	0.959160i
$35$	−0.0648780	−	2.23513i	−0.0109664	−	0.377805i
$36$	2.25320	+	6.93464i	0.375533	+	1.15577i
$37$	0.131143	−	0.403617i	0.0215598	−	0.0663543i	−0.939698	−	0.342006i	$-0.888894\pi$
$37$	0.131143	−	0.403617i	0.0215598	−	0.0663543i	0.961258	+	0.275652i	$0.0888937\pi$
$38$	1.66473	−	5.12350i	0.270054	−	0.831141i
$39$	5.41250	+	16.6580i	0.866693	+	2.66741i
$40$	1.26129	−	1.84639i	0.199427	−	0.291940i
$41$	2.25698	−	6.94626i	0.352480	−	1.08482i	−0.604976	−	0.796244i	$-0.706817\pi$
$41$	2.25698	−	6.94626i	0.352480	−	1.08482i	0.957456	−	0.288579i	$-0.0931828\pi$
$42$	−2.59536	−	1.88564i	−0.400472	−	0.290960i
$43$	−8.16279			−1.24481			−0.622407	−	0.782694i	$-0.713845\pi$
$43$	−8.16279			−1.24481			−0.622407	+	0.782694i	$0.713845\pi$
$44$	−3.07210	−	2.23201i	−0.463137	−	0.336488i
$45$	−15.6460	−	4.58628i	−2.33237	−	0.683683i
$46$	1.82501	−	1.32595i	0.269083	−	0.195500i
$47$	−0.214373	+	0.155751i	−0.0312695	+	0.0227186i	−0.603310	−	0.797507i	$-0.706152\pi$
$47$	−0.214373	+	0.155751i	−0.0312695	+	0.0227186i	0.572041	+	0.820225i	$0.306152\pi$
$48$	−0.991338	−	3.05103i	−0.143087	−	0.440378i
$49$	1.00000			0.142857
$50$	1.81831	+	4.65765i	0.257148	+	0.658692i
$51$	−18.8653			−2.64167
$52$	−1.68717	−	5.19257i	−0.233968	−	0.720079i
$53$	5.20889	−	3.78448i	0.715496	−	0.519839i	−0.169446	−	0.985540i	$-0.554198\pi$
$53$	5.20889	−	3.78448i	0.715496	−	0.519839i	0.884942	+	0.465701i	$0.154198\pi$
$54$	−11.1380	+	8.09224i	−1.51569	+	1.10121i
$55$	7.99596	−	2.85709i	1.07818	−	0.385250i
$56$	0.809017	+	0.587785i	0.108109	+	0.0785461i
$57$	17.2822			2.28909
$58$	3.79378	+	2.75634i	0.498147	+	0.361925i
$59$	2.61721	−	8.05495i	0.340732	−	1.04867i	−0.623097	−	0.782144i	$-0.714126\pi$
$59$	2.61721	−	8.05495i	0.340732	−	1.04867i	0.963829	−	0.266521i	$-0.0858741\pi$
$60$	6.88375	+	2.01782i	0.888688	+	0.260500i
$61$	1.57501	+	4.84738i	0.201659	+	0.620644i	0.999834	+	0.0182177i	$0.00579920\pi$
$61$	1.57501	+	4.84738i	0.201659	+	0.620644i	−0.798175	+	0.602426i	$0.794201\pi$
$62$	1.58071	−	4.86493i	0.200751	−	0.617847i
$63$	2.25320	−	6.93464i	0.283877	−	0.873682i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	11.7155	+	3.43415i	1.45313	+	0.425954i
$66$	3.76443	−	11.5857i	0.463370	−	1.42611i
$67$	−9.86193	−	7.16511i	−1.20483	−	0.875358i	−0.210076	−	0.977685i	$-0.567371\pi$
$67$	−9.86193	−	7.16511i	−1.20483	−	0.875358i	−0.994751	+	0.102328i	$0.967371\pi$
$68$	5.88063			0.713132
$69$	5.85470	+	4.25369i	0.704822	+	0.512084i
$70$	−2.10568	+	0.752395i	−0.251677	+	0.0899284i
$71$	−6.35208	+	4.61506i	−0.753854	+	0.547707i	−0.897019	−	0.441992i	$-0.854272\pi$
$71$	−6.35208	+	4.61506i	−0.753854	+	0.547707i	0.143165	+	0.989699i	$0.454272\pi$
$72$	5.89896	−	4.28584i	0.695199	−	0.505091i
$73$	2.54602	+	7.83583i	0.297989	+	0.917115i	0.982201	+	0.187832i	$0.0601460\pi$
$73$	2.54602	+	7.83583i	0.297989	+	0.917115i	−0.684213	+	0.729283i	$0.739854\pi$
$74$	−0.424388			−0.0493342
$75$	−12.4081	+	10.1650i	−1.43276	+	1.17376i
$76$	−5.38717			−0.617950
$77$	1.17344	+	3.61147i	0.133726	+	0.411565i
$78$	14.1701	−	10.2952i	1.60445	−	1.16570i
$79$	5.00253	−	3.63455i	0.562828	−	0.408919i	−0.269665	−	0.962954i	$-0.586913\pi$
$79$	5.00253	−	3.63455i	0.562828	−	0.408919i	0.832493	+	0.554036i	$0.186913\pi$
$80$	−2.14578	−	0.628989i	−0.239906	−	0.0703232i
$81$	−18.0343	−	13.1027i	−2.00381	−	1.45585i
$82$	−7.30373			−0.806562
$83$	6.35772	+	4.61915i	0.697850	+	0.507018i	0.879231	−	0.476395i	$-0.158057\pi$
$83$	6.35772	+	4.61915i	0.697850	+	0.507018i	−0.181381	+	0.983413i	$0.558057\pi$
$84$	−0.991338	+	3.05103i	−0.108164	+	0.332894i
$85$	−7.41717	+	10.8579i	−0.804505	+	1.17771i
$86$	2.52244	+	7.76327i	0.272002	+	0.837135i
$87$	−4.64875	+	14.3074i	−0.498398	+	1.53391i
$88$	−1.17344	+	3.61147i	−0.125089	+	0.384984i
$89$	0.135057	+	0.415663i	0.0143160	+	0.0440601i	0.957959	−	0.286904i	$-0.0926261\pi$
$89$	0.135057	+	0.415663i	0.0143160	+	0.0440601i	−0.943643	+	0.330964i	$0.892626\pi$
$90$	0.473058	+	16.2975i	0.0498647	+	1.71790i
$91$	−1.68717	+	5.19257i	−0.176863	+	0.544329i
$92$	−1.82501	−	1.32595i	−0.190270	−	0.138239i
$93$	16.4100			1.70164
$94$	0.214373	+	0.155751i	0.0221108	+	0.0160645i
$95$	6.79476	−	9.94681i	0.697128	−	1.02052i
$96$	−2.59536	+	1.88564i	−0.264888	+	0.192452i
$97$	−3.44077	+	2.49987i	−0.349357	+	0.253823i	−0.748599	−	0.663023i	$-0.769273\pi$
$97$	−3.44077	+	2.49987i	−0.349357	+	0.253823i	0.399242	+	0.916846i	$0.369273\pi$
$98$	−0.309017	−	0.951057i	−0.0312154	−	0.0960712i
$99$	27.6882			2.78277
$100$	3.86780	−	3.16861i	0.386780	−	0.316861i
$101$	6.39631			0.636457			0.318228	−	0.948014i	$-0.396912\pi$
$101$	6.39631			0.636457			0.318228	+	0.948014i	$0.396912\pi$
$102$	5.82970	+	17.9420i	0.577226	+	1.77652i
$103$	1.94836	−	1.41557i	0.191978	−	0.139480i	−0.487644	−	0.873042i	$-0.662144\pi$
$103$	1.94836	−	1.41557i	0.191978	−	0.139480i	0.679622	+	0.733562i	$0.262144\pi$
$104$	−4.41706	+	3.20918i	−0.433128	+	0.314686i
$105$	−4.38302	−	5.67862i	−0.427739	−	0.554176i
$106$	−5.20889	−	3.78448i	−0.505932	−	0.367581i
$107$	7.79037			0.753123			0.376562	−	0.926392i	$-0.377106\pi$
$107$	7.79037			0.753123			0.376562	+	0.926392i	$0.377106\pi$
$108$	11.1380	+	8.09224i	1.07176	+	0.778676i
$109$	−3.00391	+	9.24510i	−0.287723	+	0.885520i	0.697846	+	0.716247i	$0.254142\pi$
$109$	−3.00391	+	9.24510i	−0.287723	+	0.885520i	−0.985569	+	0.169272i	$0.945858\pi$
$110$	−5.18814	−	6.72173i	−0.494670	−	0.640891i
$111$	−0.420713	−	1.29482i	−0.0399323	−	0.122899i
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	1.30801	−	4.02566i	0.123048	−	0.378702i	−0.870493	−	0.492181i	$-0.836200\pi$
$113$	1.30801	−	4.02566i	0.123048	−	0.378702i	0.993540	+	0.113480i	$0.0361997\pi$
$114$	−5.34050	−	16.4364i	−0.500184	−	1.53941i
$115$	4.75007	−	1.69728i	0.442946	−	0.158272i
$116$	1.44909	−	4.45985i	0.134545	−	0.414087i
$117$	32.2070	+	23.3998i	2.97754	+	2.16331i
$118$	−8.46948			−0.779679
$119$	−4.75753	−	3.45655i	−0.436122	−	0.316861i
$120$	−0.208131	−	7.17037i	−0.0189997	−	0.654562i
$121$	−2.76658	+	2.01004i	−0.251507	+	0.182731i
$122$	4.12343	−	2.99585i	0.373318	−	0.271231i
$123$	−7.24047	−	22.2839i	−0.652851	−	2.00927i
$124$	−5.11529			−0.459367
$125$	0.972077	+	11.1380i	0.0869452	+	0.996213i
$126$	−7.29151			−0.649579
$127$	−0.423930	−	1.30472i	−0.0376177	−	0.115775i	0.930484	−	0.366332i	$-0.119386\pi$
$127$	−0.423930	−	1.30472i	−0.0376177	−	0.115775i	−0.968102	+	0.250556i	$0.919386\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−21.1854	+	15.3921i	−1.86527	+	1.35520i
$130$	−0.354220	−	12.2033i	−0.0310671	−	1.07030i
$131$	1.33820	+	0.972260i	0.116919	+	0.0849467i	0.644708	−	0.764429i	$-0.276979\pi$
$131$	1.33820	+	0.972260i	0.116919	+	0.0849467i	−0.527789	+	0.849375i	$0.676979\pi$
$132$	−12.1820			−1.06030
$133$	4.35831	+	3.16650i	0.377913	+	0.274570i
$134$	−3.76692	+	11.5934i	−0.325412	+	1.00152i
$135$	−28.9896	+	10.3585i	−2.49503	+	0.891515i
$136$	−1.81722	−	5.59282i	−0.155825	−	0.479580i
$137$	5.24999	−	16.1578i	0.448537	−	1.38046i	−0.430020	−	0.902819i	$-0.641494\pi$
$137$	5.24999	−	16.1578i	0.448537	−	1.38046i	0.878558	−	0.477636i	$-0.158506\pi$
$138$	2.23629	−	6.88261i	0.190366	−	0.585886i
$139$	1.02682	+	3.16023i	0.0870939	+	0.268048i	0.985113	−	0.171909i	$-0.0549937\pi$
$139$	1.02682	+	3.16023i	0.0870939	+	0.268048i	−0.898019	+	0.439957i	$0.854994\pi$
$140$	1.36626	+	1.77012i	0.115470	+	0.149603i
$141$	−0.262684	+	0.808458i	−0.0221220	+	0.0680845i
$142$	6.35208	+	4.61506i	0.533055	+	0.387287i
$143$	−20.7326			−1.73375
$144$	−5.89896	−	4.28584i	−0.491580	−	0.357154i
$145$	6.40690	+	8.30075i	0.532064	+	0.689340i
$146$	6.66556	−	4.84281i	0.551645	−	0.400794i
$147$	2.59536	−	1.88564i	0.214061	−	0.155525i
$148$	0.131143	+	0.403617i	0.0107799	+	0.0331771i
$149$	−13.5249			−1.10800			−0.554001	−	0.832516i	$-0.686900\pi$
$149$	−13.5249			−1.10800			−0.554001	+	0.832516i	$0.686900\pi$
$150$	13.5018	+	8.65961i	1.10242	+	0.707054i
$151$	−8.27670			−0.673548			−0.336774	−	0.941586i	$-0.609336\pi$
$151$	−8.27670			−0.673548			−0.336774	+	0.941586i	$0.609336\pi$
$152$	1.66473	+	5.12350i	0.135027	+	0.415571i
$153$	−34.6896	+	25.2035i	−2.80449	+	2.03758i
$154$	3.07210	−	2.23201i	0.247557	−	0.179861i
$155$	6.45185	−	9.44482i	0.518225	−	0.758626i
$156$	−14.1701	−	10.2952i	−1.13452	−	0.824274i
$157$	−24.1797			−1.92975			−0.964877	−	0.262703i	$-0.915386\pi$
