LMFDB - Embedded newform 525.2.bm.a.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(131,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 12, 25]))

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

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

chi := DirichletCharacter("525.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bm (of order $30$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	525.131
Dual form			525.2.bm.a.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578671 + 2.72243i) q^{2} +(1.50155 + 0.863338i) q^{3} +(-5.24969 - 2.33731i) q^{4} +(2.12367 + 0.700010i) q^{5} +(-3.21928 + 3.58828i) q^{6} +(2.47291 + 0.940586i) q^{7} +(6.12911 - 8.43599i) q^{8} +(1.50929 + 2.59269i) q^{9} +O(q^{10})$	\(q+(-0.578671 + 2.72243i) q^{2} +(1.50155 + 0.863338i) q^{3} +(-5.24969 - 2.33731i) q^{4} +(2.12367 + 0.700010i) q^{5} +(-3.21928 + 3.58828i) q^{6} +(2.47291 + 0.940586i) q^{7} +(6.12911 - 8.43599i) q^{8} +(1.50929 + 2.59269i) q^{9} +(-3.13464 + 5.37648i) q^{10} +(1.84635 + 1.66246i) q^{11} +(-5.86477 - 8.04184i) q^{12} +(-3.47374 - 1.12869i) q^{13} +(-3.99168 + 6.18805i) q^{14} +(2.58445 + 2.88455i) q^{15} +(11.7294 + 13.0268i) q^{16} +(-0.136342 + 1.29721i) q^{17} +(-7.93180 + 2.60864i) q^{18} +(-0.168459 - 0.378366i) q^{19} +(-9.51248 - 8.63852i) q^{20} +(2.90115 + 3.54730i) q^{21} +(-5.59436 + 4.06454i) q^{22} +(0.487541 - 2.29370i) q^{23} +(16.4863 - 7.37556i) q^{24} +(4.01997 + 2.97318i) q^{25} +(5.08292 - 8.80388i) q^{26} +(0.0279123 + 5.19608i) q^{27} +(-10.7836 - 10.7178i) q^{28} +(-2.55906 - 3.52224i) q^{29} +(-9.34853 + 5.36679i) q^{30} +(-4.70925 - 0.494963i) q^{31} +(-24.1911 + 13.9667i) q^{32} +(1.33712 + 4.09028i) q^{33} +(-3.45267 - 1.12184i) q^{34} +(4.59324 + 3.72856i) q^{35} +(-1.86341 - 17.1385i) q^{36} +(-6.36959 - 7.07415i) q^{37} +(1.12756 - 0.239670i) q^{38} +(-4.24155 - 4.69379i) q^{39} +(18.9215 - 13.6248i) q^{40} +(2.10984 - 6.49342i) q^{41} +(-11.3361 + 5.84548i) q^{42} +1.79166 q^{43} +(-5.80706 - 13.0429i) q^{44} +(1.39034 + 6.56254i) q^{45} +(5.96232 + 2.65460i) q^{46} +(-0.154596 - 1.47088i) q^{47} +(6.36569 + 29.6867i) q^{48} +(5.23060 + 4.65197i) q^{49} +(-10.4205 + 9.22361i) q^{50} +(-1.32465 + 1.83011i) q^{51} +(15.5979 + 14.0445i) q^{52} +(0.474096 - 1.06484i) q^{53} +(-14.1621 - 2.93083i) q^{54} +(2.75730 + 4.82298i) q^{55} +(23.0915 - 15.0965i) q^{56} +(0.0737078 - 0.713572i) q^{57} +(11.0699 - 4.92865i) q^{58} +(12.4444 - 2.64515i) q^{59} +(-6.82548 - 21.1836i) q^{60} +(-1.77967 + 8.37271i) q^{61} +(4.07261 - 12.5342i) q^{62} +(1.29371 + 7.83111i) q^{63} +(-13.1911 - 40.5981i) q^{64} +(-6.58699 - 4.82861i) q^{65} +(-11.9093 + 1.27328i) q^{66} +(-0.0169675 + 0.161435i) q^{67} +(3.74774 - 6.49127i) q^{68} +(2.71231 - 3.02319i) q^{69} +(-12.8087 + 10.3472i) q^{70} +(-5.72396 - 7.87836i) q^{71} +(31.1225 + 3.15846i) q^{72} +(-7.71171 - 6.94365i) q^{73} +(22.9448 - 13.2472i) q^{74} +(3.46932 + 7.93497i) q^{75} +2.38004i q^{76} +(3.00217 + 5.84776i) q^{77} +(15.2330 - 8.83117i) q^{78} +(0.902116 + 8.58306i) q^{79} +(15.7905 + 35.8753i) q^{80} +(-4.44406 + 7.82626i) q^{81} +(16.4570 + 9.50145i) q^{82} +(-5.93052 - 4.30878i) q^{83} +(-6.93902 - 25.4031i) q^{84} +(-1.19761 + 2.65941i) q^{85} +(-1.03678 + 4.87766i) q^{86} +(-0.801664 - 7.49815i) q^{87} +(25.3409 - 5.38638i) q^{88} +(7.33932 + 1.56002i) q^{89} +(-18.6706 - 0.0124439i) q^{90} +(-7.52862 - 6.05849i) q^{91} +(-7.92053 + 10.9017i) q^{92} +(-6.64385 - 4.80889i) q^{93} +(4.09384 + 0.430280i) q^{94} +(-0.0928926 - 0.921448i) q^{95} +(-48.3821 + 0.0866324i) q^{96} +(-4.25313 - 5.85393i) q^{97} +(-15.6915 + 11.5480i) q^{98} +(-1.52355 + 7.29614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.578671	+	2.72243i	−0.409182	+	1.92505i	−0.0304709	+	0.999536i	$0.509701\pi$
$2$	−0.578671	+	2.72243i	−0.409182	+	1.92505i	−0.378711	+	0.925515i	$0.623633\pi$
$3$	1.50155	+	0.863338i	0.866919	+	0.498449i
$3$	1.50155	+	0.863338i	0.866919	+	0.498449i
$4$	−5.24969	−	2.33731i	−2.62484	−	1.16866i
$5$	2.12367	+	0.700010i	0.949735	+	0.313054i
$5$	2.12367	+	0.700010i	0.949735	+	0.313054i
$6$	−3.21928	+	3.58828i	−1.31427	+	1.46491i
$7$	2.47291	+	0.940586i	0.934673	+	0.355508i
$7$	2.47291	+	0.940586i	0.934673	+	0.355508i
$8$	6.12911	−	8.43599i	2.16697	−	2.98257i
$9$	1.50929	+	2.59269i	0.503098	+	0.864229i
$10$	−3.13464	+	5.37648i	−0.991259	+	1.70019i
$11$	1.84635	+	1.66246i	0.556695	+	0.501250i	0.898769	−	0.438423i	$-0.144463\pi$
$11$	1.84635	+	1.66246i	0.556695	+	0.501250i	−0.342074	+	0.939673i	$0.611129\pi$
$12$	−5.86477	−	8.04184i	−1.69301	−	2.32148i
$13$	−3.47374	−	1.12869i	−0.963441	−	0.313041i	−0.215276	−	0.976553i	$-0.569065\pi$
$13$	−3.47374	−	1.12869i	−0.963441	−	0.313041i	−0.748165	+	0.663512i	$0.769065\pi$
$14$	−3.99168	+	6.18805i	−1.06682	+	1.65383i
$15$	2.58445	+	2.88455i	0.667303	+	0.744787i
$16$	11.7294	+	13.0268i	2.93234	+	3.25669i
$17$	−0.136342	+	1.29721i	−0.0330678	+	0.314619i	0.965468	+	0.260522i	$0.0838948\pi$
$17$	−0.136342	+	1.29721i	−0.0330678	+	0.314619i	−0.998536	+	0.0540972i	$0.982772\pi$
$18$	−7.93180	+	2.60864i	−1.86954	+	0.614862i
$19$	−0.168459	−	0.378366i	−0.0386472	−	0.0868030i	0.893190	−	0.449679i	$-0.148462\pi$
$19$	−0.168459	−	0.378366i	−0.0386472	−	0.0868030i	−0.931837	+	0.362876i	$0.881795\pi$
$20$	−9.51248	−	8.63852i	−2.12705	−	1.93163i
$21$	2.90115	+	3.54730i	0.633084	+	0.774083i
$22$	−5.59436	+	4.06454i	−1.19272	+	0.866563i
$23$	0.487541	−	2.29370i	0.101659	−	0.478270i	−0.897636	−	0.440737i	$-0.854717\pi$
$23$	0.487541	−	2.29370i	0.101659	−	0.478270i	0.999295	−	0.0375322i	$-0.0119497\pi$
$24$	16.4863	−	7.37556i	3.36524	−	1.50553i
$25$	4.01997	+	2.97318i	0.803994	+	0.594637i
$26$	5.08292	−	8.80388i	0.996843	−	1.72658i
$27$	0.0279123	+	5.19608i	0.00537173	+	0.999986i
$28$	−10.7836	−	10.7178i	−2.03791	−	2.02546i
$29$	−2.55906	−	3.52224i	−0.475205	−	0.654064i	0.502369	−	0.864653i	$-0.332462\pi$
$29$	−2.55906	−	3.52224i	−0.475205	−	0.654064i	−0.977575	+	0.210589i	$0.932462\pi$
$30$	−9.34853	+	5.36679i	−1.70680	+	0.979838i
$31$	−4.70925	−	0.494963i	−0.845807	−	0.0888979i	−0.328296	−	0.944575i	$-0.606475\pi$
$31$	−4.70925	−	0.494963i	−0.845807	−	0.0888979i	−0.517511	+	0.855677i	$0.673141\pi$
$32$	−24.1911	+	13.9667i	−4.27642	+	2.46899i
$33$	1.33712	+	4.09028i	0.232762	+	0.712027i
$34$	−3.45267	−	1.12184i	−0.592128	−	0.192394i
$35$	4.59324	+	3.72856i	0.776399	+	0.630242i
$36$	−1.86341	−	17.1385i	−0.310568	−	2.85642i
$37$	−6.36959	−	7.07415i	−1.04715	−	1.16298i	−0.986321	−	0.164835i	$-0.947291\pi$
$37$	−6.36959	−	7.07415i	−1.04715	−	1.16298i	−0.0608336	−	0.998148i	$-0.519376\pi$
$38$	1.12756	−	0.239670i	0.182914	−	0.0388796i
$39$	−4.24155	−	4.69379i	−0.679191	−	0.751607i
$40$	18.9215	−	13.6248i	2.99175	−	2.15428i
$41$	2.10984	−	6.49342i	0.329502	−	1.01410i	−0.639866	−	0.768487i	$-0.721010\pi$
$41$	2.10984	−	6.49342i	0.329502	−	1.01410i	0.969367	−	0.245615i	$-0.0789899\pi$
$42$	−11.3361	+	5.84548i	−1.74920	+	0.901977i
$43$	1.79166			0.273225			0.136612	−	0.990625i	$-0.456378\pi$
$43$	1.79166			0.273225			0.136612	+	0.990625i	$0.456378\pi$
$44$	−5.80706	−	13.0429i	−0.875448	−	1.96629i
$45$	1.39034	+	6.56254i	0.207260	+	0.978286i
$46$	5.96232	+	2.65460i	0.879096	+	0.391399i
$47$	−0.154596	−	1.47088i	−0.0225502	−	0.214550i	−0.999994	−	0.00335663i	$-0.998932\pi$
$47$	−0.154596	−	1.47088i	−0.0225502	−	0.214550i	0.977444	−	0.211194i	$-0.0677351\pi$
$48$	6.36569	+	29.6867i	0.918808	+	4.28491i
$49$	5.23060	+	4.65197i	0.747228	+	0.664568i
$50$	−10.4205	+	9.22361i	−1.47369	+	1.30442i
$51$	−1.32465	+	1.83011i	−0.185489	+	0.256267i
$52$	15.5979	+	14.0445i	2.16305	+	1.94762i
$53$	0.474096	−	1.06484i	0.0651221	−	0.146267i	−0.878052	−	0.478564i	$-0.841157\pi$
$53$	0.474096	−	1.06484i	0.0651221	−	0.146267i	0.943174	+	0.332298i	$0.107824\pi$
$54$	−14.1621	−	2.93083i	−1.92722	−	0.398835i
$55$	2.75730	+	4.82298i	0.371794	+	0.650330i
$56$	23.0915	−	15.0965i	3.08573	−	2.01736i
$57$	0.0737078	−	0.713572i	0.00976284	−	0.0945149i
$58$	11.0699	−	4.92865i	1.45355	−	0.647163i
$59$	12.4444	−	2.64515i	1.62013	−	0.344369i	0.693531	−	0.720426i	$-0.256054\pi$
$59$	12.4444	−	2.64515i	1.62013	−	0.344369i	0.926596	+	0.376058i	$0.122721\pi$
$60$	−6.82548	−	21.1836i	−0.881166	−	2.73480i
$61$	−1.77967	+	8.37271i	−0.227864	+	1.07202i	0.704279	+	0.709924i	$0.251271\pi$
$61$	−1.77967	+	8.37271i	−0.227864	+	1.07202i	−0.932142	+	0.362092i	$0.882063\pi$
$62$	4.07261	−	12.5342i	0.517222	−	1.59185i
$63$	1.29371	+	7.83111i	0.162992	+	0.986627i
$64$	−13.1911	−	40.5981i	−1.64889	−	5.07476i
$65$	−6.58699	−	4.82861i	−0.817016	−	0.598915i
$66$	−11.9093	+	1.27328i	−1.46593	+	0.156730i
$67$	−0.0169675	+	0.161435i	−0.00207291	+	0.0197224i	−0.995509	−	0.0946621i	$-0.969823\pi$
$67$	−0.0169675	+	0.161435i	−0.00207291	+	0.0197224i	0.993437	+	0.114385i	$0.0364896\pi$
$68$	3.74774	−	6.49127i	0.454480	−	0.787182i
$69$	2.71231	−	3.02319i	0.326523	−	0.363949i
$70$	−12.8087	+	10.3472i	−1.53094	+	1.23672i
$71$	−5.72396	−	7.87836i	−0.679309	−	0.934989i	0.320616	−	0.947209i	$-0.396110\pi$
$71$	−5.72396	−	7.87836i	−0.679309	−	0.934989i	−0.999925	+	0.0122201i	$0.996110\pi$
$72$	31.1225	+	3.15846i	3.66782	+	0.372228i
$73$	−7.71171	−	6.94365i	−0.902587	−	0.812693i	0.0803252	−	0.996769i	$-0.474404\pi$
$73$	−7.71171	−	6.94365i	−0.902587	−	0.812693i	−0.982912	+	0.184076i	$0.941071\pi$
$74$	22.9448	−	13.2472i	2.66728	−	1.53995i
$75$	3.46932	+	7.93497i	0.400602	+	0.916252i
$76$			2.38004i			0.273010i
$77$	3.00217	+	5.84776i	0.342129	+	0.666414i
$78$	15.2330	−	8.83117i	1.72479	−	0.999933i
$79$	0.902116	+	8.58306i	0.101496	+	0.965670i	0.920199	+	0.391452i	$0.128027\pi$
$79$	0.902116	+	8.58306i	0.101496	+	0.965670i	−0.818703	+	0.574218i	$0.805306\pi$
$80$	15.7905	+	35.8753i	1.76543	+	4.01098i
$81$	−4.44406	+	7.82626i	−0.493784	+	0.869584i
$82$	16.4570	+	9.50145i	1.81737	+	1.04926i
$83$	−5.93052	−	4.30878i	−0.650959	−	0.472950i	0.212638	−	0.977131i	$-0.431794\pi$
$83$	−5.93052	−	4.30878i	−0.650959	−	0.472950i	−0.863598	+	0.504181i	$0.831794\pi$
$84$	−6.93902	−	25.4031i	−0.757109	−	2.77170i
$85$	−1.19761	+	2.65941i	−0.129899	+	0.288453i
$86$	−1.03678	+	4.87766i	−0.111799	+	0.525972i
$87$	−0.801664	−	7.49815i	−0.0859474	−	0.803886i
$88$	25.3409	−	5.38638i	2.70135	−	0.574190i
$89$	7.33932	+	1.56002i	0.777966	+	0.165362i	0.579748	−	0.814796i	$-0.303151\pi$
$89$	7.33932	+	1.56002i	0.777966	+	0.165362i	0.198218	+	0.980158i	$0.436484\pi$
$90$	−18.6706	−	0.0124439i	−1.96806	−	0.00131170i
$91$	−7.52862	−	6.05849i	−0.789214	−	0.635102i
$92$	−7.92053	+	10.9017i	−0.825773	+	1.13658i
$93$	−6.64385	−	4.80889i	−0.688935	−	0.498659i
$94$	4.09384	+	0.430280i	0.422248	+	0.0443800i
$95$	−0.0928926	−	0.921448i	−0.00953058	−	0.0945386i
$96$	−48.3821	+	0.0866324i	−4.93797	+	0.00884188i
$97$	−4.25313	−	5.85393i	−0.431840	−	0.594377i	0.536534	−	0.843879i	$-0.319733\pi$
$97$	−4.25313	−	5.85393i	−0.431840	−	0.594377i	−0.968374	+	0.249502i	$0.919733\pi$
$98$	−15.6915	+	11.5480i	−1.58508	+	1.16652i
$99$	−1.52355	+	7.29614i	−0.153123	+	0.733290i
$100$	−14.1543	−	25.0042i	−1.41543	−	2.50042i
$101$	2.94227	+	5.09616i	0.292767	+	0.507087i	0.974463	−	0.224549i	$-0.0720907\pi$
$101$	2.94227	+	5.09616i	0.292767	+	0.507087i	−0.681696	+	0.731635i	$0.738757\pi$
$102$	−4.21582	−	4.66532i	−0.417428	−	0.461935i
$103$	−6.81861	+	0.716665i	−0.671858	+	0.0706151i	−0.434314	−	0.900762i	$-0.643009\pi$
$103$	−6.81861	+	0.716665i	−0.671858	+	0.0706151i	−0.237544	+	0.971377i	$0.576342\pi$
$104$	−30.8125	+	22.3866i	−3.02141	+	2.19518i
$105$	3.67796	+	9.56413i	0.358932	+	0.933364i
$106$	2.62460	+	1.90688i	0.254924	+	0.185213i
$107$	1.23056	+	0.710467i	0.118963	+	0.0686834i	0.558301	−	0.829639i	$-0.311453\pi$
$107$	1.23056	+	0.710467i	0.118963	+	0.0686834i	−0.439338	+	0.898322i	$0.644787\pi$
$108$	11.9983	−	27.3430i	1.15454	−	2.63108i
$109$	−3.27790	+	0.696740i	−0.313966	+	0.0667356i	−0.362200	−	0.932100i	$-0.617974\pi$
$109$	−3.27790	+	0.696740i	−0.313966	+	0.0667356i	0.0482335	+	0.998836i	$0.484641\pi$
$110$	−14.7258	+	4.71564i	−1.40405	+	0.449619i
$111$	−3.45687	−	16.1213i	−0.328111	−	1.53017i
$112$	16.7529	+	43.2466i	1.58300	+	4.08641i
$113$	7.88290	+	2.56131i	0.741561	+	0.240948i	0.655346	−	0.755329i	$-0.272523\pi$
$113$	7.88290	+	2.56131i	0.741561	+	0.240948i	0.0862151	+	0.996277i	$0.472523\pi$
$114$	1.90000	+	0.613588i	0.177951	+	0.0574678i
$115$	2.64099	−	4.52979i	0.246274	−	0.422405i
$116$	5.20168	+	24.4720i	0.482964	+	2.27217i
$117$	−2.31656	−	10.7098i	−0.214166	−	0.990125i
$118$			35.4098i			3.25974i
$119$	−1.55730	+	3.07964i	−0.142757	+	0.282311i
$120$	40.1744	−	4.12272i	3.66740	−	0.376351i
$121$	−0.504583	−	4.80079i	−0.0458712	−	0.436435i
$122$	−21.7643	−	9.69009i	−1.97045	−	0.877299i
$123$	8.77404	−	7.92868i	0.791129	−	0.714905i
$124$	23.5652	+	13.6054i	2.11622	+	1.22180i
$125$	6.45585	+	9.12809i	0.577429	+	0.816441i
$126$	−22.0683	−	1.00960i	−1.96600	−	0.0899425i
$127$	−0.0617640	−	0.190090i	−0.00548067	−	0.0168678i	0.948279	−	0.317439i	$-0.102823\pi$
$127$	−0.0617640	−	0.190090i	−0.00548067	−	0.0168678i	−0.953759	+	0.300571i	$0.902823\pi$
$128$	62.5980	−	6.57931i	5.53293	−	0.581535i
$129$	2.69026	+	1.54680i	0.236864	+	0.136189i
$130$	16.9573	−	15.1385i	1.48725	−	1.32773i
$131$	−6.59045	+	2.93426i	−0.575811	+	0.256367i	−0.673915	−	0.738809i	$-0.735389\pi$
$131$	−6.59045	+	2.93426i	−0.575811	+	0.256367i	0.0981046	+	0.995176i	$0.468722\pi$
$132$	2.54083	−	24.5980i	0.221151	−	2.14098i
$133$	−0.0606997	−	1.09412i	−0.00526333	−	0.0948719i
$134$	−0.429677	−	0.139611i	−0.0371185	−	0.0120605i
$135$	−3.57803	+	11.0543i	−0.307948	+	0.951403i
$136$	10.1076	+	9.10091i	0.866719	+	0.780397i
$137$	4.42315	+	20.8093i	0.377895	+	1.77786i	0.597087	+	0.802176i	$0.296325\pi$
$137$	4.42315	+	20.8093i	0.377895	+	1.77786i	−0.219192	+	0.975682i	$0.570342\pi$
$138$	6.66090	+	9.13350i	0.567013	+	0.777495i
$139$	9.12470	−	2.96480i	0.773947	−	0.251471i	0.104693	−	0.994505i	$-0.466614\pi$
$139$	9.12470	−	2.96480i	0.773947	−	0.251471i	0.669254	+	0.743034i	$0.266614\pi$
$140$	−15.3983	−	30.3096i	−1.30139	−	2.56163i
$141$	1.03774	−	2.34207i	0.0873932	−	0.197238i
$142$	24.7606	−	11.0241i	2.07786	−	0.925124i
$143$	−4.53733	−	7.85889i	−0.379431	−	0.657193i
$144$	−16.0713	+	50.0718i	−1.33928	+	4.17265i
$145$	−2.96900	−	9.27146i	−0.246562	−	0.769952i
$146$	23.3662	−	16.9765i	1.93380	−	1.40499i
$147$	3.83777	+	11.5009i	0.316534	+	0.948581i
$148$	16.9039	+	52.0248i	1.38949	+	4.27641i
$149$	16.0753	+	9.28108i	1.31694	+	0.760336i	0.983235	−	0.182342i	$-0.0583677\pi$
$149$	16.0753	+	9.28108i	1.31694	+	0.760336i	0.333705	+	0.942678i	$0.391701\pi$
$150$	−23.6100	+	4.85325i	−1.92775	+	0.396266i
$151$	−10.0803	−	17.4596i	−0.820325	−	1.42084i	−0.905440	−	0.424473i	$-0.860459\pi$
$151$	−10.0803	−	17.4596i	−0.820325	−	1.42084i	0.0851154	−	0.996371i	$-0.472874\pi$
$152$	−4.22439	−	0.897923i	−0.342644	−	0.0728311i
$153$	−3.56904	+	1.60438i	−0.288540	+	0.129706i
$154$	−17.6574	+	4.78928i	−1.42287	+	0.385931i
$155$	−9.65444	−	4.34766i	−0.775463	−	0.349213i
$156$	11.2960	+	34.5547i	0.904400	+	2.76659i
$157$	−8.97645	+	5.18255i	−0.716399	+	0.413613i	−0.813426	−	0.581669i	$-0.802400\pi$
$157$	−8.97645	+	5.18255i	−0.716399	+	0.413613i	0.0970272	+	0.995282i	$0.469067\pi$
$158$	−23.8888	−	2.51082i	−1.90049	−	0.199750i
$159$	1.63119	−	1.18960i	0.129362	−	0.0943413i
$160$	−61.1508	+	12.7268i	−4.83439	+	1.00614i
$161$	3.36307	−	5.21355i	0.265047	−	0.410885i
$162$	−18.7348	−	16.6275i	−1.47195	−	1.30638i