$157$	−24.1797			−1.92975			−0.964877	+	0.262703i	$0.915386\pi$
$158$	−5.00253	−	3.63455i	−0.397980	−	0.289149i
$159$	6.38278	−	19.6442i	0.506187	−	1.55788i
$160$	0.0648780	+	2.23513i	0.00512905	+	0.176702i
$161$	0.697091	+	2.14543i	0.0549385	+	0.169083i
$162$	−6.88848	+	21.2006i	−0.541210	+	1.66567i
$163$	6.48548	−	19.9602i	0.507982	−	1.56341i	−0.287718	−	0.957715i	$-0.592896\pi$
$163$	6.48548	−	19.9602i	0.507982	−	1.56341i	0.795699	−	0.605692i	$-0.207104\pi$
$164$	2.25698	+	6.94626i	0.176240	+	0.542412i
$165$	15.3650	−	22.4927i	1.19616	−	1.75105i
$166$	2.42843	−	7.47394i	0.188483	−	0.580090i
$167$	0.542523	+	0.394166i	0.0419817	+	0.0305015i	0.608578	−	0.793494i	$-0.291740\pi$
$167$	0.542523	+	0.394166i	0.0419817	+	0.0305015i	−0.566597	+	0.823995i	$0.691740\pi$
$168$	3.20804			0.247506
$169$	−13.5990	−	9.88024i	−1.04608	−	0.760019i
$170$	12.6185	+	3.69886i	0.967798	+	0.283689i
$171$	31.7787	−	23.0885i	2.43017	−	1.76563i
$172$	6.60383	−	4.79797i	0.503538	−	0.365841i
$173$	−0.379177	−	1.16699i	−0.0288283	−	0.0887244i	0.935607	−	0.353043i	$-0.114853\pi$
$173$	−0.379177	−	1.16699i	−0.0288283	−	0.0887244i	−0.964435	+	0.264318i	$0.914853\pi$
$174$	15.0437			1.14046
$175$	−4.99158	+	0.290021i	−0.377328	+	0.0219235i
$176$	3.79733			0.286234
$177$	−8.39612	−	25.8406i	−0.631091	−	1.94230i
$178$	0.353584	−	0.256894i	0.0265022	−	0.0192550i
$179$	−18.0592	+	13.1208i	−1.34981	+	0.980692i	−0.350786	+	0.936456i	$0.614086\pi$
$179$	−18.0592	+	13.1208i	−1.34981	+	0.980692i	−0.999021	+	0.0442365i	$0.985914\pi$
$180$	15.3536	−	5.48609i	1.14439	−	0.408909i
$181$	5.78269	+	4.20137i	0.429824	+	0.312286i	0.781579	−	0.623807i	$-0.214415\pi$
$181$	5.78269	+	4.20137i	0.429824	+	0.312286i	−0.351754	+	0.936092i	$0.614415\pi$
$182$	5.45979			0.404706
$183$	13.2281	+	9.61080i	0.977851	+	0.710450i
$184$	−0.697091	+	2.14543i	−0.0513902	+	0.158163i
$185$	−0.910644	−	0.266936i	−0.0669519	−	0.0196255i
$186$	−5.07098	−	15.6069i	−0.371823	−	1.14435i
$187$	6.90056	−	21.2377i	0.504619	−	1.55306i
$188$	0.0818831	−	0.252010i	0.00597194	−	0.0183797i
$189$	−4.25434	−	13.0935i	−0.309458	−	0.952413i
$190$	−11.5597	−	3.38847i	−0.838627	−	0.245826i
$191$	−2.43153	+	7.48348i	−0.175939	+	0.541485i	−0.999675	−	0.0254884i	$-0.991886\pi$
$191$	−2.43153	+	7.48348i	−0.175939	+	0.541485i	0.823736	+	0.566974i	$0.191886\pi$
$192$	2.59536	+	1.88564i	0.187304	+	0.136084i
$193$	−1.18703			−0.0854441			−0.0427220	−	0.999087i	$-0.513603\pi$
$193$	−1.18703			−0.0854441			−0.0427220	+	0.999087i	$0.513603\pi$
$194$	3.44077	+	2.49987i	0.247033	+	0.179480i
$195$	36.8815	−	13.1783i	2.64114	−	0.943721i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−13.1713	+	9.56948i	−0.938413	+	0.681797i	−0.948038	−	0.318157i	$-0.896936\pi$
$197$	−13.1713	+	9.56948i	−0.938413	+	0.681797i	0.00962502	+	0.999954i	$0.496936\pi$
$198$	−8.55614	−	26.3331i	−0.608058	−	1.87141i
$199$	−10.2076			−0.723595			−0.361798	−	0.932257i	$-0.617837\pi$
$199$	−10.2076			−0.723595			−0.361798	+	0.932257i	$0.617837\pi$
$200$	−4.20874	−	2.69935i	−0.297603	−	0.190873i
$201$	−39.1060			−2.75833
$202$	−1.97657	−	6.08325i	−0.139071	−	0.428016i
$203$	−3.79378	+	2.75634i	−0.266271	+	0.193457i
$204$	15.2623	−	11.0887i	1.06858	−	0.776368i
$205$	−15.6722	−	4.59397i	−1.09459	−	0.320857i
$206$	−1.94836	−	1.41557i	−0.135749	−	0.0986273i
$207$	16.4484			1.14325
$208$	4.41706	+	3.20918i	0.306268	+	0.222517i
$209$	−6.32151	+	19.4556i	−0.437268	+	1.34577i
$210$	−4.04626	+	5.92329i	−0.279218	+	0.408746i
$211$	−0.199642	−	0.614434i	−0.0137439	−	0.0422994i	0.943949	−	0.330090i	$-0.107079\pi$
$211$	−0.199642	−	0.614434i	−0.0137439	−	0.0422994i	−0.957693	+	0.287791i	$0.907079\pi$
$212$	−1.98962	+	6.12342i	−0.136648	+	0.420558i
$213$	−7.78360	+	23.9555i	−0.533324	+	1.64140i
$214$	−2.40736	−	7.40908i	−0.164563	−	0.506474i
$215$	0.529585	+	18.2449i	0.0361174	+	1.24429i
$216$	4.25434	−	13.0935i	0.289471	−	0.890901i
$217$	4.13836	+	3.00669i	0.280930	+	0.204108i
$218$	9.72087			0.658381
$219$	21.3834	+	15.5359i	1.44495	+	1.04982i
$220$	−4.78952	+	7.01134i	−0.322909	+	0.472705i
$221$	25.9751	−	18.8720i	1.74728	−	1.26947i
$222$	−1.10144	+	0.800243i	−0.0739238	+	0.0537088i
$223$	−3.45483	−	10.6329i	−0.231353	−	0.712030i	−0.997584	−	0.0694658i	$-0.977871\pi$
$223$	−3.45483	−	10.6329i	−0.231353	−	0.712030i	0.766232	−	0.642564i	$-0.222129\pi$
$224$	−1.00000			−0.0668153
$225$	−9.23585	+	35.2683i	−0.615723	+	2.35122i
$226$	−4.23283			−0.281563
$227$	−7.00240	−	21.5512i	−0.464765	−	1.43040i	−0.859277	−	0.511510i	$-0.829086\pi$
$227$	−7.00240	−	21.5512i	−0.464765	−	1.43040i	0.394512	−	0.918891i	$-0.370914\pi$
$228$	−13.9816	+	10.1582i	−0.925956	+	0.672746i
$229$	4.39614	−	3.19398i	0.290505	−	0.211064i	−0.432981	−	0.901403i	$-0.642538\pi$
$229$	4.39614	−	3.19398i	0.290505	−	0.211064i	0.723487	+	0.690339i	$0.242538\pi$
$230$	−3.08206	−	3.99310i	−0.203225	−	0.263297i
$231$	9.85542	+	7.16038i	0.648439	+	0.471118i
$232$	−4.68937			−0.307872
$233$	−12.9814	−	9.43152i	−0.850438	−	0.617880i	0.0748286	−	0.997196i	$-0.476159\pi$
$233$	−12.9814	−	9.43152i	−0.850438	−	0.617880i	−0.925267	+	0.379317i	$0.876159\pi$
$234$	12.3020	−	37.8617i	0.804207	−	2.47509i
$235$	0.362031	+	0.469045i	0.0236163	+	0.0305971i
$236$	2.61721	+	8.05495i	0.170366	+	0.524333i
$237$	6.12991	−	18.8659i	0.398180	−	1.22547i
$238$	−1.81722	+	5.59282i	−0.117793	+	0.362528i
$239$	−5.69699	−	17.5335i	−0.368508	−	1.13415i	−0.947755	−	0.318999i	$-0.896653\pi$
$239$	−5.69699	−	17.5335i	−0.368508	−	1.13415i	0.579247	−	0.815152i	$-0.303347\pi$
$240$	−6.75511	+	2.41371i	−0.436041	+	0.155804i
$241$	−7.39144	+	22.7485i	−0.476125	+	1.46536i	0.368310	+	0.929703i	$0.379937\pi$
$241$	−7.39144	+	22.7485i	−0.476125	+	1.46536i	−0.844435	+	0.535658i	$0.820063\pi$
$242$	2.76658	+	2.01004i	0.177842	+	0.129210i
$243$	−30.2103			−1.93799
$244$	−4.12343	−	2.99585i	−0.263976	−	0.191789i
$245$	−0.0648780	−	2.23513i	−0.00414490	−	0.142797i
$246$	−18.9558	+	13.7722i	−1.20858	+	0.878082i
$247$	−23.7954	+	17.2884i	−1.51407	+	1.10003i
$248$	1.58071	+	4.86493i	0.100375	+	0.308923i
$249$	25.2106			1.59766
$250$	10.2925	−	4.36633i	0.650954	−	0.276151i
$251$	8.58319			0.541766			0.270883	−	0.962612i	$-0.412684\pi$
$251$	8.58319			0.541766			0.270883	+	0.962612i	$0.412684\pi$
$252$	2.25320	+	6.93464i	0.141938	+	0.436841i
$253$	−6.93015	+	5.03505i	−0.435695	+	0.316551i
$254$	−1.10986	+	0.806363i	−0.0696390	+	0.0505957i
$255$	1.22394	+	42.1663i	0.0766463	+	2.64056i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.91959			0.182119			0.0910595	−	0.995845i	$-0.470975\pi$
$257$	2.91959			0.182119			0.0910595	+	0.995845i	$0.470975\pi$
$258$	21.1854	+	15.3921i	1.31894	+	0.958268i
$259$	0.131143	−	0.403617i	0.00814884	−	0.0250796i
$260$	−11.4966	+	4.10791i	−0.712988	+	0.254762i
$261$	10.5661	+	32.5191i	0.654024	+	2.01288i
$262$	0.511147	−	1.57315i	0.0315788	−	0.0971895i
$263$	0.782290	−	2.40764i	0.0482381	−	0.148462i	−0.924036	−	0.382305i	$-0.875130\pi$
$263$	0.782290	−	2.40764i	0.0482381	−	0.148462i	0.972274	+	0.233844i	$0.0751303\pi$
$264$	3.76443	+	11.5857i	0.231685	+	0.713053i
$265$	−8.79674	−	11.3970i	−0.540379	−	0.700112i
$266$	1.66473	−	5.12350i	0.102071	−	0.314142i
$267$	1.13431	+	0.824125i	0.0694187	+	0.0504356i
$268$	12.1900			0.744624
$269$	20.4844	+	14.8828i	1.24895	+	0.907418i	0.998161	−	0.0606227i	$-0.0193086\pi$
$269$	20.4844	+	14.8828i	1.24895	+	0.907418i	0.250793	+	0.968041i	$0.419309\pi$
$270$	18.8098	+	24.3698i	1.14473	+	1.48310i
$271$	−7.99269	+	5.80703i	−0.485521	+	0.352752i	−0.803459	−	0.595360i	$-0.797010\pi$
$271$	−7.99269	+	5.80703i	−0.485521	+	0.352752i	0.317938	+	0.948111i	$0.397010\pi$
$272$	−4.75753	+	3.45655i	−0.288468	+	0.209584i
$273$	5.41250	+	16.6580i	0.327579	+	1.00819i
$274$	−16.9893			−1.02636
$275$	−6.90471	−	17.6866i	−0.416370	−	1.06654i
$276$	−7.23680			−0.435604
$277$	4.53155	+	13.9467i	0.272275	+	0.837975i	0.989928	+	0.141574i	$0.0452164\pi$
$277$	4.53155	+	13.9467i	0.272275	+	0.837975i	−0.717653	+	0.696401i	$0.754784\pi$
$278$	2.68826	−	1.95313i	0.161231	−	0.117141i
$279$	30.1749	−	21.9233i	1.80652	−	1.31252i
$280$	1.26129	−	1.84639i	0.0753763	−	0.110343i
$281$	2.51036	+	1.82388i	0.149756	+	0.108804i	0.660140	−	0.751143i	$-0.270497\pi$
$281$	2.51036	+	1.82388i	0.149756	+	0.108804i	−0.510385	+	0.859946i	$0.670497\pi$
$282$	0.850063			0.0506205
$283$	9.09861	+	6.61053i	0.540856	+	0.392955i	0.824403	−	0.566003i	$-0.191511\pi$
$283$	9.09861	+	6.61053i	0.540856	+	0.392955i	−0.283547	+	0.958958i	$0.591511\pi$
$284$	2.42628	−	7.46732i	0.143973	−	0.443104i
$285$	−1.12124	−	38.6280i	−0.0664163	−	2.28812i
$286$	6.40672	+	19.7179i	0.378837	+	1.16594i
$287$	2.25698	−	6.94626i	0.133225	−	0.410025i
$288$	−2.25320	+	6.93464i	−0.132771	+	0.408628i
$289$	5.43309	+	16.7213i	0.319594	+	0.983608i
$290$	5.91464	−	8.65840i	0.347320	−	0.508439i
$291$	−4.21619	+	12.9761i	−0.247157	+	0.760672i
$292$	−6.66556	−	4.84281i	−0.390072	−	0.283404i
$293$	13.9600			0.815555			0.407777	−	0.913081i	$-0.366304\pi$
$293$	13.9600			0.815555			0.407777	+	0.913081i	$0.366304\pi$
$294$	−2.59536	−	1.88564i	−0.151364	−	0.109973i
$295$	−18.1736	−	5.32721i	−1.05811	−	0.310162i
$296$	0.343337	−	0.249449i	0.0199561	−	0.0144989i
$297$	42.2946	−	30.7289i	2.45418	−	1.78307i
$298$	4.17942	+	12.8629i	0.242107	+	0.745129i
$299$	−12.3164			−0.712274
$300$	4.06349	−	15.5170i	0.234605	−	0.895872i
$301$	−8.16279			−0.470495
$302$	2.55764	+	7.87160i	0.147176	+	0.452960i
$303$	16.6007	−	12.0611i	0.953686	−	0.692894i
$304$	4.35831	−	3.16650i	0.249966	−	0.181611i
$305$	10.7323	−	3.83484i	0.614532	−	0.219582i
$306$	34.6896	+	25.2035i	1.98307	+	1.44079i
$307$	−30.4259			−1.73650			−0.868248	−	0.496131i	$-0.834754\pi$
$307$	−30.4259			−1.73650			−0.868248	+	0.496131i	$0.834754\pi$
$308$	−3.07210	−	2.23201i	−0.175049	−	0.127181i
$309$	2.38745	−	7.34781i	0.135817	−	0.418002i
$310$	−10.9763	−	3.21746i	−0.623411	−	0.182740i
$311$	−1.78397	−	5.49050i	−0.101160	−	0.311337i	0.887650	−	0.460518i	$-0.152336\pi$
$311$	−1.78397	−	5.49050i	−0.101160	−	0.311337i	−0.988810	+	0.149181i	$0.952336\pi$
$312$	−5.41250	+	16.6580i	−0.306422	+	0.943071i
$313$	−2.97544	+	9.15746i	−0.168182	+	0.517610i	−0.999257	−	0.0385504i	$-0.987726\pi$
$313$	−2.97544	+	9.15746i	−0.168182	+	0.517610i	0.831075	+	0.556160i	$0.187726\pi$
$314$	7.47195	+	22.9963i	0.421667	+	1.29776i
$315$	−15.6460	−	4.58628i	−0.881551	−	0.258408i
$316$	−1.91080	+	5.88082i	−0.107491	+	0.330822i
$317$	3.74958	+	2.72423i	0.210598	+	0.153008i	0.688084	−	0.725631i	$-0.258452\pi$
$317$	3.74958	+	2.72423i	0.210598	+	0.153008i	−0.477486	+	0.878639i	$0.658452\pi$
$318$	−20.6551			−1.15828
$319$	−14.4062	−	10.4667i	−0.806593	−	0.586024i
$320$	2.10568	−	0.752395i	0.117711	−	0.0420601i
$321$	20.2188	−	14.6898i	1.12850	−	0.819905i
$322$	1.82501	−	1.32595i	0.101704	−	0.0738921i
$323$	−9.78964	−	30.1294i	−0.544710	−	1.67645i
$324$	22.2916			1.23842
$325$	6.91568	−	26.4084i	0.383613	−	1.46488i
$326$	−20.9874			−1.16239
$327$	9.63667	+	29.6586i	0.532909	+	1.64013i
$328$	5.90884	−	4.29302i	0.326261	−	0.237043i
$329$	−0.214373	+	0.155751i	−0.0118187	+	0.00858682i
$330$	−26.1398	−	7.66233i	−1.43895	−	0.421797i
$331$	18.4712	+	13.4201i	1.01527	+	0.737635i	0.965307	−	0.261116i	$-0.0840906\pi$
$331$	18.4712	+	13.4201i	1.01527	+	0.737635i	0.0499602	+	0.998751i	$0.484091\pi$
$332$	−7.85857			−0.431295
$333$	−2.50345	−	1.81886i	−0.137188	−	0.0996730i
$334$	0.207225	−	0.637774i	0.0113389	−	0.0348974i
$335$	−15.3751	+	22.5075i	−0.840032	+	1.22972i
$336$	−0.991338	−	3.05103i	−0.0540819	−	0.166447i
$337$	3.59706	−	11.0706i	0.195945	−	0.603055i	−0.804020	−	0.594603i	$-0.797309\pi$
$337$	3.59706	−	11.0706i	0.195945	−	0.603055i	0.999964	−	0.00845267i	$-0.00269060\pi$
$338$	−5.19435	+	15.9866i	−0.282535	+	0.869555i
$339$	−4.19616	−	12.9145i	−0.227904	−	0.701417i
$340$	−0.381524	−	13.1440i	−0.0206910	−	0.712831i
$341$	−6.00248	+	18.4737i	−0.325052	+	1.00041i
$342$	−31.7787	−	23.0885i	−1.71839	−	1.24849i
$343$	1.00000			0.0539949
$344$	−6.60383	−	4.79797i	−0.356055	−	0.258689i
$345$	9.12768	−	13.3620i	0.491418	−	0.719384i
$346$	−0.992699	+	0.721238i	−0.0533678	+	0.0387740i
$347$	−8.35670	+	6.07149i	−0.448611	+	0.325935i	−0.789047	−	0.614333i	$-0.789425\pi$
$347$	−8.35670	+	6.07149i	−0.448611	+	0.325935i	0.340436	+	0.940268i	$0.389425\pi$
$348$	−4.64875	−	14.3074i	−0.249199	−	0.766956i
$349$	25.4864			1.36426			0.682128	−	0.731233i	$-0.261055\pi$
$349$	25.4864			1.36426			0.682128	+	0.731233i	$0.261055\pi$
$350$	1.81831	+	4.65765i	0.0971928	+	0.248962i
$351$	75.1667			4.01210
$352$	−1.17344	−	3.61147i	−0.0625445	−	0.192492i
$353$	−23.3300	+	16.9503i	−1.24173	+	0.902171i	−0.997713	−	0.0675990i	$-0.978466\pi$
$353$	−23.3300	+	16.9503i	−1.24173	+	0.902171i	−0.244020	+	0.969770i	$0.578466\pi$
$354$	−21.9813	+	15.9704i	−1.16829	+	0.848815i
$355$	10.7274	+	13.8983i	0.569349	+	0.737645i
$356$	−0.353584	−	0.256894i	−0.0187399	−	0.0136153i
$357$	−18.8653			−0.998458
$358$	18.0592	+	13.1208i	0.954458	+	0.693454i
$359$	8.64902	−	26.6190i	0.456478	−	1.40489i	−0.412913	−	0.910770i	$-0.635489\pi$
$359$	8.64902	−	26.6190i	0.456478	−	1.40489i	0.869391	−	0.494124i	$-0.164511\pi$
$360$	−9.96211	−	12.9069i	−0.525049	−	0.680251i
$361$	3.09683	+	9.53107i	0.162991	+	0.501635i
$362$	2.20879	−	6.79796i	0.116092	−	0.357293i
$363$	−3.39006	+	10.4335i	−0.177932	+	0.547618i
$364$	−1.68717	−	5.19257i	−0.0884316	−	0.272164i
$365$	17.3489	−	6.19904i	0.908083	−	0.324473i
$366$	5.05269	−	15.5506i	0.264109	−	0.812843i
$367$	16.6637	+	12.1069i	0.869836	+	0.631973i	0.930543	−	0.366183i	$-0.119335\pi$
$367$	16.6637	+	12.1069i	0.869836	+	0.631973i	−0.0607067	+	0.998156i	$0.519335\pi$
$368$	2.25583			0.117593
$369$	−43.0844	−	31.3026i	−2.24288	−	1.62955i
$370$	0.0275335	+	0.948562i	0.00143140	+	0.0493134i
$371$	5.20889	−	3.78448i	0.270432	−	0.196480i
$372$	−13.2760	+	9.64558i	−0.688329	+	0.500100i
$373$	0.689466	+	2.12196i	0.0356992	+	0.109871i	0.967318	−	0.253566i	$-0.0816034\pi$
$373$	0.689466	+	2.12196i	0.0356992	+	0.109871i	−0.931619	+	0.363436i	$0.881603\pi$
$374$	−22.3307			−1.15469
$375$	23.5251	+	27.0741i	1.21483	+	1.39810i
$376$	−0.264979			−0.0136653
$377$	−7.91175	−	24.3498i	−0.407476	−	1.25408i
$378$	−11.1380	+	8.09224i	−0.572877	+	0.416220i
$379$	20.0609	−	14.5751i	1.03046	−	0.748673i	0.0620597	−	0.998072i	$-0.480233\pi$
$379$	20.0609	−	14.5751i	1.03046	−	0.748673i	0.968401	+	0.249399i	$0.0802331\pi$
$380$	0.349508	+	12.0410i	0.0179294	+	0.617690i
$381$	−3.56048	−	2.58684i	−0.182409	−	0.132528i
$382$	7.86859			0.402592
$383$	−18.2231	−	13.2398i	−0.931156	−	0.676524i	0.0151198	−	0.999886i	$-0.495187\pi$
$383$	−18.2231	−	13.2398i	−0.931156	−	0.676524i	−0.946276	+	0.323361i	$0.895187\pi$
$384$	0.991338	−	3.05103i	0.0505890	−	0.155697i
$385$	7.99596	−	2.85709i	0.407512	−	0.145611i
$386$	0.366811	+	1.12893i	0.0186702	+	0.0574610i
$387$	−18.3924	+	56.6060i	−0.934938	+	2.87744i
$388$	1.31426	−	4.04487i	0.0667213	−	0.205347i
$389$	−1.54725	−	4.76196i	−0.0784489	−	0.241441i	0.904139	−	0.427238i	$-0.140513\pi$
$389$	−1.54725	−	4.76196i	−0.0784489	−	0.241441i	−0.982588	+	0.185797i	$0.940513\pi$
$390$	−23.9304	−	31.0040i	−1.21176	−	1.56995i
$391$	4.09934	−	12.6165i	0.207312	−	0.638042i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$	5.30644			0.267674
$394$	13.1713	+	9.56948i	0.663558	+	0.482103i
$395$	−8.44823	−	10.9455i	−0.425077	−	0.550727i
$396$	−22.4003	+	16.2747i	−1.12566	+	0.817836i
$397$	21.0702	−	15.3084i	1.05748	−	0.768307i	0.0838621	−	0.996477i	$-0.473274\pi$
$397$	21.0702	−	15.3084i	1.05748	−	0.768307i	0.973621	+	0.228171i	$0.0732745\pi$
$398$	3.15431	+	9.70797i	0.158111	+	0.486617i
$399$	17.2822			0.865194
$400$	−1.26666	+	4.83690i	−0.0633329	+	0.241845i
$401$	14.9465			0.746393			0.373197	−	0.927752i	$-0.378262\pi$
$401$	14.9465			0.746393			0.373197	+	0.927752i	$0.378262\pi$
$402$	12.0844	+	37.1920i	0.602717	+	1.85497i
$403$	−22.5945	+	16.4159i	−1.12551	+	0.817734i
$404$	−5.17473	+	3.75966i	−0.257452	+	0.187050i
$405$	−28.1161	+	41.1590i	−1.39710	+	2.04521i
$406$	3.79378	+	2.75634i	0.188282	+	0.136795i
$407$	1.61154			0.0798811
$408$	−15.2623	−	11.0887i	−0.755599	−	0.548975i
$409$	10.0165	−	30.8275i	0.495282	−	1.52432i	−0.321234	−	0.947000i	$-0.604098\pi$
$409$	10.0165	−	30.8275i	0.495282	−	1.52432i	0.816516	−	0.577323i	$-0.195902\pi$
$410$	0.473851	+	16.3248i	0.0234018	+	0.806222i
$411$	−16.8422	−	51.8349i	−0.830764	−	2.55683i
$412$	−0.744208	+	2.29044i	−0.0366645	+	0.112842i
$413$	2.61721	−	8.05495i	0.128785	−	0.396358i
$414$	−5.08285	−	15.6434i	−0.249808	−	0.768831i
$415$	9.91191	−	14.5100i	0.486557	−	0.712267i
$416$	1.68717	−	5.19257i	0.0827202	−	0.254586i