$163$	4.68579	+	5.20410i	0.367019	+	0.407616i	0.898161	−	0.439667i	$-0.144903\pi$
$163$	4.68579	+	5.20410i	0.367019	+	0.407616i	−0.531142	+	0.847283i	$0.678237\pi$
$164$	−26.2531	+	29.1571i	−2.05003	+	2.27678i
$165$	−0.0236431	+	9.62242i	−0.00184061	+	0.749104i
$166$	15.1622	−	13.6521i	1.17681	−	1.05961i
$167$	2.17228	+	1.57825i	0.168096	+	0.122129i	0.668653	−	0.743575i	$-0.266871\pi$
$167$	2.17228	+	1.57825i	0.168096	+	0.122129i	−0.500557	+	0.865704i	$0.666871\pi$
$168$	47.7064	−	2.73237i	3.68063	−	0.210807i
$169$	0.275697	+	0.200305i	0.0212074	+	0.0154081i
$170$	−6.54704	−	4.79932i	−0.502135	−	0.368091i
$171$	0.726730	−	1.00783i	0.0555744	−	0.0770705i
$172$	−9.40563	−	4.18766i	−0.717173	−	0.319306i
$173$	9.76827	+	2.07631i	0.742668	+	0.157859i	0.563681	−	0.825992i	$-0.309385\pi$
$173$	9.76827	+	2.07631i	0.742668	+	0.157859i	0.178987	+	0.983851i	$0.442718\pi$
$174$	20.8771	+	2.15648i	1.58269	+	0.163483i
$175$	7.14451	+	11.1336i	0.540074	+	0.841618i
$176$			43.5515i			3.28282i
$177$	20.9696	+	6.77194i	1.57617	+	0.509010i
$178$	−8.49410	+	19.0781i	−0.636660	+	1.42996i
$179$	8.15158	−	18.3087i	0.609278	−	1.36846i	−0.300667	−	0.953729i	$-0.597209\pi$
$179$	8.15158	−	18.3087i	0.609278	−	1.36846i	0.909944	−	0.414730i	$-0.136124\pi$
$180$	8.03985	−	37.7010i	0.599255	−	2.81006i
$181$	−0.733492	+	1.00957i	−0.0545200	+	0.0750404i	−0.835406	−	0.549633i	$-0.814768\pi$
$181$	−0.733492	+	1.00957i	−0.0545200	+	0.0750404i	0.780886	+	0.624673i	$0.214768\pi$
$182$	20.8504	−	16.9903i	1.54554	−	1.25940i
$183$	−9.90075	+	11.0356i	−0.731884	+	0.815772i
$184$	−16.3614	−	18.1712i	−1.20618	−	1.33960i
$185$	−8.57496	−	19.4820i	−0.630443	−	1.43234i
$186$	16.9365	−	15.3047i	1.24184	−	1.12219i
$187$	−2.40829	+	2.16844i	−0.176112	+	0.158572i
$188$	−2.62633	+	8.08302i	−0.191545	+	0.589515i
$189$	−4.81833	+	12.8757i	−0.350482	+	0.936569i
$190$	2.56233	+	0.280321i	0.185891	+	0.0203367i
$191$	11.3358	−	10.2068i	0.820231	−	0.738539i	−0.147895	−	0.989003i	$-0.547250\pi$
$191$	11.3358	−	10.2068i	0.820231	−	0.738539i	0.968126	+	0.250464i	$0.0805832\pi$
$192$	15.2428	−	72.3484i	1.10005	−	5.22129i
$193$	−6.26331	−	10.8484i	−0.450843	−	0.780883i	0.547596	−	0.836743i	$-0.315543\pi$
$193$	−6.26331	−	10.8484i	−0.450843	−	0.780883i	−0.998439	+	0.0558601i	$0.982210\pi$
$194$	18.3981	−	8.19136i	1.32091	−	0.588106i
$195$	−5.72196	−	12.9372i	−0.409758	−	0.926451i
$196$	−16.5859	−	36.6469i	−1.18471	−	2.61764i
$197$	1.44857	+	1.99378i	0.103206	+	0.142051i	0.857496	−	0.514490i	$-0.172019\pi$
$197$	1.44857	+	1.99378i	0.103206	+	0.142051i	−0.754290	+	0.656541i	$0.772019\pi$
$198$	−18.9816	−	8.36984i	−1.34896	−	0.594818i
$199$	−8.46865	+	4.88938i	−0.600327	+	0.346599i	−0.769170	−	0.639044i	$-0.779330\pi$
$199$	−8.46865	+	4.88938i	−0.600327	+	0.346599i	0.168843	+	0.985643i	$0.445997\pi$
$200$	49.7206	−	15.6895i	3.51578	−	1.10941i
$201$	−0.164851	+	0.227754i	−0.0116277	+	0.0160645i
$202$	−15.5766	+	5.06113i	−1.09596	+	0.356100i
$203$	−3.01536	−	11.1172i	−0.211637	−	0.780275i
$204$	11.2316	−	6.51139i	0.786367	−	0.455889i
$205$	9.02607	−	12.3130i	0.630408	−	0.859976i
$206$	1.99466	−	18.9779i	0.138975	−	1.32225i
$207$	6.68269	−	2.19783i	0.464479	−	0.152760i
$208$	−26.0416	−	58.4904i	−1.80566	−	4.05558i
$209$	0.317983	−	0.978651i	0.0219953	−	0.0676947i
$210$	−28.1660	+	4.47852i	−1.94364	+	0.309047i
$211$	2.38676	+	7.34570i	0.164312	+	0.505699i	0.998985	−	0.0450464i	$-0.0143436\pi$
$211$	2.38676	+	7.34570i	0.164312	+	0.505699i	−0.834673	+	0.550745i	$0.814344\pi$
$212$	−4.97771	+	4.48195i	−0.341871	+	0.307822i
$213$	−1.79312	−	16.7715i	−0.122862	−	1.14916i
$214$	−2.64629	+	2.93900i	−0.180897	+	0.200906i
$215$	3.80489	+	1.25418i	0.259491	+	0.0855342i
$216$	44.0051	+	31.6118i	2.99417	+	2.15091i
$217$	−11.1800	−	5.65346i	−0.758949	−	0.383782i
$218$		−	9.32706i		−	0.631708i
$219$	−5.58478	−	17.0840i	−0.377384	−	1.15443i
$220$	−3.20216	−	31.7638i	−0.215889	−	2.14152i
$221$	1.93776	−	4.35228i	0.130348	−	0.292766i
$222$	45.8895	−	0.0821692i	3.07990	−	0.00551484i
$223$	19.6174	−	6.37407i	1.31368	−	0.426839i	0.433357	−	0.901222i	$-0.357329\pi$
$223$	19.6174	−	6.37407i	1.31368	−	0.426839i	0.880318	+	0.474383i	$0.157329\pi$
$224$	−72.9593	+	11.7847i	−4.87480	+	0.787399i
$225$	−1.64122	+	14.9099i	−0.109414	+	0.993996i
$226$	−11.5346	+	19.9785i	−0.767270	+	1.32895i
$227$	−5.99116	+	6.65386i	−0.397647	+	0.441632i	−0.908404	−	0.418093i	$-0.862699\pi$
$227$	−5.99116	+	6.65386i	−0.397647	+	0.441632i	0.510757	+	0.859725i	$0.329365\pi$
$228$	−2.05478	+	3.57375i	−0.136081	+	0.236677i
$229$	20.7483	−	2.18073i	1.37109	−	0.144107i	0.609816	−	0.792543i	$-0.291243\pi$
$229$	20.7483	−	2.18073i	1.37109	−	0.144107i	0.761269	+	0.648436i	$0.224576\pi$
$230$	10.8038	+	9.81117i	0.712380	+	0.646930i
$231$	−0.540692	+	11.3726i	−0.0355749	+	0.748261i
$232$	−45.3983			−2.98055
$233$	1.81941	+	4.08647i	0.119194	+	0.267713i	0.963282	−	0.268490i	$-0.0865247\pi$
$233$	1.81941	+	4.08647i	0.119194	+	0.267713i	−0.844089	+	0.536203i	$0.819858\pi$
$234$	30.4973	−	0.109217i	1.99367	−	0.00713972i
$235$	0.701322	−	3.23189i	0.0457492	−	0.210826i
$236$	−71.5119	−	15.2003i	−4.65503	−	0.989457i
$237$	−6.05551	+	13.6667i	−0.393348	+	0.887748i
$238$	−7.48296	−	6.02174i	−0.485048	−	0.390332i
$239$	−5.77714	+	1.87711i	−0.373692	+	0.121420i	−0.489841	−	0.871812i	$-0.662945\pi$
$239$	−5.77714	+	1.87711i	−0.373692	+	0.121420i	0.116149	+	0.993232i	$0.462945\pi$
$240$	−7.26237	+	67.5010i	−0.468784	+	4.35717i
$241$	1.28802	+	6.05965i	0.0829686	+	0.390336i	0.999963	−	0.00856282i	$-0.00272566\pi$
$241$	1.28802	+	6.05965i	0.0829686	+	0.390336i	−0.916995	+	0.398899i	$0.869392\pi$
$242$	13.3618	+	1.40438i	0.858930	+	0.0902772i
$243$	−13.4297	+	7.91478i	−0.861514	+	0.507733i
$244$	28.9124	−	39.7945i	1.85092	−	2.54758i
$245$	7.85165	+	13.5407i	0.501623	+	0.865086i
$246$	16.5080	+	28.4748i	1.05251	+	1.81549i
$247$	0.158127	+	1.50448i	0.0100614	+	0.0957278i
$248$	−33.0390	+	36.6935i	−2.09798	+	2.33004i
$249$	−5.18503	−	11.5899i	−0.328588	−	0.734479i
$250$	−28.5864	+	12.2934i	−1.80796	+	0.777506i
$251$	−9.37525			−0.591760			−0.295880	−	0.955225i	$-0.595613\pi$
$251$	−9.37525			−0.591760			−0.295880	+	0.955225i	$0.595613\pi$
$252$	11.5122	−	44.1347i	0.725199	−	2.78022i
$253$	4.71335	−	3.42445i	0.296326	−	0.215293i
$254$	0.553249	−	0.0581488i	0.0347139	−	0.00364858i
$255$	−4.09423	+	2.95929i	−0.256391	+	0.185318i
$256$	−9.38781	+	89.3191i	−0.586738	+	5.58244i
$257$	−3.38567	+	5.86415i	−0.211192	+	0.365796i	−0.952088	−	0.305824i	$-0.901068\pi$
$257$	−3.38567	+	5.86415i	−0.211192	+	0.365796i	0.740896	+	0.671620i	$0.234401\pi$
$258$	−5.76785	+	6.42895i	−0.359090	+	0.400249i
$259$	−9.09760	−	23.4849i	−0.565298	−	1.45928i
$260$	23.2937	+	40.7445i	1.44461	+	2.52687i
$261$	5.26970	−	11.9509i	0.326186	−	0.739745i
$262$	−4.17462	−	19.6400i	−0.257909	−	1.21337i
$263$	−3.67617	−	17.2950i	−0.226682	−	1.06646i	−0.933366	−	0.358926i	$-0.883143\pi$
$263$	−3.67617	−	17.2950i	−0.226682	−	1.06646i	0.706684	−	0.707529i	$-0.250190\pi$
$264$	42.7009	+	13.7899i	2.62806	+	0.848709i
$265$	1.75222	−	1.92949i	0.107638	−	0.118528i
$266$	3.01378	+	0.467882i	0.184787	+	0.0286877i
$267$	9.67351	+	8.67876i	0.592009	+	0.531131i
$268$	0.466398	−	0.807825i	0.0284898	−	0.0493458i
$269$	0.213416	−	2.03052i	0.0130122	−	0.123803i	−0.986087	−	0.166227i	$-0.946841\pi$
$269$	0.213416	−	2.03052i	0.0130122	−	0.123803i	0.999100	+	0.0424243i	$0.0135081\pi$
$270$	−28.0241	−	16.1377i	−1.70549	−	0.982112i
$271$	3.78972	−	0.398315i	0.230209	−	0.0241959i	0.0112785	−	0.999936i	$-0.496410\pi$
$271$	3.78972	−	0.398315i	0.230209	−	0.0241959i	0.218930	+	0.975740i	$0.429743\pi$
$272$	−18.4977	+	13.4393i	−1.12159	+	0.814880i
$273$	−6.07407	−	15.5969i	−0.367619	−	0.943965i
$274$	−59.2115			−3.57709
$275$	2.47947	+	12.1726i	0.149518	+	0.734033i