$417$	8.62403	+	6.26572i	0.422320	+	0.306834i
$418$	20.4568			1.00058
$419$	5.57526	+	4.05067i	0.272369	+	0.197888i	0.715582	−	0.698528i	$-0.246161\pi$
$419$	5.57526	+	4.05067i	0.272369	+	0.197888i	−0.443213	+	0.896416i	$0.646161\pi$
$420$	6.88375	+	2.01782i	0.335892	+	0.0984597i
$421$	−7.92621	+	5.75873i	−0.386300	+	0.280663i	−0.763938	−	0.645290i	$-0.776736\pi$
$421$	−7.92621	+	5.75873i	−0.386300	+	0.280663i	0.377638	+	0.925953i	$0.376736\pi$
$422$	−0.522669	+	0.379741i	−0.0254431	+	0.0184855i
$423$	0.597051	+	1.83753i	0.0290296	+	0.0893440i
$424$	6.43854			0.312683
$425$	24.7501	+	15.8739i	1.20056	+	0.769996i
$426$	25.1883			1.22038
$427$	1.57501	+	4.84738i	0.0762201	+	0.234581i
$428$	−6.30254	+	4.57906i	−0.304645	+	0.221337i
$429$	−53.8085	+	39.0941i	−2.59790	+	1.88748i
$430$	17.1882	−	6.14164i	0.828891	−	0.296176i
$431$	14.6000	+	10.6075i	0.703259	+	0.510947i	0.880992	−	0.473131i	$-0.156876\pi$
$431$	14.6000	+	10.6075i	0.703259	+	0.510947i	−0.177733	+	0.984079i	$0.556876\pi$
$432$	−13.7673			−0.662381
$433$	−13.4768	−	9.79143i	−0.647651	−	0.470546i	0.214819	−	0.976654i	$-0.431084\pi$
$433$	−13.4768	−	9.79143i	−0.647651	−	0.470546i	−0.862470	+	0.506108i	$0.831084\pi$
$434$	1.58071	−	4.86493i	0.0758766	−	0.233524i
$435$	32.2804	+	9.46231i	1.54773	+	0.453683i
$436$	−3.00391	−	9.24510i	−0.143861	−	0.442760i
$437$	−3.75534	+	11.5578i	−0.179642	+	0.552883i
$438$	8.16772	−	25.1376i	0.390269	−	1.20112i
$439$	7.30777	+	22.4910i	0.348781	+	1.07344i	0.959529	+	0.281611i	$0.0908689\pi$
$439$	7.30777	+	22.4910i	0.348781	+	1.07344i	−0.610748	+	0.791825i	$0.709131\pi$
$440$	8.14823	+	2.38848i	0.388451	+	0.113866i
$441$	2.25320	−	6.93464i	0.107295	−	0.330221i
$442$	−25.9751	−	18.8720i	−1.23551	−	0.897651i
$443$	−7.83861			−0.372423			−0.186212	−	0.982510i	$-0.559621\pi$
$443$	−7.83861			−0.372423			−0.186212	+	0.982510i	$0.559621\pi$
$444$	1.10144	+	0.800243i	0.0522720	+	0.0379778i
$445$	0.920296	−	0.328837i	0.0436262	−	0.0155884i
$446$	−9.04487	+	6.57148i	−0.428287	+	0.311169i
$447$	−35.1019	+	25.5030i	−1.66026	+	1.20625i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	−21.0863			−0.995125			−0.497562	−	0.867428i	$-0.665771\pi$
$449$	−21.0863			−0.995125			−0.497562	+	0.867428i	$0.665771\pi$
$450$	36.3962	−	2.11469i	1.71573	−	0.0996875i
$451$	27.7346			1.30597
$452$	1.30801	+	4.02566i	0.0615238	+	0.189351i
$453$	−21.4810	+	15.6068i	−1.00926	+	0.733274i
$454$	−18.3325	+	13.3194i	−0.860387	+	0.625108i
$455$	11.7155	+	3.43415i	0.549231	+	0.160995i
$456$	13.9816	+	10.1582i	0.654749	+	0.475703i
$457$	41.0210			1.91888			0.959441	−	0.281908i	$-0.0909673\pi$
$457$	41.0210			1.91888			0.959441	+	0.281908i	$0.0909673\pi$
$458$	−4.39614	−	3.19398i	−0.205418	−	0.149245i
$459$	−25.0182	+	76.9982i	−1.16775	+	3.59397i
$460$	−2.84525	+	4.16515i	−0.132661	+	0.194201i
$461$	5.90362	+	18.1695i	0.274959	+	0.846237i	0.989230	+	0.146368i	$0.0467583\pi$
$461$	5.90362	+	18.1695i	0.274959	+	0.846237i	−0.714271	+	0.699869i	$0.753242\pi$
$462$	3.76443	−	11.5857i	0.175137	−	0.539017i
$463$	5.22297	−	16.0746i	0.242732	−	0.747052i	−0.753269	−	0.657712i	$-0.771524\pi$
$463$	5.22297	−	16.0746i	0.242732	−	0.747052i	0.996001	−	0.0893397i	$-0.0284757\pi$
$464$	1.44909	+	4.45985i	0.0672725	+	0.207044i
$465$	−1.06465	−	36.6785i	−0.0493720	−	1.70093i
$466$	−4.95844	+	15.2605i	−0.229696	+	0.706930i
$467$	11.0828	+	8.05210i	0.512849	+	0.372607i	0.813903	−	0.581000i	$-0.197338\pi$
$467$	11.0828	+	8.05210i	0.512849	+	0.372607i	−0.301054	+	0.953607i	$0.597338\pi$
$468$	−39.8101			−1.84022
$469$	−9.86193	−	7.16511i	−0.455382	−	0.330854i
$470$	0.334215	−	0.489255i	0.0154162	−	0.0225676i
$471$	−62.7551	+	45.5942i	−2.89160	+	2.10087i
$472$	6.85195	−	4.97823i	0.315387	−	0.229142i
$473$	−9.57853	−	29.4797i	−0.440421	−	1.35548i
$474$	−19.8368			−0.911134
$475$	−22.6732	−	14.5418i	−1.04032	−	0.667225i
$476$	5.88063			0.269538
$477$	−14.5073	−	44.6490i	−0.664245	−	2.04434i
$478$	−14.9149	+	10.8363i	−0.682193	+	0.495642i
$479$	−29.6687	+	21.5555i	−1.35560	+	0.984898i	−0.356884	+	0.934149i	$0.616161\pi$
$479$	−29.6687	+	21.5555i	−1.35560	+	0.984898i	−0.998711	+	0.0507494i	$0.983839\pi$
$480$	4.38302	+	5.67862i	0.200057	+	0.259192i
$481$	1.87455	+	1.36194i	0.0854721	+	0.0620991i
$482$	23.9192			1.08949
$483$	5.85470	+	4.25369i	0.266398	+	0.193549i
$484$	1.05674	−	3.25231i	0.0480336	−	0.147832i
$485$	5.81075	+	7.52837i	0.263852	+	0.341846i
$486$	9.33550	+	28.7317i	0.423467	+	1.30330i
$487$	−8.85910	+	27.2655i	−0.401444	+	1.23552i	0.522384	+	0.852710i	$0.325043\pi$
$487$	−8.85910	+	27.2655i	−0.401444	+	1.23552i	−0.923828	+	0.382808i	$0.874957\pi$
$488$	−1.57501	+	4.84738i	−0.0712974	+	0.219431i
$489$	−20.8057	−	64.0332i	−0.940864	−	2.89568i
$490$	−2.10568	+	0.752395i	−0.0951251	+	0.0339897i
$491$	−3.43886	+	10.5837i	−0.155194	+	0.477637i	−0.998180	−	0.0602972i	$-0.980795\pi$
$491$	−3.43886	+	10.5837i	−0.155194	+	0.477637i	0.842987	+	0.537934i	$0.180795\pi$
$492$	18.9558	+	13.7722i	0.854593	+	0.620898i
$493$	27.5765			1.24198
$494$	23.7954	+	17.2884i	1.07061	+	0.777842i
$495$	−1.79636	−	61.8867i	−0.0807402	−	2.78160i
$496$	4.13836	−	3.00669i	0.185818	−	0.135004i
$497$	−6.35208	+	4.61506i	−0.284930	+	0.207014i
$498$	−7.79050	−	23.9767i	−0.349101	−	1.07442i
$499$	23.2436			1.04053			0.520264	−	0.854006i	$-0.325834\pi$
$499$	23.2436			1.04053			0.520264	+	0.854006i	$0.325834\pi$
$500$	−7.33318	−	8.43946i	−0.327950	−	0.377424i
$501$	2.15130			0.0961128
$502$	−2.65235	−	8.16310i	−0.118380	−	0.364337i
$503$	34.7646	−	25.2580i	1.55008	−	1.12620i	0.606482	−	0.795097i	$-0.292580\pi$
$503$	34.7646	−	25.2580i	1.55008	−	1.12620i	0.943596	−	0.331100i	$-0.107420\pi$
$504$	5.89896	−	4.28584i	0.262760	−	0.190907i
$505$	−0.414980	−	14.2966i	−0.0184664	−	0.636189i
$506$	6.93015	+	5.03505i	0.308083	+	0.223835i
$507$	−53.9248			−2.39488
$508$	1.10986	+	0.806363i	0.0492422	+	0.0357766i
$509$	3.91144	−	12.0382i	0.173372	−	0.533583i	−0.826184	−	0.563401i	$-0.809493\pi$
$509$	3.91144	−	12.0382i	0.173372	−	0.533583i	0.999555	+	0.0298180i	$0.00949276\pi$
$510$	39.7244	−	14.1942i	1.75902	−	0.628528i
$511$	2.54602	+	7.83583i	0.112629	+	0.346637i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	22.9188	−	70.5369i	1.01189	−	3.11428i
$514$	−0.902203	−	2.77669i	−0.0397945	−	0.122475i
$515$	−3.29038	−	4.26300i	−0.144991	−	0.187850i
$516$	8.09208	−	24.9049i	0.356234	−	1.09638i
$517$	−0.814043	−	0.591437i	−0.0358016	−	0.0260114i
$518$	−0.424388			−0.0186466
$519$	−3.18462	−	2.31376i	−0.139789	−	0.101563i
$520$	7.45950	+	9.66448i	0.327121	+	0.423816i
$521$	−17.8911	+	12.9986i	−0.783823	+	0.569480i	−0.906124	−	0.423013i	$-0.860973\pi$
$521$	−17.8911	+	12.9986i	−0.783823	+	0.569480i	0.122301	+	0.992493i	$0.460973\pi$
$522$	27.6624	−	20.0979i	1.21075	−	0.879661i
$523$	8.62909	+	26.5576i	0.377324	+	1.16128i	0.941898	+	0.335900i	$0.109041\pi$
$523$	8.62909	+	26.5576i	0.377324	+	1.16128i	−0.564574	+	0.825383i	$0.690959\pi$
$524$	−1.65411			−0.0722600
$525$	−12.4081	+	10.1650i	−0.541532	+	0.443638i
$526$	−2.53154			−0.110381
$527$	−9.29559	−	28.6089i	−0.404922	−	1.24622i
$528$	9.85542	−	7.16038i	0.428902	−	0.311616i
$529$	14.4905	−	10.5279i	0.630021	−	0.457737i
$530$	−8.12085	+	11.8881i	−0.352747	+	0.516384i
$531$	−49.9611	−	36.2988i	−2.16813	−	1.57524i
$532$	−5.38717			−0.233563
$533$	32.2610	+	23.4390i	1.39738	+	1.01526i
$534$	0.433268	−	1.33346i	0.0187493	−	0.0577045i
$535$	−0.505423	−	17.4125i	−0.0218514	−	0.752806i
$536$	−3.76692	−	11.5934i	−0.162706	−	0.500758i
$537$	−22.1290	+	68.1062i	−0.954938	+	2.93900i
$538$	7.82433	−	24.0808i	0.337331	−	1.03820i
$539$	1.17344	+	3.61147i	0.0505436	+	0.155557i
$540$	17.3646	−	25.4199i	0.747252	−	1.09390i
$541$	5.79358	−	17.8308i	0.249085	−	0.766606i	−0.745852	−	0.666112i	$-0.767957\pi$
$541$	5.79358	−	17.8308i	0.249085	−	0.766606i	0.994938	−	0.100495i	$-0.0320426\pi$
$542$	7.99269	+	5.80703i	0.343315	+	0.249433i
$543$	22.9304			0.984039
$544$	4.75753	+	3.45655i	0.203978	+	0.148198i
$545$	20.8589	+	6.11433i	0.893495	+	0.261909i
$546$	14.1701	−	10.2952i	0.606424	−	0.440593i
$547$	16.6721	−	12.1130i	0.712846	−	0.517913i	−0.171244	−	0.985229i	$-0.554779\pi$
$547$	16.6721	−	12.1130i	0.712846	−	0.517913i	0.884091	+	0.467316i	$0.154779\pi$
$548$	5.24999	+	16.1578i	0.224269	+	0.690228i
$549$	37.1637			1.58611
$550$	−14.6873	+	12.0322i	−0.626269	+	0.513057i
$551$	−25.2624			−1.07621
$552$	2.23629	+	6.88261i	0.0951830	+	0.292943i
$553$	5.00253	−	3.63455i	0.212729	−	0.154557i
$554$	11.8638	−	8.61953i	0.504043	−	0.366209i
$555$	−2.86679	+	1.02435i	−0.121689	+	0.0434813i
$556$	−2.68826	−	1.95313i	−0.114007	−	0.0828313i
$557$	2.56000			0.108471			0.0542353	−	0.998528i	$-0.482728\pi$
$557$	2.56000			0.108471			0.0542353	+	0.998528i	$0.482728\pi$
$558$	−30.1749	−	21.9233i	−1.27740	−	0.928089i
$559$	13.7720	−	42.3858i	0.582493	−	1.79273i
$560$	−2.14578	−	0.628989i	−0.0906758	−	0.0265797i
$561$	−22.1373	−	68.1315i	−0.934636	−	2.87651i
$562$	0.958872	−	2.95110i	0.0404476	−	0.124485i
$563$	11.4632	−	35.2801i	0.483116	−	1.48688i	−0.351574	−	0.936160i	$-0.614353\pi$
$563$	11.4632	−	35.2801i	0.483116	−	1.48688i	0.834690	−	0.550719i	$-0.185647\pi$
$564$	−0.262684	−	0.808458i	−0.0110610	−	0.0340422i
$565$	−9.08271	−	2.66240i	−0.382113	−	0.112008i
$566$	3.47536	−	10.6961i	0.146080	−	0.449589i
$567$	−18.0343	−	13.1027i	−0.757369	−	0.550261i
$568$	−7.85161			−0.329446
$569$	−35.3365	−	25.6734i	−1.48138	−	1.07629i	−0.977108	−	0.212743i	$-0.931760\pi$
$569$	−35.3365	−	25.6734i	−1.48138	−	1.07629i	−0.504274	−	0.863544i	$-0.668240\pi$
$570$	−36.3909	+	13.0031i	−1.52425	+	0.544638i
$571$	3.52309	−	2.55968i	0.147437	−	0.107119i	−0.511622	−	0.859211i	$-0.670955\pi$
$571$	3.52309	−	2.55968i	0.147437	−	0.107119i	0.659058	+	0.752092i	$0.270955\pi$
$572$	16.7730	−	12.1863i	0.701315	−	0.509535i
$573$	7.80044	+	24.0073i	0.325868	+	1.00292i
$574$	−7.30373			−0.304852
$575$	−4.10180	−	10.5069i	−0.171057	−	0.438168i
$576$	7.29151			0.303813
$577$	12.2686	+	37.7588i	0.510747	+	1.57192i	0.790889	+	0.611960i	$0.209619\pi$
$577$	12.2686	+	37.7588i	0.510747	+	1.57192i	−0.280141	+	0.959959i	$0.590381\pi$
$578$	14.2240	−	10.3344i	0.591641	−	0.429853i
$579$	−3.08076	+	2.23830i	−0.128032	+	0.0930207i
$580$	−10.0624	−	2.94956i	−0.417816	−	0.122474i
$581$	6.35772	+	4.61915i	0.263762	+	0.191635i
$582$	13.6439			0.565557
$583$	19.7799	+	14.3709i	0.819198	+	0.595182i
$584$	−2.54602	+	7.83583i	−0.105355	+	0.324249i
$585$	50.2120	−	73.5050i	2.07601	−	3.03906i
$586$	−4.31389	−	13.2768i	−0.178205	−	0.548459i
$587$	−0.297905	+	0.916859i	−0.0122959	+	0.0378428i	−0.957016	−	0.290034i	$-0.906333\pi$
$587$	−0.297905	+	0.916859i	−0.0122959	+	0.0378428i	0.944720	+	0.327877i	$0.106333\pi$
$588$	−0.991338	+	3.05103i	−0.0408821	+	0.125822i
$589$	8.51556	+	26.2082i	0.350877	+	1.07989i
$590$	0.549483	+	18.9304i	0.0226218	+	0.779350i
$591$	−16.1396	+	49.6724i	−0.663892	+	2.04325i
$592$	−0.343337	−	0.249449i	−0.0141111	−	0.0102523i
$593$	25.7427			1.05713			0.528563	−	0.848894i	$-0.322731\pi$
$593$	25.7427			1.05713			0.528563	+	0.848894i	$0.322731\pi$
$594$	−42.2946	−	30.7289i	−1.73537	−	1.26082i
$595$	−7.41717	+	10.8579i	−0.304074	+	0.445132i
$596$	10.9419	−	7.94973i	0.448196	−	0.325633i
$597$	−26.4923	+	19.2478i	−1.08426	+	0.787759i
$598$	3.80597	+	11.7136i	0.155638	+	0.479003i
$599$	−46.9046			−1.91647			−0.958235	−	0.285981i	$-0.907681\pi$
$599$	−46.9046			−1.91647			−0.958235	+	0.285981i	$0.907681\pi$
$600$	−16.0132	+	0.930398i	−0.653736	+	0.0379834i
$601$	16.4580			0.671337			0.335669	−	0.941980i	$-0.391038\pi$
$601$	16.4580			0.671337			0.335669	+	0.941980i	$0.391038\pi$
$602$	2.52244	+	7.76327i	0.102807	+	0.316407i
$603$	−71.9084	+	52.2445i	−2.92833	+	2.12756i
$604$	6.69599	−	4.86492i	0.272456	−	0.197951i
$605$	4.67218	+	6.05325i	0.189951	+	0.246100i
$606$	−16.6007	−	12.0611i	−0.674358	−	0.489950i
$607$	−17.8133			−0.723019			−0.361510	−	0.932368i	$-0.617739\pi$
$607$	−17.8133			−0.723019			−0.361510	+	0.932368i	$0.617739\pi$
$608$	−4.35831	−	3.16650i	−0.176753	−	0.128418i
$609$	−4.64875	+	14.3074i	−0.188377	+	0.579764i
$610$	−6.96362	−	9.02202i	−0.281949	−	0.365291i
$611$	−0.447064	−	1.37592i	−0.0180863	−	0.0556638i
$612$	13.2503	−	40.7801i	0.535610	−	1.64844i
$613$	0.0961898	−	0.296042i	0.00388507	−	0.0119570i	−0.949095	−	0.314989i	$-0.897999\pi$
$613$	0.0961898	−	0.296042i	0.00388507	−	0.0119570i	0.952980	+	0.303032i	$0.0979990\pi$
$614$	9.40211	+	28.9367i	0.379438	+	1.16779i
$615$	−49.3375	+	17.6291i	−1.98948	+	0.710873i
$616$	−1.17344	+	3.61147i	−0.0472792	+	0.145510i
$617$	−29.2677	−	21.2642i	−1.17827	−	0.856066i	−0.186298	−	0.982493i	$-0.559649\pi$
$617$	−29.2677	−	21.2642i	−1.17827	−	0.856066i	−0.991976	+	0.126427i	$0.959649\pi$
$618$	−7.72595			−0.310783
$619$	15.8795	+	11.5371i	0.638249	+	0.463715i	0.859248	−	0.511559i	$-0.170932\pi$
$619$	15.8795	+	11.5371i	0.638249	+	0.463715i	−0.220999	+	0.975274i	$0.570932\pi$
$620$	0.331870	+	11.4333i	0.0133282	+	0.459173i
$621$	25.1255	−	18.2547i	1.00825	−	0.732537i
$622$	−4.67049	+	3.39331i	−0.187270	+	0.136059i
$623$	0.135057	+	0.415663i	0.00541094	+	0.0166532i
$624$	17.5152			0.701169
$625$	24.8318	−	2.89533i	0.993271	−	0.115813i
$626$	9.62872			0.384841
$627$	20.2796	+	62.4143i	0.809891	+	2.49259i
$628$	19.5618	−	14.2125i	0.780602	−	0.567140i
$629$	−2.01904	+	1.46692i	−0.0805045	+	0.0584899i
$630$	0.473058	+	16.2975i	0.0188471	+	0.649306i
$631$	−34.8652	−	25.3311i	−1.38796	−	1.00841i	−0.996085	−	0.0883959i	$-0.971826\pi$
$631$	−34.8652	−	25.3311i	−1.38796	−	1.00841i	−0.391877	−	0.920018i	$-0.628174\pi$
$632$	6.18346			0.245965
$633$	−1.67674	−	1.21822i	−0.0666445	−	0.0484201i
$634$	1.43221	−	4.40790i	0.0568805	−	0.175060i
$635$	−2.88872	+	1.03218i	−0.114635	+	0.0409610i
$636$	6.38278	+	19.6442i	0.253094	+	0.778942i
$637$	−1.68717	+	5.19257i	−0.0668480	+	0.205737i
$638$	−5.50268	+	16.9355i	−0.217853	+	0.670483i
$639$	17.6912	+	54.4481i	0.699855	+	2.15393i
$640$	−1.36626	−	1.77012i	−0.0540062	−	0.0699702i
$641$	−10.9631	+	33.7409i	−0.433016	+	1.33269i	0.462090	+	0.886833i	$0.347100\pi$
$641$	−10.9631	+	33.7409i	−0.433016	+	1.33269i	−0.895106	+	0.445854i	$0.852900\pi$
$642$	−20.2188	−	14.6898i	−0.797972	−	0.579761i
$643$	29.4923			1.16306			0.581532	−	0.813524i	$-0.302454\pi$
$643$	29.4923			1.16306			0.581532	+	0.813524i	$0.302454\pi$
$644$	−1.82501	−	1.32595i	−0.0719154	−	0.0522496i
$645$	35.7777	+	46.3533i	1.40874	+	1.82516i
$646$	−25.6296	+	18.6210i	−1.00838	+	0.732634i
$647$	−4.20466	+	3.05486i	−0.165302	+	0.120099i	−0.667361	−	0.744734i	$-0.732576\pi$
$647$	−4.20466	+	3.05486i	−0.165302	+	0.120099i	0.502059	+	0.864834i	$0.332576\pi$
$648$	−6.88848	−	21.2006i	−0.270605	−	0.832837i
$649$	32.1614			1.26244
$650$	−27.2530	+	1.58345i	−1.06895	+	0.0621081i
$651$	16.4100			0.643161
$652$	6.48548	+	19.9602i	0.253991	+	0.781703i
$653$	−21.8799	+	15.8967i	−0.856228	+	0.622086i	−0.926856	−	0.375417i	$-0.877500\pi$
$653$	−21.8799	+	15.8967i	−0.856228	+	0.622086i	0.0706282	+	0.997503i	$0.477500\pi$
$654$	25.2291	−	18.3300i	0.986537	−	0.716761i
$655$	2.08630	−	3.05413i	0.0815186	−	0.119335i
$656$	−5.90884	−	4.29302i	−0.230701	−	0.167614i
$657$	60.0753			2.34376
$658$	0.214373	+	0.155751i	0.00835712	+	0.00607180i
$659$	−2.53583	+	7.80448i	−0.0987819	+	0.304019i	−0.988221	−	0.153035i	$-0.951095\pi$
$659$	−2.53583	+	7.80448i	−0.0987819	+	0.304019i	0.889439	+	0.457054i	$0.151095\pi$
$660$	0.790341	+	27.2282i	0.0307640	+	1.05986i
$661$	−12.8914	−	39.6756i	−0.501416	−	1.54320i	−0.806713	−	0.590943i	$-0.798756\pi$
$661$	−12.8914	−	39.6756i	−0.501416	−	1.54320i	0.305297	−	0.952257i	$-0.401244\pi$
$662$	7.05536	−	21.7142i	0.274214	−	0.843945i
$663$	31.8289	−	97.9593i	1.23613	−	3.80442i
$664$	2.42843	+	7.47394i	0.0942414	+	0.290045i
$665$	6.79476	−	9.94681i	0.263490	−	0.385721i
$666$	−0.956232	+	2.94298i	−0.0370533	+	0.114038i
$667$	−8.55813	−	6.21785i	−0.331372	−	0.240756i
$668$	−0.670595			−0.0259461
$669$	−29.0163	−	21.0816i	−1.12183	−	0.815060i
$670$	26.1571	+	7.66739i	1.01054	+	0.296217i
$671$	−15.6580	+	11.3762i	−0.604471	+	0.439174i
$672$	−2.59536	+	1.88564i	−0.100118	+	0.0727401i
$673$	6.48685	+	19.9645i	0.250050	+	0.769574i	0.994765	+	0.102192i	$0.0325855\pi$
$673$	6.48685	+	19.9645i	0.250050	+	0.769574i	−0.744715	+	0.667383i	$0.767415\pi$
$674$	−11.6403			−0.448369
$675$	25.0333	+	64.1235i	0.963531	+	2.46811i
$676$	16.8093			0.646510
$677$	8.34844	+	25.6938i	0.320857	+	0.987495i	0.973276	+	0.229637i	$0.0737539\pi$
$677$	8.34844	+	25.6938i	0.320857	+	0.987495i	−0.652420	+	0.757858i	$0.726246\pi$
$678$	−10.9857	+	7.98158i	−0.421903	+	0.306531i
$679$	−3.44077	+	2.49987i	−0.132045	+	0.0959360i
$680$	−12.3828	+	4.42456i	−0.474857	+	0.169674i