$276$	−21.3049	+	9.53130i	−1.28240	+	0.573717i
$277$	13.1684	−	14.6250i	0.791212	−	0.878730i	−0.203746	−	0.979024i	$-0.565312\pi$
$277$	13.1684	−	14.6250i	0.791212	−	0.878730i	0.994958	+	0.100294i	$0.0319783\pi$
$278$	2.79126	+	26.5570i	0.167408	+	1.59278i
$279$	−5.82437	−	12.9567i	−0.348696	−	0.775696i
$280$	59.6065	−	15.8958i	3.56217	−	0.949954i
$281$	4.58504	−	6.31076i	0.273520	−	0.376469i	−0.650054	−	0.759888i	$-0.725254\pi$
$281$	4.58504	−	6.31076i	0.273520	−	0.376469i	0.923574	+	0.383420i	$0.125254\pi$
$282$	5.77562	+	4.18046i	0.343933	+	0.248943i
$283$	−16.3676	−	1.72031i	−0.972954	−	0.102262i	−0.395308	−	0.918549i	$-0.629362\pi$
$283$	−16.3676	−	1.72031i	−0.972954	−	0.102262i	−0.577647	+	0.816287i	$0.696029\pi$
$284$	11.6348	+	54.7376i	0.690401	+	3.24808i
$285$	0.656039	−	1.46380i	0.0388604	−	0.0867078i
$286$	24.0209	−	7.80487i	1.42039	−	0.461512i
$287$	11.3251	−	14.0732i	0.668498	−	0.830713i
$288$	−72.7228	−	41.6400i	−4.28523	−	2.45366i
$289$	14.9643	+	3.18077i	0.880256	+	0.187104i
$290$	26.9590	−	2.71778i	1.58309	−	0.159593i
$291$	−1.33236	−	12.4619i	−0.0781043	−	0.730527i
$292$	24.2546	+	54.4767i	1.41939	+	3.18801i
$293$	−18.9930			−1.10959			−0.554793	−	0.831989i	$-0.687202\pi$
$293$	−18.9930			−1.10959			−0.554793	+	0.831989i	$0.687202\pi$
$294$	−33.5313	+	3.79281i	−1.95559	+	0.221201i
$295$	28.2795	+	3.09380i	1.64650	+	0.180128i
$296$	−98.7174	+	10.3756i	−5.73783	+	0.603070i
$297$	−8.58673	+	9.64017i	−0.498252	+	0.559379i
$298$	−34.5694	+	38.3932i	−2.00255	+	2.22406i
$299$	−4.28246	+	7.41743i	−0.247661	+	0.428961i
$300$	0.333667	−	49.7650i	0.0192643	−	2.87319i
$301$	4.43061	+	1.68521i	0.255376	+	0.0971337i
$302$	53.3659	−	17.3396i	3.07086	−	0.997783i
$303$	0.0182502	+	10.1923i	0.00104845	+	0.585533i
$304$	2.95297	−	6.63247i	0.169364	−	0.380398i
$305$	−9.64042	+	16.5351i	−0.552009	+	0.946797i
$306$	−2.30251	−	10.6449i	−0.131626	−	0.608527i
$307$		−	8.64444i		−	0.493365i	−0.969096	−	0.246682i	$-0.920660\pi$
$307$		−	8.64444i		−	0.493365i	0.969096	−	0.246682i	$-0.0793404\pi$
$308$	−2.09242	−	37.7159i	−0.119227	−	2.14907i
$309$	−10.8572	−	4.81066i	−0.617645	−	0.273669i
$310$	17.4230	−	23.7677i	0.989558	−	1.34991i
$311$	3.09035	−	3.43219i	0.175238	−	0.194621i	−0.649127	−	0.760680i	$-0.724866\pi$
$311$	3.09035	−	3.43219i	0.175238	−	0.194621i	0.824365	+	0.566058i	$0.191532\pi$
$312$	−65.5936	+	7.01294i	−3.71351	+	0.397029i
$313$	−5.95215	+	5.35934i	−0.336435	+	0.302928i	−0.819980	−	0.572392i	$-0.806016\pi$
$313$	−5.95215	+	5.35934i	−0.336435	+	0.302928i	0.483545	+	0.875319i	$0.339349\pi$
$314$	−8.91475	−	27.4368i	−0.503088	−	1.54835i
$315$	−2.73444	+	17.5363i	−0.154068	+	0.988060i
$316$	15.3255	−	47.1669i	0.862124	−	2.65335i
$317$	8.54133	+	19.1841i	0.479729	+	1.07749i	0.977645	+	0.210263i	$0.0674320\pi$
$317$	8.54133	+	19.1841i	0.479729	+	1.07749i	−0.497916	+	0.867225i	$0.665901\pi$
$318$	2.29468	+	5.12920i	0.128679	+	0.287631i
$319$	1.13067	−	10.7576i	0.0633054	−	0.602311i
$320$	0.405446	−	95.4509i	0.0226651	−	5.33587i
$321$	1.23438	+	2.12919i	0.0688963	+	0.118840i
$322$	12.2474	+	12.1727i	0.682522	+	0.678356i
$323$	0.513788	−	0.166940i	0.0285879	−	0.00928878i
$324$	41.6223	−	30.6983i	2.31235	−	1.70546i
$325$	−10.6085	−	14.8653i	−0.588456	−	0.824581i
$326$	−16.8793	+	9.74529i	−0.934860	+	0.539741i
$327$	−5.52345	−	1.78375i	−0.305448	−	0.0986417i
$328$	−41.8470	−	57.5974i	−2.31061	−	3.18029i
$329$	1.00119	−	3.78278i	0.0551974	−	0.208551i
$330$	−26.1827	−	5.63258i	−1.44131	−	0.310063i
$331$	−2.56800	+	1.14335i	−0.141150	+	0.0628440i	−0.476096	−	0.879393i	$-0.657949\pi$
$331$	−2.56800	+	1.14335i	−0.141150	+	0.0628440i	0.334946	+	0.942237i	$0.391282\pi$
$332$	21.0624	+	36.4812i	1.15595	+	2.00217i
$333$	8.72747	−	27.1913i	0.478262	−	1.49008i
$334$	−5.55372	+	5.00059i	−0.303886	+	0.273620i
$335$	−0.149040	+	0.330958i	−0.00814290	+	0.0180821i
$336$	−12.1811	+	79.4002i	−0.664535	+	4.33164i
$337$	−5.93433	+	18.2640i	−0.323264	+	0.994904i	0.648954	+	0.760827i	$0.275207\pi$
$337$	−5.93433	+	18.2640i	−0.323264	+	0.994904i	−0.972218	+	0.234076i	$0.924793\pi$
$338$	−0.704856	+	0.634655i	−0.0383391	+	0.0345207i
$339$	9.62528	+	10.6515i	0.522774	+	0.578512i
$340$	12.5029	−	11.1619i	0.678066	−	0.605338i
$341$	−7.87206	−	8.74281i	−0.426296	−	0.473450i
$342$	2.32321	+	2.56167i	0.125625	+	0.138519i
$343$	8.55923	+	16.4238i	0.462155	+	0.886799i
$344$	10.9812	−	15.1144i	0.592069	−	0.814913i
$345$	7.87631	−	4.52162i	0.424046	−	0.243436i
$346$	−11.3052	+	25.3920i	−0.607773	+	1.36508i
$347$	11.6646	−	26.1992i	0.626189	−	1.40644i	−0.270038	−	0.962850i	$-0.587036\pi$
$347$	11.6646	−	26.1992i	0.626189	−	1.40644i	0.896227	−	0.443595i	$-0.146297\pi$
$348$	−13.3170	+	41.2367i	−0.713867	+	2.21052i
$349$			23.7914i			1.27352i	0.771061	+	0.636761i	$0.219726\pi$
$349$			23.7914i			1.27352i	−0.771061	+	0.636761i	$0.780274\pi$
$350$	−34.4447	+	13.0078i	−1.84114	+	0.695295i
$351$	5.76778	−	18.0813i	0.307861	−	0.965109i
$352$	−67.8842	−	14.4292i	−3.61824	−	0.769081i
$353$	−13.4570	−	5.99143i	−0.716242	−	0.318892i	0.0160604	−	0.999871i	$-0.494888\pi$
$353$	−13.4570	−	5.99143i	−0.716242	−	0.318892i	−0.732302	+	0.680980i	$0.761554\pi$
$354$	−30.5706	+	53.1695i	−1.62481	+	2.82593i
$355$	−6.64089	−	20.7379i	−0.352462	−	1.10065i
$356$	−34.8829	−	25.3439i	−1.84879	−	1.34322i
$357$	−4.99713	+	3.27976i	−0.264476	+	0.173583i
$358$	45.1272	+	32.7869i	2.38505	+	1.73284i
$359$	11.3012	−	10.1756i	0.596452	−	0.537048i	−0.314661	−	0.949204i	$-0.601891\pi$
$359$	11.3012	−	10.1756i	0.596452	−	0.537048i	0.911113	+	0.412156i	$0.135224\pi$
$360$	63.8831	+	28.4936i	3.36693	+	1.50175i
$361$	12.5987	−	13.9923i	0.663089	−	0.736435i
$362$	−2.32402	−	2.58109i	−0.122148	−	0.135659i
$363$	3.38705	−	7.64424i	0.177774	−	0.401219i
$364$	25.3623	+	49.4019i	1.32935	+	2.58936i
$365$	−11.5165	−	20.1443i	−0.602802	−	1.05440i
$366$	−24.3143	−	33.3401i	−1.27093	−	1.74271i
$367$	−12.6171	−	1.32611i	−0.658607	−	0.0692223i	−0.230671	−	0.973032i	$-0.574092\pi$
$367$	−12.6171	−	1.32611i	−0.658607	−	0.0692223i	−0.427935	+	0.903809i	$0.640759\pi$
$368$	35.5981	−	20.5526i	1.85568	−	1.07138i
$369$	20.0198	−	4.33033i	1.04219	−	0.225428i
$370$	58.0004	−	12.0711i	3.01530	−	0.627547i
$371$	2.17397	−	2.18732i	0.112867	−	0.113560i
$372$	23.6383	+	40.7739i	1.22559	+	2.11403i
$373$	−34.2826	−	7.28700i	−1.77509	−	0.377306i	−0.800152	−	0.599797i	$-0.795248\pi$
$373$	−34.2826	−	7.28700i	−1.77509	−	0.377306i	−0.974935	+	0.222491i	$0.928581\pi$
$374$	−4.50981	−	7.81122i	−0.233197	−	0.403909i
$375$	1.81314	+	19.2798i	0.0936300	+	0.995607i
$376$	−13.3559	−	7.71103i	−0.688778	−	0.397666i
$377$	4.91399	+	15.1237i	0.253083	+	0.778911i
$378$	−32.2650	−	20.5684i	−1.65953	−	1.05792i
$379$	18.6490	−	13.5493i	0.957936	−	0.695981i	0.00526528	−	0.999986i	$-0.498324\pi$
$379$	18.6490	−	13.5493i	0.957936	−	0.695981i	0.952670	+	0.304005i	$0.0983240\pi$
$380$	−1.66605	+	5.05443i	−0.0854668	+	0.259287i
$381$	0.0713704	−	0.338753i	0.00365642	−	0.0173548i
$382$	21.2276	+	36.7674i	1.08610	+	1.88118i
$383$	−13.9821	+	6.22524i	−0.714452	+	0.318095i	−0.731577	−	0.681759i	$-0.761215\pi$
$383$	−13.9821	+	6.22524i	−0.714452	+	0.318095i	0.0171247	+	0.999853i	$0.494549\pi$
$384$	99.6741	+	44.1641i	5.08647	+	2.25374i
$385$	2.28214	+	14.5203i	0.116308	+	0.740022i
$386$	33.1584	−	10.7738i	1.68772	−	0.548372i
$387$	2.70414	+	4.64520i	0.137459	+	0.236129i
$388$	8.64515	+	40.6722i	0.438891	+	2.06482i
$389$	−5.82437	−	5.24429i	−0.295308	−	0.265896i	0.508136	−	0.861277i	$-0.330335\pi$
$389$	−5.82437	−	5.24429i	−0.295308	−	0.265896i	−0.803444	+	0.595381i	$0.797001\pi$
$390$	38.5318	−	8.09128i	1.95113	−	0.409718i
$391$	2.90894	+	0.945171i	0.147111	+	0.0477994i
$392$	71.3029	−	15.6128i	3.60134	−	0.788567i