$681$	−58.8114	−	42.7290i	−2.25366	−	1.63738i
$682$	19.4244			0.743800
$683$	5.18671	+	3.76836i	0.198464	+	0.144192i	0.682579	−	0.730812i	$-0.260858\pi$
$683$	5.18671	+	3.76836i	0.198464	+	0.144192i	−0.484115	+	0.875004i	$0.660858\pi$
$684$	−12.1384	+	37.3581i	−0.464122	+	1.42842i
$685$	−36.4554	−	10.6861i	−1.39289	−	0.408295i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	5.38686	−	16.5791i	0.205522	−	0.632531i
$688$	−2.52244	+	7.76327i	−0.0961671	+	0.295972i
$689$	10.8629	+	33.4326i	0.413843	+	1.27368i
$690$	−15.5286	−	4.55187i	−0.591163	−	0.173287i
$691$	6.24963	−	19.2344i	0.237747	−	0.731710i	−0.758998	−	0.651093i	$-0.774311\pi$
$691$	6.24963	−	19.2344i	0.237747	−	0.731710i	0.996745	−	0.0806173i	$-0.0256892\pi$
$692$	0.992699	+	0.721238i	0.0377368	+	0.0274174i
$693$	27.6882			1.05179
$694$	8.35670	+	6.07149i	0.317216	+	0.230471i
$695$	6.99691	−	2.50011i	0.265408	−	0.0948345i
$696$	−12.1706	+	8.84245i	−0.461325	+	0.335172i
$697$	−34.7477	+	25.2457i	−1.31616	+	0.956249i
$698$	−7.87573	−	24.2390i	−0.298101	−	0.917460i
$699$	−51.4757			−1.94699
$700$	3.86780	−	3.16861i	0.146189	−	0.119762i
$701$	−5.92807			−0.223900			−0.111950	−	0.993714i	$-0.535710\pi$
$701$	−5.92807			−0.223900			−0.111950	+	0.993714i	$0.535710\pi$
$702$	−23.2278	−	71.4878i	−0.876676	−	2.69813i
$703$	1.84962	−	1.34382i	0.0697596	−	0.0506833i
$704$	−3.07210	+	2.23201i	−0.115784	+	0.0841221i
$705$	1.82405	+	0.534681i	0.0686977	+	0.0201372i
$706$	23.3300	+	16.9503i	0.878037	+	0.637931i
$707$	6.39631			0.240558
$708$	21.9813	+	15.9704i	0.826109	+	0.600203i
$709$	11.0025	−	33.8623i	0.413208	−	1.27172i	−0.500635	−	0.865658i	$-0.666900\pi$
$709$	11.0025	−	33.8623i	0.413208	−	1.27172i	0.913844	−	0.406066i	$-0.133100\pi$
$710$	9.90313	−	14.4971i	0.371658	−	0.544067i
$711$	−13.9326	−	42.8801i	−0.522513	−	1.60813i
$712$	−0.135057	+	0.415663i	−0.00506147	+	0.0155776i
$713$	−3.56582	+	10.9745i	−0.133541	+	0.410997i
$714$	5.82970	+	17.9420i	0.218171	+	0.671461i
$715$	1.34509	+	46.3400i	0.0503034	+	1.73302i
$716$	6.89800	−	21.2298i	0.257790	−	0.793397i
$717$	−47.8476	−	34.7633i	−1.78690	−	1.29826i
$718$	−27.9888			−1.04453
$719$	10.6292	+	7.72259i	0.396403	+	0.288004i	0.768074	−	0.640361i	$-0.221215\pi$
$719$	10.6292	+	7.72259i	0.396403	+	0.288004i	−0.371671	+	0.928365i	$0.621215\pi$
$720$	−9.19669	+	13.4630i	−0.342740	+	0.501735i
$721$	1.94836	−	1.41557i	0.0725608	−	0.0527185i
$722$	8.10761	−	5.89052i	0.301734	−	0.219223i
$723$	23.7120	+	72.9781i	0.881860	+	2.71409i
$724$	−7.14780			−0.265646
$725$	18.1376	−	14.8588i	0.673612	−	0.551841i
$726$	10.9705			0.407152
$727$	11.0704	+	34.0710i	0.410577	+	1.26362i	0.916148	+	0.400840i	$0.131282\pi$
$727$	11.0704	+	34.0710i	0.410577	+	1.26362i	−0.505571	+	0.862785i	$0.668718\pi$
$728$	−4.41706	+	3.20918i	−0.163707	+	0.118940i
$729$	−24.3037	+	17.6577i	−0.900138	+	0.653989i
$730$	−11.2567	−	14.5842i	−0.416631	−	0.539784i
$731$	38.8347	+	28.2151i	1.43635	+	1.04357i
$732$	−16.3509			−0.604345
$733$	−30.7342	−	22.3297i	−1.13519	−	0.824766i	−0.148750	−	0.988875i	$-0.547525\pi$
$733$	−30.7342	−	22.3297i	−1.13519	−	0.824766i	−0.986442	+	0.164109i	$0.947525\pi$
$734$	6.36495	−	19.5893i	0.234935	−	0.723055i
$735$	−4.38302	−	5.67862i	−0.161670	−	0.209459i
$736$	−0.697091	−	2.14543i	−0.0256951	−	0.0790814i
$737$	14.3042	−	44.0239i	0.526903	−	1.62164i
$738$	−16.4568	+	50.6487i	−0.605782	+	1.86440i
$739$	4.95404	+	15.2470i	0.182237	+	0.560869i	0.999890	−	0.0148430i	$-0.00472485\pi$
$739$	4.95404	+	15.2470i	0.182237	+	0.560869i	−0.817652	+	0.575712i	$0.804725\pi$
$740$	0.893628	−	0.319308i	0.0328504	−	0.0117380i
$741$	−29.1580	+	89.7391i	−1.07115	+	3.29665i
$742$	−5.20889	−	3.78448i	−0.191224	−	0.138933i
$743$	−43.6949			−1.60301			−0.801505	−	0.597988i	$-0.795967\pi$
$743$	−43.6949			−1.60301			−0.801505	+	0.597988i	$0.795967\pi$
$744$	13.2760	+	9.64558i	0.486722	+	0.353624i
$745$	0.877467	+	30.2298i	0.0321479	+	1.10753i
$746$	1.80505	−	1.31144i	0.0660874	−	0.0480153i
$747$	46.3574	−	33.6806i	1.69613	−	1.23231i
$748$	6.90056	+	21.2377i	0.252309	+	0.776529i
$749$	7.79037			0.284654
$750$	18.4793	−	30.7401i	0.674770	−	1.12247i
$751$	39.1640			1.42911			0.714557	−	0.699578i	$-0.246628\pi$
$751$	39.1640			1.42911			0.714557	+	0.699578i	$0.246628\pi$
$752$	0.0818831	+	0.252010i	0.00298597	+	0.00918986i
$753$	22.2764	−	16.1848i	0.811799	−	0.589806i
$754$	−20.7132	+	15.0490i	−0.754331	+	0.548054i
$755$	0.536975	+	18.4995i	0.0195425	+	0.673264i
$756$	11.1380	+	8.09224i	0.405085	+	0.294312i
$757$	−1.52427			−0.0554006			−0.0277003	−	0.999616i	$-0.508818\pi$
$757$	−1.52427			−0.0554006			−0.0277003	+	0.999616i	$0.508818\pi$
$758$	−20.0609	−	14.5751i	−0.728646	−	0.529392i
$759$	−8.49194	+	26.1355i	−0.308238	+	0.948659i
$760$	11.3437	−	4.05328i	0.411478	−	0.147028i
$761$	−11.3810	−	35.0271i	−0.412561	−	1.26973i	−0.914414	−	0.404780i	$-0.867348\pi$
$761$	−11.3810	−	35.0271i	−0.412561	−	1.26973i	0.501853	−	0.864953i	$-0.332652\pi$
$762$	−1.35998	+	4.18560i	−0.0492670	+	0.151628i
$763$	−3.00391	+	9.24510i	−0.108749	+	0.334695i
$764$	−2.43153	−	7.48348i	−0.0879696	−	0.270743i
$765$	58.5835	+	75.9005i	2.11809	+	2.74419i
$766$	−6.96060	+	21.4225i	−0.251497	+	0.774027i
$767$	37.4102	+	27.1801i	1.35080	+	0.981416i
$768$	−3.20804			−0.115760
$769$	10.7686	+	7.82387i	0.388327	+	0.282136i	0.764770	−	0.644304i	$-0.222853\pi$
$769$	10.7686	+	7.82387i	0.388327	+	0.282136i	−0.376443	+	0.926440i	$0.622853\pi$
$770$	−5.18814	−	6.72173i	−0.186968	−	0.242234i
$771$	7.57738	−	5.50529i	0.272893	−	0.198268i
$772$	0.960325	−	0.697717i	0.0345628	−	0.0251114i
$773$	−0.229689	−	0.706910i	−0.00826133	−	0.0254258i	0.946841	−	0.321702i	$-0.104255\pi$
$773$	−0.229689	−	0.706910i	−0.00826133	−	0.0254258i	−0.955102	+	0.296277i	$0.904255\pi$
$774$	59.5191			2.13937
$775$	−21.5290	−	13.8079i	−0.773343	−	0.495996i
$776$	−4.25303			−0.152675
$777$	−0.420713	−	1.29482i	−0.0150930	−	0.0464514i
$778$	−4.05077	+	2.94305i	−0.145227	+	0.105514i
$779$	31.8319	−	23.1272i	1.14050	−	0.828619i
$780$	−22.0917	+	32.3399i	−0.791010	+	1.15795i
$781$	−24.1209	−	17.5249i	−0.863115	−	0.627090i
$782$	−13.2657			−0.474382
$783$	52.2302	+	37.9475i	1.86656	+	1.35613i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	1.56873	+	54.0448i	0.0559905	+	1.92894i
$786$	−1.63978	−	5.04672i	−0.0584890	−	0.180011i
$787$	8.01052	−	24.6538i	0.285544	−	0.878815i	−0.700691	−	0.713465i	$-0.747125\pi$
$787$	8.01052	−	24.6538i	0.285544	−	0.878815i	0.986235	−	0.165350i	$-0.0528753\pi$
$788$	5.03097	−	15.4837i	0.179221	−	0.551585i
$789$	−2.50962	−	7.72381i	−0.0893447	−	0.274975i
$790$	−7.79912	+	11.4171i	−0.277480	+	0.406202i
$791$	1.30801	−	4.02566i	0.0465077	−	0.143136i
$792$	22.4003	+	16.2747i	0.795959	+	0.578298i
$793$	−27.8277			−0.988189
$794$	−21.0702	−	15.3084i	−0.747754	−	0.543275i
$795$	−44.3213	−	12.9918i	−1.57191	−	0.460773i
$796$	8.25809	−	5.99986i	0.292700	−	0.212659i
$797$	7.88227	−	5.72680i	0.279204	−	0.202854i	−0.439366	−	0.898308i	$-0.644797\pi$
$797$	7.88227	−	5.72680i	0.279204	−	0.202854i	0.718570	+	0.695454i	$0.244797\pi$
$798$	−5.34050	−	16.4364i	−0.189052	−	0.581842i
$799$	1.55825			0.0551268
$800$	4.99158	−	0.290021i	0.176479	−	0.0102538i
$801$	3.18678			0.112599
$802$	−4.61873	−	14.2150i	−0.163093	−	0.501948i
$803$	−25.3113	+	18.3897i	−0.893216	+	0.648959i
$804$	31.6374	−	22.9860i	1.11577	−	0.810652i
$805$	4.75007	−	1.69728i	0.167418	−	0.0598212i
$806$	22.5945	+	16.4159i	0.795859	+	0.578225i
$807$	81.2278			2.85935
$808$	5.17473	+	3.75966i	0.182046	+	0.132264i
$809$	−5.61826	+	17.2912i	−0.197527	+	0.607927i	0.802410	+	0.596773i	$0.203551\pi$
$809$	−5.61826	+	17.2912i	−0.197527	+	0.607927i	−0.999938	+	0.0111541i	$0.996449\pi$
$810$	47.8329	+	14.0212i	1.68068	+	0.492654i
$811$	5.76341	+	17.7380i	0.202381	+	0.622864i	0.999811	+	0.0194524i	$0.00619229\pi$
$811$	5.76341	+	17.7380i	0.202381	+	0.622864i	−0.797430	+	0.603411i	$0.793808\pi$
$812$	1.44909	−	4.45985i	0.0508532	−	0.156510i
$813$	−9.79393	+	30.1426i	−0.343488	+	1.05715i
$814$	−0.497994	−	1.53267i	−0.0174547	−	0.0537199i
$815$	−45.0344	−	13.2009i	−1.57749	−	0.462407i
$816$	−5.82970	+	17.9420i	−0.204080	+	0.628095i
$817$	−35.5759	−	25.8474i	−1.24464	−	0.904287i
$818$	−32.4140			−1.13333
$819$	32.2070	+	23.3998i	1.12541	+	0.817655i
$820$	15.3793	−	5.49529i	0.537070	−	0.191904i