$393$	−12.4291	−	1.28386i	−0.626967	−	0.0647621i
$394$	−6.26617	+	2.78988i	−0.315685	+	0.140552i
$395$	−4.09243	+	18.8591i	−0.205912	+	0.948904i
$396$	25.0515	−	34.7414i	1.25889	−	1.74582i
$397$	−31.1650	+	3.27557i	−1.56413	+	0.164396i	−0.846636	−	0.532173i	$-0.821376\pi$
$397$	−31.1650	+	3.27557i	−1.56413	+	0.164396i	−0.717490	+	0.696569i	$0.754709\pi$
$398$	−8.41044	−	25.8847i	−0.421577	−	1.29748i
$399$	0.853448	−	1.69527i	0.0427259	−	0.0848698i
$400$	8.42070	+	87.2408i	0.421035	+	4.36204i
$401$	18.7985	+	10.8533i	0.938751	+	0.541988i	0.889568	−	0.456802i	$-0.151005\pi$
$401$	18.7985	+	10.8533i	0.938751	+	0.541988i	0.0491823	+	0.998790i	$0.484338\pi$
$402$	−0.524650	−	0.580589i	−0.0261672	−	0.0289571i
$403$	15.8001	+	7.03464i	0.787057	+	0.350420i
$404$	−3.53468	−	33.6303i	−0.175857	−	1.67317i
$405$	−14.9162	+	13.5095i	−0.741191	+	0.671294i
$406$	32.0108	−	1.77590i	1.58867	−	0.0881366i
$407$		−	23.6505i		−	1.17231i
$408$	7.31987	+	22.3917i	0.362387	+	1.10856i
$409$	−6.24596	−	29.3849i	−0.308843	−	1.45299i	−0.809385	−	0.587278i	$-0.800199\pi$
$409$	−6.24596	−	29.3849i	−0.308843	−	1.45299i	0.500542	−	0.865712i	$-0.333134\pi$
$410$	28.2982	+	31.6980i	1.39755	+	1.56545i
$411$	−11.3239	+	35.0648i	−0.558566	+	1.72962i
$412$	37.4707	+	12.1750i	1.84605	+	0.599817i
$413$	33.2620	+	5.16384i	1.63672	+	0.254096i
$414$	2.11636	+	19.4650i	0.104013	+	0.956652i
$415$	−9.57830	−	13.3019i	−0.470180	−	0.652962i
$416$	99.7975	−	21.2126i	4.89297	−	1.04003i
$417$	16.2608	+	3.42592i	0.796295	+	0.167768i
$418$	2.48030	+	1.43200i	0.121316	+	0.0700416i
$419$	−0.719627	−	0.522839i	−0.0351561	−	0.0255424i	0.570068	−	0.821597i	$-0.306917\pi$
$419$	−0.719627	−	0.522839i	−0.0351561	−	0.0255424i	−0.605225	+	0.796055i	$0.706917\pi$
$420$	3.04621	−	58.8052i	0.148640	−	2.86940i
$421$	−17.2709	+	12.5481i	−0.841733	+	0.611555i	−0.922854	−	0.385149i	$-0.874150\pi$
$421$	−17.2709	+	12.5481i	−0.841733	+	0.611555i	0.0811210	+	0.996704i	$0.474150\pi$
$422$	−21.3793	+	2.24706i	−1.04073	+	0.109385i
$423$	3.58021	−	2.62082i	0.174076	−	0.127428i
$424$	−6.07717	−	10.5260i	−0.295133	−	0.511186i
$425$	−4.40493	+	4.80938i	−0.213671	+	0.233289i
$426$	46.6968	+	4.82351i	2.26247	+	0.233700i
$427$	−12.2762	+	19.0310i	−0.594088	+	0.920977i
$428$	−4.79950	−	6.60594i	−0.231993	−	0.319310i
$429$	−0.0281440	−	15.7178i	−0.00135881	−	0.758860i
$430$	−5.61619	+	9.63280i	−0.270837	+	0.464535i
$431$	−34.3165	−	3.60681i	−1.65297	−	0.173734i	−0.768343	−	0.640039i	$-0.778918\pi$
$431$	−34.3165	−	3.60681i	−1.65297	−	0.173734i	−0.884624	+	0.466305i	$0.845585\pi$
$432$	−67.3607	+	61.3103i	−3.24089	+	2.94979i
$433$	−13.7307	+	18.8987i	−0.659857	+	0.908215i	−0.999477	−	0.0323480i	$-0.989702\pi$
$433$	−13.7307	+	18.8987i	−0.659857	+	0.908215i	0.339620	+	0.940563i	$0.389702\pi$
$434$	21.8607	−	27.1654i	1.04935	−	1.30398i
$435$	3.54631	−	16.4848i	0.170032	−	0.790385i
$436$	18.8365	+	4.00382i	0.902104	+	0.191748i
$437$	−0.949988	+	0.201926i	−0.0454441	+	0.00965944i
$438$	49.7419	−	5.31815i	2.37676	−	0.254111i
$439$	−1.14128	+	5.36932i	−0.0544705	+	0.256263i	−0.996954	−	0.0779884i	$-0.975150\pi$
$439$	−1.14128	+	5.36932i	−0.0544705	+	0.256263i	0.942484	+	0.334252i	$0.108484\pi$
$440$	57.5864	+	6.29999i	2.74532	+	0.300340i
$441$	−4.16660	+	20.5825i	−0.198410	+	0.980119i
$442$	10.7275	+	7.79395i	0.510253	+	0.370721i
$443$	−5.22806	−	3.01842i	−0.248393	−	0.143409i	0.370635	−	0.928778i	$-0.379140\pi$
$443$	−5.22806	−	3.01842i	−0.248393	−	0.143409i	−0.619028	+	0.785369i	$0.712473\pi$
$444$	−19.5330	+	92.7115i	−0.926995	+	4.39989i
$445$	14.4943	+	8.45057i	0.687095	+	0.400595i
$446$	6.00097	+	57.0954i	0.284154	+	2.70355i
$447$	16.1251	+	27.8144i	0.762693	+	1.31558i
$448$	5.56549	−	112.803i	0.262945	−	5.32944i
$449$			24.1987i			1.14201i	0.820947	+	0.571004i	$0.193446\pi$
$449$			24.1987i			1.14201i	−0.820947	+	0.571004i	$0.806554\pi$
$450$	−39.6416	−	13.0961i	−1.86872	−	0.617354i
$451$	14.6905	−	8.48159i	0.691750	−	0.399382i
$452$	−35.3962	−	31.8709i	−1.66490	−	1.49908i
$453$	−0.0625259	−	34.9192i	−0.00293772	−	1.64065i
$454$	−14.6478	−	20.1609i	−0.687454	−	0.946200i
$455$	−11.7473	−	18.1364i	−0.550723	−	0.850246i
$456$	−5.56792	−	4.99535i	−0.260742	−	0.233929i
$457$	13.1017	−	22.6928i	0.612872	−	1.06153i	−0.377881	−	0.925854i	$-0.623347\pi$
$457$	13.1017	−	22.6928i	0.612872	−	1.06153i	0.990754	−	0.135672i	$-0.0433194\pi$
$458$	−6.06953	+	57.7478i	−0.283611	+	2.69838i
$459$	−6.74421	−	0.672236i	−0.314793	−	0.0313773i
$460$	−24.4519	+	17.6071i	−1.14008	+	0.820937i
$461$	10.8951	+	33.5318i	0.507437	+	1.56173i	0.796635	+	0.604461i	$0.206611\pi$
$461$	10.8951	+	33.5318i	0.507437	+	1.56173i	−0.289198	+	0.957269i	$0.593389\pi$
$462$	−30.6482	−	8.05298i	−1.42588	−	0.374659i
$463$	8.61390	−	26.5109i	0.400322	−	1.23206i	−0.524417	−	0.851462i	$-0.675717\pi$
$463$	8.61390	−	26.5109i	0.400322	−	1.23206i	0.924739	−	0.380603i	$-0.124283\pi$
$464$	15.8673	−	74.6499i	0.736622	−	3.46554i
$465$	−10.7431	−	14.8633i	−0.498199	−	0.689268i
$466$	−12.1780	+	2.58851i	−0.564134	+	0.119910i
$467$	−10.1587	+	4.52296i	−0.470090	+	0.209297i	−0.628089	−	0.778142i	$-0.716162\pi$
$467$	−10.1587	+	4.52296i	−0.470090	+	0.209297i	0.157999	+	0.987439i	$0.449496\pi$
$468$	−12.8710	+	61.6378i	−0.594962	+	2.84921i
$469$	−0.193803	+	0.383255i	−0.00894897	+	0.0176971i
$470$	8.39278	+	3.77950i	0.387130	+	0.174336i
$471$	−17.9529	+	0.0321462i	−0.827224	+	0.00148122i
$472$	53.9588	−	121.194i	2.48366	−	5.57838i
$473$	3.30802	+	2.97855i	0.152103	+	0.136954i
$474$	−33.7025	−	24.3943i	−1.54801	−	1.12047i
$475$	0.447749	−	2.02188i	0.0205442	−	0.0927702i
$476$	15.3734	−	12.5273i	0.704640	−	0.574187i
$477$	3.47634	−	0.377970i	0.159171	−	0.0173060i
$478$	−1.76723	−	16.8141i	−0.0808314	−	0.769060i
$479$	−27.7677	−	12.3630i	−1.26874	−	0.564878i	−0.341686	−	0.939814i	$-0.610998\pi$
$479$	−27.7677	−	12.3630i	−1.26874	−	0.564878i	−0.927051	+	0.374936i	$0.877665\pi$
$480$	−102.808	−	33.6839i	−4.69254	−	1.53745i
$481$	14.1418	+	31.7630i	0.644811	+	1.44827i
$482$	−17.2423			−0.785367
$483$	9.55086	−	4.92493i	0.434579	−	0.224092i
$484$	−8.57204	+	26.3820i	−0.389638	+	1.19918i
$485$	−4.93445	−	15.4091i	−0.224062	−	0.699690i
$486$	−13.7761	−	41.1414i	−0.624896	−	1.86621i
$487$	−25.7653	+	5.47658i	−1.16754	+	0.248168i	−0.750593	−	0.660765i	$-0.770232\pi$
$487$	−25.7653	+	5.47658i	−1.16754	+	0.248168i	−0.416944	+	0.908932i	$0.636899\pi$
$488$	59.7243	+	66.3305i	2.70359	+	3.00264i
$489$	2.54304	+	11.8596i	0.115000	+	0.536311i
$490$	−41.4073	+	13.5400i	−1.87059	+	0.611673i
$491$	−11.5175	−	3.74226i	−0.519777	−	0.168886i	0.0373672	−	0.999302i	$-0.488103\pi$
$491$	−11.5175	−	3.74226i	−0.519777	−	0.168886i	−0.557144	+	0.830416i	$0.688103\pi$
$492$	−64.5928	+	21.1154i	−2.91207	+	0.951956i
$493$	4.91799	−	2.83940i	0.221495	−	0.127880i
$494$	−4.18735	−	0.440108i	−0.188398	−	0.0198014i
$495$	−8.34290	+	14.4281i	−0.374986	+	0.648495i
$496$	−48.7888	−	67.1520i	−2.19068	−	3.01521i
$497$	−6.74459	−	24.8664i	−0.302536	−	1.11541i
$498$	34.5531	−	7.40918i	1.54836	−	0.332013i
$499$	−17.1527	+	29.7094i	−0.767862	+	1.32998i	0.170858	+	0.985296i	$0.445346\pi$
$499$	−17.1527	+	29.7094i	−0.767862	+	1.32998i	−0.938720	+	0.344681i	$0.887987\pi$
$500$	−12.5560	−	63.0090i	−0.561521	−	2.81785i
$501$	1.89922	+	4.24523i	0.0848507	+	0.189663i
$502$	5.42518	−	25.5235i	0.242138	−	1.13917i
$503$	−31.9427	+	23.2077i	−1.42425	+	1.03478i	−0.433203	+	0.901296i	$0.642617\pi$
$503$	−31.9427	+	23.2077i	−1.42425	+	1.03478i	−0.991051	+	0.133485i	$0.957383\pi$
$504$	73.9925	+	37.0840i	3.29589	+	1.65185i
$505$	2.68105	+	12.8822i	0.119305	+	0.573250i
$506$	6.59536	+	14.8134i	0.293199	+	0.658537i
$507$	0.241041	+	0.538788i	0.0107050	+	0.0239284i
$508$	−0.120058	+	1.14228i	−0.00532671	+	0.0506803i