$821$	24.1122	−	17.5185i	0.841520	−	0.611400i	−0.0812745	−	0.996692i	$-0.525899\pi$
$821$	24.1122	−	17.5185i	0.841520	−	0.611400i	0.922795	+	0.385291i	$0.125899\pi$
$822$	−44.0934	+	32.0357i	−1.53793	+	1.11737i
$823$	−7.35317	−	22.6307i	−0.256315	−	0.788857i	−0.993568	−	0.113240i	$-0.963877\pi$
$823$	−7.35317	−	22.6307i	−0.256315	−	0.788857i	0.737252	−	0.675617i	$-0.236123\pi$
$824$	2.40831			0.0838974
$825$	−51.2708	−	32.8833i	−1.78502	−	1.14485i
$826$	−8.46948			−0.294691
$827$	−15.8606	−	48.8139i	−0.551527	−	1.69743i	−0.704943	−	0.709264i	$-0.749028\pi$
$827$	−15.8606	−	48.8139i	−0.551527	−	1.69743i	0.153417	−	0.988162i	$-0.450972\pi$
$828$	−13.3071	+	9.66815i	−0.462452	+	0.335991i
$829$	19.5635	−	14.2137i	0.679469	−	0.493663i	−0.193712	−	0.981058i	$-0.562053\pi$
$829$	19.5635	−	14.2137i	0.679469	−	0.493663i	0.873181	+	0.487395i	$0.162053\pi$
$830$	−16.8628	−	4.94296i	−0.585315	−	0.171573i
$831$	38.0594	+	27.6518i	1.32027	+	0.959230i
$832$	−5.45979			−0.189284
$833$	−4.75753	−	3.45655i	−0.164839	−	0.119762i
$834$	3.29409	−	10.1382i	0.114065	−	0.351056i
$835$	0.845813	−	1.23818i	0.0292706	−	0.0428490i
$836$	−6.32151	−	19.4556i	−0.218634	−	0.672886i
$837$	21.7622	−	66.9771i	0.752211	−	2.31507i
$838$	2.12956	−	6.55411i	0.0735645	−	0.226408i
$839$	−5.46044	−	16.8055i	−0.188515	−	0.580190i	0.811476	−	0.584386i	$-0.198664\pi$
$839$	−5.46044	−	16.8055i	−0.188515	−	0.580190i	−0.999991	+	0.00419569i	$0.998664\pi$
$840$	−0.208131	−	7.17037i	−0.00718120	−	0.247401i
$841$	−2.16616	+	6.66675i	−0.0746951	+	0.229888i
$842$	7.92621	+	5.75873i	0.273155	+	0.198459i
$843$	9.95446			0.342850
$844$	0.522669	+	0.379741i	0.0179910	+	0.0130712i
$845$	−21.2013	+	31.0365i	−0.729347	+	1.06769i
$846$	1.56310	−	1.13566i	0.0537405	−	0.0390448i
$847$	−2.76658	+	2.01004i	−0.0950608	+	0.0690657i
$848$	−1.98962	−	6.12342i	−0.0683238	−	0.210279i
$849$	36.0792			1.23824
$850$	7.44875	−	28.4440i	0.255490	−	0.975622i
$851$	0.957350			0.0328175
$852$	−7.78360	−	23.9555i	−0.266662	−	0.820700i
$853$	−1.28442	+	0.933188i	−0.0439778	+	0.0319517i	−0.609557	−	0.792742i	$-0.708653\pi$
$853$	−1.28442	+	0.933188i	−0.0439778	+	0.0319517i	0.565579	+	0.824694i	$0.308653\pi$
$854$	4.12343	−	2.99585i	0.141101	−	0.102516i
$855$	−53.6676	−	69.5314i	−1.83539	−	2.37792i
$856$	6.30254	+	4.57906i	0.215416	+	0.156509i
$857$	−15.4400			−0.527422			−0.263711	−	0.964602i	$-0.584947\pi$
$857$	−15.4400			−0.527422			−0.263711	+	0.964602i	$0.584947\pi$
$858$	53.8085	+	39.0941i	1.83699	+	1.33465i
$859$	5.08606	−	15.6533i	0.173534	−	0.534083i	−0.826029	−	0.563627i	$-0.809405\pi$
$859$	5.08606	−	15.6533i	0.173534	−	0.534083i	0.999563	+	0.0295438i	$0.00940545\pi$
$860$	−11.1525	−	14.4491i	−0.380297	−	0.492711i
$861$	−7.24047	−	22.2839i	−0.246754	−	0.759432i
$862$	5.57672	−	17.1634i	0.189944	−	0.584587i
$863$	−6.09141	+	18.7474i	−0.207354	+	0.638170i	0.792255	+	0.610191i	$0.208907\pi$
$863$	−6.09141	+	18.7474i	−0.207354	+	0.638170i	−0.999609	+	0.0279790i	$0.991093\pi$
$864$	4.25434	+	13.0935i	0.144736	+	0.445450i
$865$	−2.58377	+	0.923221i	−0.0878507	+	0.0313905i
$866$	−5.14766	+	15.8429i	−0.174925	+	0.538363i
$867$	45.6312	+	33.1530i	1.54972	+	1.12594i
$868$	−5.11529			−0.173624
$869$	18.9962	+	13.8016i	0.644403	+	0.468186i
$870$	−0.976003	−	33.6245i	−0.0330896	−	1.13998i
$871$	53.8440	−	39.1200i	1.82444	−	1.32553i
$872$	−7.86435	+	5.71379i	−0.266321	+	0.193493i
$873$	9.58292	+	29.4932i	0.324333	+	0.998194i
$874$	12.1526			0.411066
$875$	0.972077	+	11.1380i	0.0328622	+	0.376533i
$876$	−26.4313			−0.893030
$877$	9.31852	+	28.6794i	0.314664	+	0.968436i	0.975893	+	0.218251i	$0.0700353\pi$
$877$	9.31852	+	28.6794i	0.314664	+	0.968436i	−0.661229	+	0.750184i	$0.729965\pi$
$878$	19.1320	−	13.9002i	0.645673	−	0.469109i
$879$	36.2313	−	26.3236i	1.22205	−	0.887873i
$880$	−0.246363	−	8.48750i	−0.00830489	−	0.286114i
$881$	−15.4609	−	11.2330i	−0.520890	−	0.378449i	0.296049	−	0.955173i	$-0.404331\pi$
$881$	−15.4609	−	11.2330i	−0.520890	−	0.378449i	−0.816939	+	0.576724i	$0.804331\pi$
$882$	−7.29151			−0.245518
$883$	−30.4336	−	22.1113i	−1.02417	−	0.744104i	−0.0570377	−	0.998372i	$-0.518166\pi$
$883$	−30.4336	−	22.1113i	−1.02417	−	0.744104i	−0.967134	+	0.254268i	$0.918166\pi$
$884$	−9.92161	+	30.5356i	−0.333700	+	1.02702i
$885$	−57.2123	+	20.4429i	−1.92317	+	0.687180i
$886$	2.42226	+	7.45496i	0.0813775	+	0.250454i
$887$	14.9470	−	46.0021i	0.501871	−	1.54460i	−0.304098	−	0.952641i	$-0.598355\pi$
$887$	14.9470	−	46.0021i	0.501871	−	1.54460i	0.805969	−	0.591958i	$-0.201645\pi$
$888$	0.420713	−	1.29482i	0.0141182	−	0.0434513i
$889$	−0.423930	−	1.30472i	−0.0142182	−	0.0437590i
$890$	−0.597130	−	0.773638i	−0.0200158	−	0.0259324i
$891$	26.1578	−	80.5055i	0.876320	−	2.69704i
$892$	9.04487	+	6.57148i	0.302845	+	0.220029i
$893$	−1.42749			−0.0477690
$894$	35.1019	+	25.5030i	1.17398	+	0.852949i
$895$	30.4982	+	39.5133i	1.01944	+	1.32078i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−31.9654	+	23.2242i	−1.06729	+	0.775434i
$898$	6.51603	+	20.0543i	0.217443	+	0.669220i
$899$	−23.9875			−0.800027
$900$	−13.2582	−	33.9613i	−0.441941	−	1.13204i
$901$	−37.8627			−1.26139
$902$	−8.57047	−	26.3772i	−0.285365	−	0.878265i
$903$	−21.1854	+	15.3921i	−0.705004	+	0.512216i
$904$	3.42443	−	2.48799i	0.113895	−	0.0827494i
$905$	9.01543	−	13.1976i	0.299683	−	0.438704i
$906$	21.4810	+	15.6068i	0.713658	+	0.518503i
$907$	−9.91684			−0.329283			−0.164642	−	0.986353i	$-0.552647\pi$
$907$	−9.91684			−0.329283			−0.164642	+	0.986353i	$0.552647\pi$
$908$	18.3325	+	13.3194i	0.608386	+	0.442018i
$909$	14.4122	−	44.3561i	0.478022	−	1.47120i
$910$	−0.354220	−	12.2033i	−0.0117423	−	0.404536i
$911$	5.74321	+	17.6758i	0.190281	+	0.585624i	0.999999	−	0.00119425i	$-0.000380142\pi$
$911$	5.74321	+	17.6758i	0.190281	+	0.585624i	−0.809718	+	0.586819i	$0.800380\pi$
$912$	5.34050	−	16.4364i	0.176842	−	0.544263i
$913$	−9.22154	+	28.3810i	−0.305189	+	0.939274i
$914$	−12.6762	−	39.0133i	−0.419291	−	1.29045i
$915$	20.6231	−	30.1901i	0.681780	−	0.998053i
$916$	−1.67918	+	5.16797i	−0.0554816	+	0.170755i
$917$	1.33820	+	0.972260i	0.0441913	+	0.0321068i
$918$	80.9607			2.67210
$919$	−22.1365	−	16.0831i	−0.730215	−	0.530532i	0.159417	−	0.987211i	$-0.449039\pi$
$919$	−22.1365	−	16.0831i	−0.730215	−	0.530532i	−0.889631	+	0.456679i	$0.849039\pi$
$920$	4.84052	+	1.41890i	0.159587	+	0.0467796i
$921$	−78.9660	+	57.3722i	−2.60202	+	1.89048i
$922$	15.4559	−	11.2293i	0.509012	−	0.369819i
$923$	−13.2470	−	40.7700i	−0.436029	−	1.34196i
$924$	−12.1820			−0.400757
$925$	−0.537555	+	2.05272i	−0.0176747	+	0.0674931i
$926$	−16.9019			−0.555430
$927$	−5.42640	−	16.7008i	−0.178226	−	0.548525i
$928$	3.79378	−	2.75634i	0.124537	−	0.0904813i
$929$	10.0957	−	7.33495i	0.331229	−	0.240652i	−0.409723	−	0.912210i	$-0.634375\pi$
$929$	10.0957	−	7.33495i	0.331229	−	0.240652i	0.740952	+	0.671558i	$0.234375\pi$
$930$	−34.5544	+	12.3468i	−1.13308	+	0.404869i
$931$	4.35831	+	3.16650i	0.142838	+	0.103778i
$932$	16.0459			0.525600
$933$	−14.9831	−	10.8859i	−0.490526	−	0.356388i
$934$	4.23324	−	13.0286i	0.138516	−	0.426308i
$935$	−47.9167	−	14.0458i	−1.56704	−	0.459346i
$936$	12.3020	+	37.8617i	0.402103	+	1.23755i
$937$	−12.2187	+	37.6052i	−0.399167	+	1.22851i	0.526502	+	0.850174i	$0.323503\pi$
$937$	−12.2187	+	37.6052i	−0.399167	+	1.22851i	−0.925669	+	0.378335i	$0.876497\pi$
$938$	−3.76692	+	11.5934i	−0.122994	+	0.378538i
$939$	9.54532	+	29.3775i	0.311500	+	0.958698i
$940$	−0.568587	−	0.166669i	−0.0185453	−	0.00543615i
$941$	11.3733	−	35.0033i	0.370758	−	1.14108i	−0.575538	−	0.817775i	$-0.695207\pi$
$941$	11.3733	−	35.0033i	0.370758	−	1.14108i	0.946296	−	0.323301i	$-0.104793\pi$
$942$	62.7551	+	45.5942i	2.04467	+	1.48554i
$943$	16.4760			0.536532
$944$	−6.85195	−	4.97823i	−0.223012	−	0.162028i
$945$	−28.9896	+	10.3585i	−0.943033	+	0.336961i
$946$	−25.0769	+	18.2194i	−0.815321	+	0.592365i
$947$	−38.4373	+	27.9263i	−1.24904	+	0.907483i	−0.998166	−	0.0605356i	$-0.980719\pi$
$947$	−38.4373	+	27.9263i	−1.24904	+	0.907483i	−0.250877	+	0.968019i	$0.580719\pi$
$948$	6.12991	+	18.8659i	0.199090	+	0.612736i
$949$	−44.9836			−1.46023
$950$	−6.82369	+	26.0572i	−0.221390	+	0.845406i
$951$	14.8684			0.482142
$952$	−1.81722	−	5.59282i	−0.0588963	−	0.181264i
$953$	41.5882	−	30.2156i	1.34717	−	0.978779i	0.348027	−	0.937484i	$-0.386852\pi$