$509$	−7.81865	−	8.68349i	−0.346555	−	0.384889i	0.544517	−	0.838750i	$-0.316713\pi$
$509$	−7.81865	−	8.68349i	−0.346555	−	0.384889i	−0.891073	+	0.453861i	$0.850046\pi$
$510$	−5.68726	−	12.8587i	−0.251836	−	0.569394i
$511$	−12.5393	−	24.4246i	−0.554705	−	1.08048i
$512$	−118.008	−	38.3433i	−5.21528	−	1.69455i
$513$	1.96132	−	0.885888i	0.0865942	−	0.0391129i
$514$	−14.0056	−	12.6107i	−0.617759	−	0.556233i
$515$	−14.9822	−	3.25113i	−0.660194	−	0.143262i
$516$	−10.5076	−	14.4082i	−0.462573	−	0.634286i
$517$	2.15984	−	2.97277i	0.0949899	−	0.130742i
$518$	69.2006	−	11.1776i	3.04050	−	0.491115i
$519$	12.8750	+	11.5510i	0.565149	+	0.507033i
$520$	−81.1064	+	25.9727i	−3.55675	+	1.13898i
$521$	37.2062	+	16.5653i	1.63003	+	0.725738i	0.998758	−	0.0498197i	$-0.0158647\pi$
$521$	37.2062	+	16.5653i	1.63003	+	0.725738i	0.631276	+	0.775558i	$0.282531\pi$
$522$	29.4862	+	21.2621i	1.29058	+	0.930615i
$523$	−3.75941	+	17.6866i	−0.164387	+	0.773382i	0.816273	+	0.577666i	$0.196036\pi$
$523$	−3.75941	+	17.6866i	−0.164387	+	0.773382i	−0.980661	+	0.195716i	$0.937297\pi$
$524$	41.4561			1.81102
$525$	1.11580	+	22.8857i	0.0486975	+	0.998814i
$526$	49.2118			2.14574
$527$	1.28414	−	6.04140i	0.0559380	−	0.263168i
$528$	−37.5997	+	65.3947i	−1.63632	+	2.84594i
$529$	15.9882	+	7.11840i	0.695138	+	0.309495i
$530$	4.23895	+	5.88684i	0.184128	+	0.255708i
$531$	25.6404	+	28.2722i	1.11270	+	1.22691i
$532$	−2.23864	+	5.88564i	−0.0970572	+	0.255175i
$533$	−14.6581	+	20.1751i	−0.634911	+	0.873880i
$534$	−29.2251	+	21.3133i	−1.26469	+	0.922319i
$535$	2.11598	+	2.37021i	0.0914819	+	0.102473i
$536$	1.25787	+	1.13259i	0.0543316	+	0.0489204i
$537$	28.0466	−	20.4539i	1.21030	−	0.882651i
$538$	5.40445	+	1.75601i	0.233002	+	0.0757071i
$539$	1.92378	+	17.2848i	0.0828633	+	0.744509i
$540$	44.6209	−	49.6687i	1.92018	−	2.13740i
$541$	25.7539	+	28.6026i	1.10725	+	1.22972i	0.971009	+	0.239044i	$0.0768340\pi$
$541$	25.7539	+	28.6026i	1.10725	+	1.22972i	0.136236	+	0.990676i	$0.456499\pi$
$542$	−1.10861	+	10.5477i	−0.0476190	+	0.453064i
$543$	−1.97297	+	0.882659i	−0.0846682	+	0.0378785i
$544$	−14.8195	−	33.2851i	−0.635381	−	1.42709i
$545$	−7.44892	−	0.814918i	−0.319077	−	0.0349072i
$546$	45.9763	−	7.51079i	1.96760	−	0.321432i
$547$	−14.4010	+	10.4629i	−0.615742	+	0.447363i	−0.851432	−	0.524466i	$-0.824265\pi$
$547$	−14.4010	+	10.4629i	−0.615742	+	0.447363i	0.235690	+	0.971828i	$0.424265\pi$
$548$	25.4176	−	119.581i	1.08579	−	5.10823i
$549$	−24.3939	+	8.02274i	−1.04111	+	0.342402i
$550$	−34.5738	−	0.293723i	−1.47423	−	0.0125244i
$551$	−0.901598	+	1.56161i	−0.0384094	+	0.0665270i
$552$	−8.87959	−	41.4104i	−0.377940	−	1.76254i
$553$	−5.84225	+	22.0737i	−0.248438	+	0.938668i
$554$	32.1954	+	44.3131i	1.36785	+	1.88268i
$555$	3.94381	−	36.6562i	0.167405	−	1.55597i
$556$	−54.8315	−	5.76302i	−2.32537	−	0.244407i
$557$	−15.8718	+	9.16359i	−0.672510	+	0.388274i	−0.797027	−	0.603944i	$-0.793595\pi$
$557$	−15.8718	+	9.16359i	−0.672510	+	0.388274i	0.124517	+	0.992217i	$0.460262\pi$
$558$	38.6441	−	8.35880i	1.63593	−	0.353856i
$559$	−6.22374	−	2.02222i	−0.263236	−	0.0855306i
$560$	5.30464	+	103.569i	0.224162	+	4.37658i
$561$	−5.48826	+	1.17684i	−0.231715	+	0.0496863i
$562$	14.5274	+	16.1343i	0.612801	+	0.680585i
$563$	−33.5222	+	7.12537i	−1.41279	+	0.300298i	−0.850211	−	0.526443i	$-0.823525\pi$
$563$	−33.5222	+	7.12537i	−1.41279	+	0.300298i	−0.562582	+	0.826741i	$0.690192\pi$
$564$	−10.9219	+	9.86963i	−0.459897	+	0.415586i
$565$	14.9478	+	10.9575i	0.628857	+	0.460985i
$566$	14.1549	−	43.5643i	0.594974	−	1.83114i
$567$	−18.3510	+	15.1736i	−0.770671	+	0.637233i
$568$	−101.545			−4.26071
$569$	8.00248	+	17.9739i	0.335482	+	0.753504i	0.999981	+	0.00621481i	$0.00197825\pi$
$569$	8.00248	+	17.9739i	0.335482	+	0.753504i	−0.664499	+	0.747289i	$0.731355\pi$
$570$	3.60546	+	2.63308i	0.151016	+	0.110287i
$571$	−33.0936	−	14.7342i	−1.38493	−	0.616609i	−0.427165	−	0.904174i	$-0.640488\pi$
$571$	−33.0936	−	14.7342i	−1.38493	−	0.616609i	−0.957761	+	0.287565i	$0.907154\pi$
$572$	5.45090	+	51.8619i	0.227914	+	2.16845i
$573$	25.8332	−	5.53938i	1.07920	−	0.231411i
$574$	31.7598	+	38.9755i	1.32563	+	1.62680i
$575$	8.77950	−	7.77106i	0.366130	−	0.324076i
$576$	85.3489	−	95.4749i	3.55620	−	3.97812i
$577$	28.5981	+	25.7499i	1.19056	+	1.07198i	0.995840	+	0.0911211i	$0.0290450\pi$
$577$	28.5981	+	25.7499i	1.19056	+	1.07198i	0.194716	+	0.980860i	$0.437622\pi$
$578$	−17.3189	+	38.8988i	−0.720370	+	1.61798i
$579$	−0.0388499	−	21.6967i	−0.00161455	−	0.901685i
$580$	−6.08397	+	55.6117i	−0.252623	+	2.30915i
$581$	−10.6129	−	16.2334i	−0.440297	−	0.673475i
$582$	34.6976	+	3.58406i	1.43826	+	0.148564i
$583$	2.64559	−	1.17789i	0.109569	−	0.0487834i
$584$	−105.842	+	22.4975i	−4.37979	+	0.930953i
$585$	2.57737	−	24.3658i	0.106561	−	1.00740i
$586$	10.9907	−	51.7073i	0.454023	−	2.13601i
$587$	−3.71764	+	11.4417i	−0.153444	+	0.472251i	−0.998000	−	0.0632160i	$-0.979864\pi$
$587$	−3.71764	+	11.4417i	−0.153444	+	0.472251i	0.844556	+	0.535467i	$0.179864\pi$
$588$	6.73419	−	69.3464i	0.277713	−	2.85980i
$589$	0.606041	+	1.86520i	0.0249715	+	0.0768543i
$590$	−24.7872	+	75.1988i	−1.02047	+	3.09589i
$591$	0.453785	+	4.24436i	0.0186662	+	0.174590i
$592$	17.4421	−	165.951i	0.716866	−	6.82052i
$593$	4.25991	−	7.37838i	0.174934	−	0.302994i	−0.765205	−	0.643787i	$-0.777362\pi$
$593$	4.25991	−	7.37838i	0.174934	−	0.302994i	0.940138	+	0.340793i	$0.110696\pi$
$594$	−21.2758	−	28.9553i	−0.872957	−	1.18805i
$595$	−5.46298	+	5.45003i	−0.223960	+	0.223430i
$596$	−62.6976	−	86.2958i	−2.56819	−	3.53481i
$597$	−16.9373	+	0.0303277i	−0.693196	+	0.00124123i
$598$	−17.7153	−	15.9509i	−0.724433	−	0.652283i
$599$	−10.6011	+	6.12052i	−0.433147	+	0.250078i	−0.700687	−	0.713469i	$-0.747123\pi$
$599$	−10.6011	+	6.12052i	−0.433147	+	0.250078i	0.267539	+	0.963547i	$0.413790\pi$
$600$	88.2032	+	19.3672i	3.60088	+	0.790661i
$601$		−	31.7366i		−	1.29456i	−0.762251	−	0.647282i	$-0.775906\pi$
$601$		−	31.7366i		−	1.29456i	0.762251	−	0.647282i	$-0.224094\pi$
$602$	−7.15172	+	11.0869i	−0.291483	+	0.451866i
$603$	−0.444159	+	0.199662i	−0.0180876	+	0.00813085i
$604$	12.1099	+	115.218i	0.492747	+	4.68817i
$605$	2.28903	−	10.5485i	0.0930623	−	0.428858i
$606$	−27.7584	−	5.84830i	−1.12761	−	0.237571i
$607$	−35.2712	−	20.3638i	−1.43161	−	0.826542i	−0.434369	−	0.900735i	$-0.643029\pi$
$607$	−35.2712	−	20.3638i	−1.43161	−	0.826542i	−0.997244	+	0.0741927i	$0.976362\pi$
$608$	9.35974	+	6.80025i	0.379588	+	0.275786i
$609$	5.07021	−	19.2963i	0.205455	−	0.781926i
$610$	−39.4371	−	35.8138i	−1.59676	−	1.45006i
$611$	−1.12314	+	5.28395i	−0.0454373	+	0.213766i
$612$	22.4863	−	0.0805276i	0.908954	−	0.00325513i
$613$	−17.6968	+	3.76157i	−0.714766	+	0.151928i	−0.550921	−	0.834558i	$-0.685723\pi$
$613$	−17.6968	+	3.76157i	−0.714766	+	0.151928i	−0.163846	+	0.986486i	$0.552390\pi$
$614$	23.5339	+	5.00229i	0.949752	+	0.201876i
$615$	24.1833	−	10.6960i	0.975167	−	0.431304i
$616$	67.7323	+	10.5153i	2.72901	+	0.423672i
$617$	5.57696	−	7.67602i	0.224520	−	0.309025i	−0.681865	−	0.731478i	$-0.738831\pi$
$617$	5.57696	−	7.67602i	0.224520	−	0.309025i	0.906385	+	0.422453i	$0.138831\pi$
$618$	19.3794	−	26.7742i	0.779556	−	1.07702i
$619$	3.77478	+	0.396745i	0.151721	+	0.0159465i	0.180084	−	0.983651i	$-0.442363\pi$
$619$	3.77478	+	0.396745i	0.151721	+	0.0159465i	−0.0283634	+	0.999598i	$0.509030\pi$
$620$	40.5209	+	45.3893i	1.62736	+	1.82288i
$621$	11.9319	+	2.46928i	0.478809	+	0.0990887i
$622$	7.55560	+	10.3994i	0.302952	+	0.416977i
$623$	16.6822	+	10.7611i	0.668357	+	0.431132i
$624$	11.3943	−	110.309i	0.456135	−	4.41589i
$625$	7.32035	+	23.9042i	0.292814	+	0.956169i
$626$	−11.1461	−	19.3056i	−0.445488	−	0.771607i
$627$	1.32237	−	1.19496i	0.0528105	−	0.0477223i
$628$	59.2368	−	6.22604i	2.36381	−	0.248446i
$629$	10.0451	−	7.29819i	0.400524	−	0.290998i
$630$	−46.1591	−	17.5921i	−1.83902	−	0.700886i
$631$	−10.0337	−	7.28994i	−0.399437	−	0.290208i	0.369875	−	0.929082i	$-0.379401\pi$
$631$	−10.0337	−	7.28994i	−0.399437	−	0.290208i	−0.769312	+	0.638874i	$0.779401\pi$
$632$	77.9358	+	44.9962i	3.10012	+	1.78985i
$633$	−2.75798	+	13.0905i	−0.109620	+	0.520301i
$634$	−57.1701	+	12.1519i	−2.27052	+	0.482613i
$635$	0.00189840	−	0.446925i	7.53357e−5	−	0.0177357i
$636$	−11.3437	+	2.43242i	−0.449807	+	0.0964516i
$637$	−12.9191	−	22.0634i	−0.511873	−	0.874185i
$638$	28.6326	+	9.30329i	1.13357	+	0.368321i
$639$	11.7870	−	26.7312i	0.466286	−	1.05747i
$640$	137.543	+	29.8469i	5.43687	+	1.17980i
$641$	4.72326	+	22.2212i	0.186558	+	0.877685i	0.967459	+	0.253030i	$0.0814270\pi$
$641$	4.72326	+	22.2212i	0.186558	+	0.877685i	−0.780901	+	0.624655i	$0.785240\pi$
$642$	−6.51089	+	2.12841i	−0.256964	+	0.0840017i
$643$		−	5.63641i		−	0.222278i	−0.993805	−	0.111139i	$-0.964550\pi$
$643$		−	5.63641i		−	0.222278i	0.993805	−	0.111139i	$-0.0354499\pi$
$644$	−29.8407	+	19.5090i	−1.17589	+	0.768761i
$645$	4.63045	+	5.16811i	0.182324	+	0.203494i
$646$	0.157168	+	1.49536i	0.00618370	+	0.0588340i
$647$	31.8858	+	14.1965i	1.25356	+	0.558121i	0.922685	−	0.385554i	$-0.125990\pi$
$647$	31.8858	+	14.1965i	1.25356	+	0.558121i	0.330874	+	0.943675i	$0.392656\pi$
$648$	38.7841	+	85.4580i	1.52358	+	3.35711i
$649$	27.3742	+	15.8045i	1.07453	+	0.620381i
$650$	46.6087	−	20.2789i	1.82815	−	0.795403i
$651$	−11.9065	−	18.1411i	−0.466652	−	0.711005i
$652$	−12.4353	−	38.2720i	−0.487005	−	1.49885i
$653$	7.17957	−	0.754604i	0.280958	−	0.0295299i	0.0369988	−	0.999315i	$-0.488220\pi$
$653$	7.17957	−	0.754604i	0.280958	−	0.0295299i	0.243960	+	0.969785i	$0.421554\pi$
$654$	8.05240	−	14.0050i	0.314874	−	0.547640i
$655$	−16.0500	+	1.61802i	−0.627125	+	0.0632214i
$656$	109.335	−	48.6793i	4.26883	−	1.90061i
$657$	6.36348	−	30.4741i	0.248263	−	1.18891i
$658$	9.71900	+	4.91465i	0.378886	+	0.191593i
$659$	4.28226	+	1.39139i	0.166813	+	0.0542009i	0.391233	−	0.920292i	$-0.372049\pi$
$659$	4.28226	+	1.39139i	0.166813	+	0.0542009i	−0.224420	+	0.974493i	$0.572049\pi$
$660$	22.6147	−	50.4594i	0.880276	−	1.96413i
$661$	−17.4292	−	15.6933i	−0.677917	−	0.610399i	0.256515	−	0.966540i	$-0.417426\pi$
$661$	−17.4292	−	15.6933i	−0.677917	−	0.610399i	−0.934432	+	0.356141i	$0.884092\pi$
$662$	−1.62666	−	7.65282i	−0.0632219	−	0.297435i
$663$	6.66712	−	4.86221i	0.258930	−	0.188833i
$664$	−72.6976	+	23.6209i	−2.82121	+	0.916668i
$665$	0.636986	−	2.36603i	0.0247012	−	0.0917509i
$666$	68.9763	+	39.4948i	2.67278	+	1.53039i
$667$	−9.32661	+	4.15248i	−0.361128	+	0.160785i
$668$	−7.71492	−	13.3626i	−0.298499	−	0.517016i
$669$	34.9594	+	7.36544i	1.35161	+	0.284765i
$670$	−0.814765	−	0.597266i	−0.0314771	−	0.0230744i
$671$	−17.2052	+	12.5003i	−0.664198	+	0.482568i
$672$	−119.726	−	45.2932i	−4.61854	−	1.74723i
$673$	7.72685	+	23.7808i	0.297848	+	0.916682i	0.982250	+	0.187577i	$0.0600634\pi$
$673$	7.72685	+	23.7808i	0.297848	+	0.916682i	−0.684402	+	0.729105i	$0.739937\pi$
$674$	−46.2885	−	26.7247i	−1.78297	−	1.02940i
$675$	−15.3367	+	20.9711i	−0.590309	+	0.807177i
$676$	−0.979146	−	1.69593i	−0.0376595	−	0.0652281i
$677$	−42.8588	−	9.10991i	−1.64720	−	0.350122i	−0.711433	−	0.702754i	$-0.751954\pi$
$677$	−42.8588	−	9.10991i	−1.64720	−	0.350122i	−0.935762	+	0.352631i	$0.885287\pi$
$678$	−34.5680	+	20.0404i	−1.32758	+	0.769649i
$679$	−5.01150	−	18.4767i	−0.192324	−	0.709071i
$680$	15.0945	+	26.4028i	0.578847	+	1.01250i
$681$	−14.7406	+	4.81869i	−0.564859	+	0.184653i
$682$	28.3571	−	16.3720i	1.08585	−	0.626914i
$683$	21.4794	+	2.25758i	0.821887	+	0.0863838i	0.506131	−	0.862457i	$-0.331075\pi$
$683$	21.4794	+	2.25758i	0.821887	+	0.0863838i	0.315756	+	0.948840i	$0.397742\pi$
$684$	−6.17071	+	3.59219i	−0.235943	+	0.137351i
$685$	−5.17339	+	47.2884i	−0.197665	+	1.80680i
$686$	−49.6655	+	13.7980i	−1.89624	+	0.526809i
$687$	33.0373	+	14.6383i	1.26045	+	0.558487i
$688$	21.0150	+	23.3395i	0.801188	+	0.889810i
$689$	−2.84875	+	3.16386i	−0.108529	+	0.120533i
$690$	7.75202	+	24.0593i	0.295114	+	0.915920i
$691$	−18.4199	+	16.5853i	−0.700724	+	0.630935i	−0.940461	−	0.339903i	$-0.889606\pi$
$691$	−18.4199	+	16.5853i	−0.700724	+	0.630935i	0.239736	+	0.970838i	$0.422939\pi$
$692$	−46.4274	−	33.7315i	−1.76491	−	1.28228i
$693$	−10.6303	+	16.6097i	−0.403810	+	0.630950i
$694$	64.5755	+	46.9168i	2.45125	+	1.78094i
$695$	21.4533	+	0.0911269i	0.813769	+	0.00345664i
$696$	−68.1678	−	39.1941i	−2.58389	−	1.48565i
$697$	8.13566	+	3.62223i	0.308160	+	0.137202i
$698$	−64.7704	−	13.7674i	−2.45159	−	0.521103i
$699$	−0.796067	+	7.70679i	−0.0301100	+	0.291498i
$700$	−11.4838	−	75.1466i	−0.434048	−	2.84028i
$701$		−	26.2513i		−	0.991496i	−0.868466	−	0.495748i	$-0.834894\pi$
$701$		−	26.2513i		−	0.991496i	0.868466	−	0.495748i	$-0.165106\pi$
$702$	45.8875	+	26.1655i	1.73191	+	0.987554i
$703$	−1.60360	+	3.60174i	−0.0604809	+	0.135842i
$704$	43.1372	−	96.8878i	1.62580	−	3.65160i
$705$	3.84329	−	4.24737i	0.144747	−	0.159965i
$706$	24.0984	−	33.1686i	0.906956	−	1.24832i
$707$	2.48260	+	15.3698i	0.0933678	+	0.578041i
$708$	−94.2556	−	84.5630i	−3.54234	−	3.17807i
$709$	−13.1517	−	14.6065i	−0.493924	−	0.548558i	0.443716	−	0.896168i	$-0.353660\pi$
$709$	−13.1517	−	14.6065i	−0.493924	−	0.548558i	−0.937639	+	0.347610i	$0.886993\pi$
$710$	60.3004	−	6.07898i	2.26303	−	0.228140i
$711$	−20.8916	+	15.2933i	−0.783498	+	0.573542i
$712$	58.1438	−	52.3529i	2.17903	−	1.96201i
$713$	−3.43125	+	10.5603i	−0.128501	+	0.395486i
$714$	−6.03723	−	15.5023i	−0.225938	−	0.580158i
$715$	−4.13451	−	19.8659i	−0.154622	−	0.742942i
$716$	−85.5865	+	77.0624i	−3.19852	+	2.87996i
$717$	−10.2952	−	2.16906i	−0.384483	−	0.0810051i
$718$	21.1628	+	36.6550i	0.789787	+	1.36795i
$719$	15.7932	−	7.03158i	0.588987	−	0.262234i	−0.0905302	−	0.995894i	$-0.528856\pi$
$719$	15.7932	−	7.03158i	0.588987	−	0.262234i	0.679517	+	0.733660i	$0.262189\pi$
$720$	−69.1809	+	95.0861i	−2.57822	+	3.54365i
$721$	−17.5359	−	4.64124i	−0.653072	−	0.172849i
$722$	30.8025	+	42.3960i	1.14635	+	1.57782i
$723$	−3.29751	+	10.2109i	−0.122636	+	0.379746i
$724$	6.21027	−	3.58550i	0.230803	−	0.133254i
$725$	0.184930	−	21.7679i	0.00686812	−	0.808438i
$726$	18.8510	+	13.6445i	0.699624	+	0.506395i
$727$	−19.6675	+	6.39037i	−0.729428	+	0.237006i	−0.650106	−	0.759843i	$-0.725276\pi$
$727$	−19.6675	+	6.39037i	−0.729428	+	0.237006i	−0.0793222	+	0.996849i	$0.525276\pi$
$728$	−97.2531	+	26.3783i	−3.60444	+	0.977644i
$729$	−26.9984	+	0.290069i	−0.999942	+	0.0107433i
$730$	61.5058	−	19.6960i	2.27643	−	0.728982i
$731$	−0.244278	+	2.32415i	−0.00903496	+	0.0859619i
$732$	77.7694	−	34.7922i	2.87444	−	1.28595i
$733$	12.0290	+	27.0177i	0.444303	+	0.997920i	0.987399	+	0.158250i	$0.0505852\pi$
$733$	12.0290	+	27.0177i	0.444303	+	0.997920i	−0.543096	+	0.839670i	$0.682748\pi$
$734$	10.9114	−	33.5818i	0.402747	−	1.23953i
$735$	0.0993925	+	27.1107i	0.00366615	+	0.999993i
$736$	20.2413	+	62.2964i	0.746105	+	2.29628i
$737$	−0.299707	+	0.269857i	−0.0110398	+	0.00994032i
$738$	0.204158	+	57.0083i	0.00751514	+	2.09851i
$739$	33.5122	−	37.2191i	1.23277	−	1.36913i	0.327183	−	0.944961i	$-0.393901\pi$
$739$	33.5122	−	37.2191i	1.23277	−	1.36913i	0.905584	−	0.424166i	$-0.139433\pi$
$740$	−0.519563	+	122.317i	−0.0190995	+	4.49645i
$741$	−1.06144	+	2.39557i	−0.0389930	+	0.0880034i
$742$	4.69682	+	7.18422i	0.172426	+	0.263741i
$743$			15.6287i			0.573360i	0.958026	+	0.286680i	$0.0925517\pi$
$743$			15.6287i			0.573360i	−0.958026	+	0.286680i	$0.907448\pi$
$744$	−81.2886	+	26.5733i	−2.98018	+	0.974224i
$745$	27.6418	+	30.9629i	1.01272	+	1.13439i
$746$	39.6767	−	89.1154i	1.45267	−	3.26275i
$747$	2.22041	−	21.8792i	0.0812405	−	0.800518i