$953$	41.5882	−	30.2156i	1.34717	−	0.978779i	0.999147	−	0.0412948i	$-0.0131483\pi$
$954$	−37.9807	+	27.5946i	−1.22967	+	0.893408i
$955$	16.8843	+	4.94926i	0.546362	+	0.160154i
$956$	14.9149	+	10.8363i	0.482383	+	0.350472i
$957$	−57.1257			−1.84661
$958$	29.6687	+	21.5555i	0.958551	+	0.696428i
$959$	5.24999	−	16.1578i	0.169531	−	0.521763i
$960$	4.04626	−	5.92329i	0.130592	−	0.191173i
$961$	−1.49373	−	4.59722i	−0.0481848	−	0.148297i
$962$	0.716014	−	2.20366i	0.0230852	−	0.0710490i
$963$	17.5533	−	54.0234i	0.565646	−	1.74088i
$964$	−7.39144	−	22.7485i	−0.238062	−	0.732681i
$965$	0.0770119	+	2.65316i	0.00247910	+	0.0854081i
$966$	2.23629	−	6.88261i	0.0719516	−	0.221444i
$967$	25.2817	+	18.3682i	0.813005	+	0.590683i	0.914700	−	0.404133i	$-0.132427\pi$
$967$	25.2817	+	18.3682i	0.813005	+	0.590683i	−0.101695	+	0.994816i	$0.532427\pi$
$968$	−3.41968			−0.109913
$969$	−82.2208	−	59.7369i	−2.64131	−	1.91903i
$970$	5.36429	−	7.85274i	0.172237	−	0.252136i
$971$	9.56989	−	6.95294i	0.307113	−	0.223130i	−0.423544	−	0.905876i	$-0.639214\pi$
$971$	9.56989	−	6.95294i	0.307113	−	0.223130i	0.730657	+	0.682745i	$0.239214\pi$
$972$	24.4407	−	17.7572i	0.783935	−	0.569562i
$973$	1.02682	+	3.16023i	0.0329184	+	0.101312i
$974$	28.6687			0.918603
$975$	−31.8481	−	81.5798i	−1.01995	−	2.61264i
$976$	5.09684			0.163146
$977$	13.5909	+	41.8286i	0.434813	+	1.33822i	0.893278	+	0.449504i	$0.148399\pi$
$977$	13.5909	+	41.8286i	0.434813	+	1.33822i	−0.458465	+	0.888712i	$0.651601\pi$
$978$	−54.4699	+	39.5747i	−1.74176	+	1.26546i
$979$	−1.34267	+	0.975509i	−0.0429120	+	0.0311774i
$980$	1.36626	+	1.77012i	0.0436436	+	0.0565444i
$981$	57.3430	+	41.6621i	1.83082	+	1.33017i
$982$	11.1284			0.355121
$983$	−7.81457	−	5.67762i	−0.249246	−	0.181088i	0.456147	−	0.889905i	$-0.349229\pi$
$983$	−7.81457	−	5.67762i	−0.249246	−	0.181088i	−0.705393	+	0.708817i	$0.749229\pi$
$984$	7.24047	−	22.2839i	0.230818	−	0.710384i
$985$	22.2435	+	28.8186i	0.708737	+	0.918236i
$986$	−8.52159	−	26.2268i	−0.271383	−	0.835230i
$987$	−0.262684	+	0.808458i	−0.00836132	+	0.0257335i
$988$	9.08905	−	27.9732i	0.289161	−	0.889946i
$989$	−5.69021	−	17.5127i	−0.180938	−	0.556870i
$990$	−58.3027	+	20.8325i	−1.85298	+	0.662100i
$991$	6.67975	−	20.5581i	0.212189	−	0.653051i	−0.787152	−	0.616759i	$-0.788445\pi$
$991$	6.67975	−	20.5581i	0.212189	−	0.653051i	0.999341	−	0.0362920i	$-0.0115547\pi$
$992$	−4.13836	−	3.00669i	−0.131393	−	0.0954626i
$993$	73.2447			2.32435
$994$	6.35208	+	4.61506i	0.201476	+	0.146381i
$995$	0.662246	+	22.8152i	0.0209946	+	0.723290i
$996$	−20.3958	+	14.8184i	−0.646266	+	0.469539i
$997$	46.9530	−	34.1133i	1.48702	−	1.08038i	0.511805	−	0.859102i	$-0.328977\pi$
$997$	46.9530	−	34.1133i	1.48702	−	1.08038i	0.975211	−	0.221279i	$-0.0710230\pi$
$998$	−7.18267	−	22.1060i	−0.227364	−	0.699753i
$999$	−5.84270			−0.184855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.d.281.5	yes	20
25.11	even	5		8750.2.a.w.1.1		10
25.14	even	10		8750.2.a.x.1.10		10
25.21	even	5	inner	350.2.h.d.71.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.d.71.5	✓	20	25.21	even	5	inner
350.2.h.d.281.5	yes	20	1.1	even	1	trivial
8750.2.a.w.1.1		10	25.11	even	5
8750.2.a.x.1.10		10	25.14	even	10

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(2.59536 - 1.88564i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.0648780 - 2.23513i) q^{5} +(-2.59536 - 1.88564i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(2.25320 - 6.93464i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(2.59536 - 1.88564i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.0648780 - 2.23513i) q^{5} +(-2.59536 - 1.88564i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(2.25320 - 6.93464i) q^{9} +(-2.10568 + 0.752395i) q^{10} +(1.17344 + 3.61147i) q^{11} +(-0.991338 + 3.05103i) q^{12} +(-1.68717 + 5.19257i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-4.38302 - 5.67862i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.75753 - 3.45655i) q^{17} -7.29151 q^{18} +(4.35831 + 3.16650i) q^{19} +(1.36626 + 1.77012i) q^{20} +(2.59536 - 1.88564i) q^{21} +(3.07210 - 2.23201i) q^{22} +(0.697091 + 2.14543i) q^{23} +3.20804 q^{24} +(-4.99158 + 0.290021i) q^{25} +5.45979 q^{26} +(-4.25434 - 13.0935i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-3.79378 + 2.75634i) q^{29} +(-4.04626 + 5.92329i) q^{30} +(4.13836 + 3.00669i) q^{31} -1.00000 q^{32} +(9.85542 + 7.16038i) q^{33} +(-1.81722 + 5.59282i) q^{34} +(-0.0648780 - 2.23513i) q^{35} +(2.25320 + 6.93464i) q^{36} +(0.131143 - 0.403617i) q^{37} +(1.66473 - 5.12350i) q^{38} +(5.41250 + 16.6580i) q^{39} +(1.26129 - 1.84639i) q^{40} +(2.25698 - 6.94626i) q^{41} +(-2.59536 - 1.88564i) q^{42} -8.16279 q^{43} +(-3.07210 - 2.23201i) q^{44} +(-15.6460 - 4.58628i) q^{45} +(1.82501 - 1.32595i) q^{46} +(-0.214373 + 0.155751i) q^{47} +(-0.991338 - 3.05103i) q^{48} +1.00000 q^{49} +(1.81831 + 4.65765i) q^{50} -18.8653 q^{51} +(-1.68717 - 5.19257i) q^{52} +(5.20889 - 3.78448i) q^{53} +(-11.1380 + 8.09224i) q^{54} +(7.99596 - 2.85709i) q^{55} +(0.809017 + 0.587785i) q^{56} +17.2822 q^{57} +(3.79378 + 2.75634i) q^{58} +(2.61721 - 8.05495i) q^{59} +(6.88375 + 2.01782i) q^{60} +(1.57501 + 4.84738i) q^{61} +(1.58071 - 4.86493i) q^{62} +(2.25320 - 6.93464i) q^{63} +(0.309017 + 0.951057i) q^{64} +(11.7155 + 3.43415i) q^{65} +(3.76443 - 11.5857i) q^{66} +(-9.86193 - 7.16511i) q^{67} +5.88063 q^{68} +(5.85470 + 4.25369i) q^{69} +(-2.10568 + 0.752395i) q^{70} +(-6.35208 + 4.61506i) q^{71} +(5.89896 - 4.28584i) q^{72} +(2.54602 + 7.83583i) q^{73} -0.424388 q^{74} +(-12.4081 + 10.1650i) q^{75} -5.38717 q^{76} +(1.17344 + 3.61147i) q^{77} +(14.1701 - 10.2952i) q^{78} +(5.00253 - 3.63455i) q^{79} +(-2.14578 - 0.628989i) q^{80} +(-18.0343 - 13.1027i) q^{81} -7.30373 q^{82} +(6.35772 + 4.61915i) q^{83} +(-0.991338 + 3.05103i) q^{84} +(-7.41717 + 10.8579i) q^{85} +(2.52244 + 7.76327i) q^{86} +(-4.64875 + 14.3074i) q^{87} +(-1.17344 + 3.61147i) q^{88} +(0.135057 + 0.415663i) q^{89} +(0.473058 + 16.2975i) q^{90} +(-1.68717 + 5.19257i) q^{91} +(-1.82501 - 1.32595i) q^{92} +16.4100 q^{93} +(0.214373 + 0.155751i) q^{94} +(6.79476 - 9.94681i) q^{95} +(-2.59536 + 1.88564i) q^{96} +(-3.44077 + 2.49987i) q^{97} +(-0.309017 - 0.951057i) q^{98} +27.6882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9} - 9 q^{11} - 2 q^{12} + 5 q^{13} + 5 q^{14} - 5 q^{16} - 12 q^{17} - 34 q^{18} + 2 q^{19} + 5 q^{20} + 3 q^{21} - 6 q^{22} - 5 q^{23} + 2 q^{24} - 35 q^{25} + 20 q^{26} - 6 q^{27} - 5 q^{28} - 22 q^{29} - 25 q^{30} - 7 q^{31} - 20 q^{32} + 25 q^{33} - 18 q^{34} - 5 q^{35} - 6 q^{36} - 3 q^{37} + 8 q^{38} - 22 q^{39} + 19 q^{41} - 3 q^{42} + 2 q^{43} + 6 q^{44} + 45 q^{45} - 10 q^{46} - 14 q^{47} - 2 q^{48} + 20 q^{49} + 10 q^{50} + 38 q^{51} + 5 q^{52} - q^{53} - 19 q^{54} - 20 q^{55} + 5 q^{56} + 116 q^{57} + 22 q^{58} + 17 q^{59} - 5 q^{60} - 38 q^{61} + 7 q^{62} - 6 q^{63} - 5 q^{64} + 15 q^{65} - 16 q^{67} - 12 q^{68} + 35 q^{69} + q^{71} + 11 q^{72} + 19 q^{73} + 18 q^{74} + 35 q^{75} + 12 q^{76} - 9 q^{77} - 18 q^{78} - 64 q^{79} - 40 q^{81} + 26 q^{82} + 57 q^{83} - 2 q^{84} - 40 q^{85} - 2 q^{86} - 78 q^{87} + 9 q^{88} - 6 q^{89} + 10 q^{90} + 5 q^{91} + 10 q^{92} - 22 q^{93} + 14 q^{94} + 60 q^{95} - 3 q^{96} - 18 q^{97} + 5 q^{98} + 112 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9 - 9 * q^11 - 2 * q^12 + 5 * q^13 + 5 * q^14 - 5 * q^16 - 12 * q^17 - 34 * q^18 + 2 * q^19 + 5 * q^20 + 3 * q^21 - 6 * q^22 - 5 * q^23 + 2 * q^24 - 35 * q^25 + 20 * q^26 - 6 * q^27 - 5 * q^28 - 22 * q^29 - 25 * q^30 - 7 * q^31 - 20 * q^32 + 25 * q^33 - 18 * q^34 - 5 * q^35 - 6 * q^36 - 3 * q^37 + 8 * q^38 - 22 * q^39 + 19 * q^41 - 3 * q^42 + 2 * q^43 + 6 * q^44 + 45 * q^45 - 10 * q^46 - 14 * q^47 - 2 * q^48 + 20 * q^49 + 10 * q^50 + 38 * q^51 + 5 * q^52 - q^53 - 19 * q^54 - 20 * q^55 + 5 * q^56 + 116 * q^57 + 22 * q^58 + 17 * q^59 - 5 * q^60 - 38 * q^61 + 7 * q^62 - 6 * q^63 - 5 * q^64 + 15 * q^65 - 16 * q^67 - 12 * q^68 + 35 * q^69 + q^71 + 11 * q^72 + 19 * q^73 + 18 * q^74 + 35 * q^75 + 12 * q^76 - 9 * q^77 - 18 * q^78 - 64 * q^79 - 40 * q^81 + 26 * q^82 + 57 * q^83 - 2 * q^84 - 40 * q^85 - 2 * q^86 - 78 * q^87 + 9 * q^88 - 6 * q^89 + 10 * q^90 + 5 * q^91 + 10 * q^92 - 22 * q^93 + 14 * q^94 + 60 * q^95 - 3 * q^96 - 18 * q^97 + 5 * q^98 + 112 * q^99

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