$748$	17.7111	−	5.75468i	0.647582	−	0.210412i
$749$	2.37482	+	2.91437i	0.0867742	+	0.106489i
$750$	−53.5373	−	6.22054i	−1.95491	−	0.227142i
$751$	−11.3874	+	19.7236i	−0.415532	+	0.719723i	−0.995484	−	0.0949278i	$-0.969738\pi$
$751$	−11.3874	+	19.7236i	−0.415532	+	0.719723i	0.579952	+	0.814651i	$0.303071\pi$
$752$	17.3476	−	19.2664i	0.632600	−	0.702574i
$753$	−14.0774	−	8.09401i	−0.513009	−	0.294962i
$754$	−44.0169	+	4.62636i	−1.60300	+	0.168482i
$755$	−9.18539	−	44.1349i	−0.334291	−	1.60623i
$756$	55.3893	−	56.3315i	2.01449	−	2.04876i
$757$	37.2887			1.35528			0.677641	−	0.735393i	$-0.263002\pi$
$757$	37.2887			1.35528			0.677641	+	0.735393i	$0.263002\pi$
$758$	26.0954	+	58.6113i	0.947828	+	2.12886i
$759$	10.0338	−	1.07276i	0.364203	−	0.0389388i
$760$	−8.34268	−	4.86401i	−0.302621	−	0.176436i
$761$	−12.2489	−	2.60358i	−0.444021	−	0.0943795i	−0.0195248	−	0.999809i	$-0.506215\pi$
$761$	−12.2489	−	2.60358i	−0.444021	−	0.0943795i	−0.424496	+	0.905430i	$0.639549\pi$
$762$	0.880931	+	0.390327i	0.0319128	+	0.0141401i
$763$	−8.76132	−	1.36017i	−0.317181	−	0.0492416i
$764$	−83.3660	+	27.0872i	−3.01608	+	0.979982i
$765$	−8.70255	+	0.908811i	−0.314641	+	0.0328581i
$766$	−8.85675	−	41.6677i	−0.320007	−	1.50552i
$767$	−46.2142	−	4.85731i	−1.66870	−	0.175387i
$768$	−91.2088	+	126.012i	−3.29121	+	4.54707i
$769$	−1.13791	+	1.56620i	−0.0410340	+	0.0564785i	−0.829041	−	0.559188i	$-0.811113\pi$
$769$	−1.13791	+	1.56620i	−0.0410340	+	0.0564785i	0.788007	+	0.615666i	$0.211113\pi$
$770$	−40.8511	−	2.18950i	−1.47217	−	0.0789042i
$771$	−10.1465	+	5.88233i	−0.365417	+	0.211847i
$772$	7.52440	+	71.5899i	0.270809	+	2.57658i
$773$	30.0060	−	33.3250i	1.07924	−	1.19862i	0.100196	−	0.994968i	$-0.468053\pi$
$773$	30.0060	−	33.3250i	1.07924	−	1.19862i	0.979044	−	0.203649i	$-0.0652802\pi$
$774$	−14.2111	+	4.67378i	−0.510806	+	0.167996i
$775$	−17.4595	−	15.9912i	−0.627162	−	0.574421i
$776$	−75.4516			−2.70856
$777$	6.61492	−	43.1180i	0.237309	−	1.54685i
$778$	17.6476	−	12.8217i	0.632698	−	0.459682i
$779$	−2.81231	+	0.295586i	−0.100761	+	0.0105905i
$780$	−0.199737	+	81.2902i	−0.00715174	+	2.91066i
$781$	2.52902	−	24.0620i	0.0904955	−	0.861007i
$782$	−4.25648	+	7.37244i	−0.152211	+	0.263638i
$783$	18.2304	−	13.3954i	0.651502	−	0.478712i
$784$	0.751346	+	122.702i	0.0268338	+	4.38223i
$785$	−22.6909	+	4.72245i	−0.809872	+	0.168551i
$786$	10.6876	−	33.0946i	0.381214	−	1.18044i
$787$	2.39448	+	11.2651i	0.0853540	+	0.401559i	0.999996	−	0.00270513i	$-0.000861071\pi$
$787$	2.39448	+	11.2651i	0.0853540	+	0.401559i	−0.914642	+	0.404264i	$0.867528\pi$
$788$	−2.94443	−	13.8525i	−0.104891	−	0.493474i
$789$	9.41150	−	29.1431i	0.335058	−	1.03752i
$790$	−48.9745	−	22.0546i	−1.74243	−	0.784666i
$791$	17.0846	+	13.7484i	0.607458	+	0.488838i
$792$	52.2121	+	57.5715i	1.85528	+	2.04571i
$793$	15.6323	−	27.0759i	0.555118	−	0.961493i
$794$	9.11674	−	86.7400i	0.323541	−	3.07829i
$795$	4.29685	−	1.38447i	0.152394	−	0.0491020i
$796$	55.8858	−	5.87383i	1.98082	−	0.208192i
$797$	−23.9394	+	17.3930i	−0.847975	+	0.616090i	−0.924587	−	0.380971i	$-0.875590\pi$
$797$	−23.9394	+	17.3930i	−0.847975	+	0.616090i	0.0766116	+	0.997061i	$0.475590\pi$
$798$	4.12140	+	3.30446i	0.145896	+	0.116977i
$799$	1.92912			0.0682474
$800$	−138.773	−	15.7787i	−4.90637	−	0.557861i
$801$	7.03255	+	21.3831i	0.248483	+	0.755534i
$802$	−40.4255	+	44.8971i	−1.42747	+	1.58537i
$803$	−2.69495	−	25.6408i	−0.0951029	−	0.904843i
$804$	1.39775	−	0.810329i	0.0492947	−	0.0285781i
$805$	10.7916	−	8.71769i	0.380354	−	0.307258i
$806$	−28.2944	+	38.9438i	−0.996626	+	1.37174i
$807$	2.07348	−	2.86467i	0.0729899	−	0.100841i
$808$	61.0246	+	6.41395i	2.14684	+	0.225642i
$809$	4.60469	+	21.6634i	0.161892	+	0.761644i	0.981916	+	0.189315i	$0.0606267\pi$
$809$	4.60469	+	21.6634i	0.161892	+	0.761644i	−0.820024	+	0.572329i	$0.806040\pi$
$810$	−28.1472	−	48.4259i	−0.988992	−	1.70151i
$811$	−20.7592	+	6.74508i	−0.728955	+	0.236852i	−0.649901	−	0.760018i	$-0.725190\pi$
$811$	−20.7592	+	6.74508i	−0.728955	+	0.236852i	−0.0790537	+	0.996870i	$0.525190\pi$
$812$	−10.1547	+	65.4097i	−0.356360	+	2.29543i
$813$	6.03432	+	2.67372i	0.211633	+	0.0937714i
$814$	64.3869	+	13.6859i	2.25676	+	0.479689i
$815$	6.30816	+	14.3319i	0.220965	+	0.502024i
$816$	−39.3778	+	4.21008i	−1.37850	+	0.147382i
$817$	−0.301821	−	0.677901i	−0.0105594	−	0.0237168i
$818$	83.6128			2.92345
$819$	4.34486	−	28.6634i	0.151822	−	1.00158i
$820$	−76.1633	+	43.5426i	−2.65974	+	1.52057i
$821$	−1.05804	+	0.111204i	−0.0369257	+	0.00388105i	−0.122973	−	0.992410i	$-0.539243\pi$
$821$	−1.05804	+	0.111204i	−0.0369257	+	0.00388105i	0.0860476	+	0.996291i	$0.472576\pi$
$822$	−88.9089	−	51.1195i	−3.10105	−	1.78300i
$823$	21.7909	−	24.2012i	0.759581	−	0.843601i	−0.232050	−	0.972704i	$-0.574543\pi$
$823$	21.7909	−	24.2012i	0.759581	−	0.843601i	0.991631	+	0.129103i	$0.0412099\pi$
$824$	−35.7462	+	61.9143i	−1.24528	+	2.15689i
$825$	−6.78600	+	20.4183i	−0.236258	+	0.710875i
$826$	−33.3060	+	87.5654i	−1.15886	+	3.04679i
$827$	−2.57667	+	0.837210i	−0.0895995	+	0.0291126i	−0.353474	−	0.935444i	$-0.615000\pi$
$827$	−2.57667	+	0.837210i	−0.0895995	+	0.0291126i	0.263874	+	0.964557i	$0.415000\pi$
$828$	−40.2191	−	4.08163i	−1.39771	−	0.141846i
$829$	−19.5210	+	43.8449i	−0.677992	+	1.52279i	0.165820	+	0.986156i	$0.446973\pi$
$829$	−19.5210	+	43.8449i	−0.677992	+	1.52279i	−0.843812	+	0.536639i	$0.819694\pi$
$830$	41.7561	−	18.3789i	1.44938	−	0.637940i
$831$	32.3993	−	10.5913i	1.12392	−	0.367410i
$832$			155.916i			5.40540i
$833$	−6.74773	+	6.15092i	−0.233795	+	0.213117i
$834$	−18.7365	+	42.2865i	−0.648791	+	1.46426i
$835$	3.50842	+	4.87231i	0.121414	+	0.168613i
$836$	−3.95672	+	4.39439i	−0.136846	+	0.151983i
$837$	2.44042	−	24.4835i	0.0843532	−	0.846272i
$838$	1.83982	−	1.65658i	0.0635556	−	0.0572257i
$839$	−17.0209	−	52.3848i	−0.587625	−	1.80853i	−0.588461	−	0.808526i	$-0.700266\pi$
$839$	−17.0209	−	52.3848i	−0.587625	−	1.80853i	0.000835472	−	1.00000i	$-0.499734\pi$
$840$	103.226	+	27.5923i	3.56162	+	0.952026i
$841$	3.10409	−	9.55339i	0.107037	−	0.329427i
$842$	−24.1671	−	54.2801i	−0.832852	−	1.87062i
$843$	12.3330	−	5.51748i	0.424770	−	0.190032i
$844$	4.63943	−	44.1413i	0.159696	−	1.51940i
$845$	0.445274	+	0.618374i	0.0153179	+	0.0212727i
$846$	5.06323	+	11.2635i	0.174077	+	0.387246i
$847$	3.26776	−	12.3465i	0.112282	−	0.424232i
$848$	19.4322	−	6.31391i	0.667305	−	0.216821i
$849$	−23.0916	−	16.7139i	−0.792501	−	0.573620i
$850$	−10.5442	−	14.7752i	−0.361663	−	0.506785i
$851$	−19.3314	+	11.1610i	−0.662673	+	0.382594i
$852$	−29.7868	+	92.2360i	−1.02048	+	3.15995i
$853$	−10.9746	−	15.1052i	−0.375762	−	0.517193i	0.578693	−	0.815545i	$-0.303563\pi$
$853$	−10.9746	−	15.1052i	−0.375762	−	0.517193i	−0.954456	+	0.298353i	$0.903563\pi$
$854$	−44.7068	−	44.4339i	−1.52984	−	1.52050i
$855$	2.24883	−	1.63158i	0.0769082	−	0.0557988i
$856$	13.5358	−	6.02650i	0.462642	−	0.205982i
$857$	−17.5694	−	30.4311i	−0.600159	−	1.03951i	−0.992797	−	0.119813i	$-0.961771\pi$
$857$	−17.5694	−	30.4311i	−0.600159	−	1.03951i	0.392637	−	0.919693i	$-0.371563\pi$
$858$	42.8068	+	9.01879i	1.46140	+	0.307896i
$859$	31.6559	−	28.5031i	1.08008	−	0.972512i	0.0803778	−	0.996764i	$-0.474387\pi$
$859$	31.6559	−	28.5031i	1.08008	−	0.972512i	0.999706	+	0.0242527i	$0.00772064\pi$
$860$	−17.0431	−	15.4773i	−0.581164	−	0.527770i
$861$	29.1550	−	11.3542i	0.993601	−	0.386950i
$862$	29.6772	−	91.3372i	1.01081	−	3.11096i
$863$	34.6555	−	31.2040i	1.17969	−	1.06220i	0.182817	−	0.983147i	$-0.441478\pi$
$863$	34.6555	−	31.2040i	1.17969	−	1.06220i	0.996871	−	0.0790490i	$-0.0251884\pi$
$864$	−73.2474	−	125.309i	−2.49193	−	4.26309i
$865$	19.2912	+	11.2473i	0.655920	+	0.382419i
$866$	−43.5049	−	48.3171i	−1.47836	−	1.64188i
$867$	19.7236	+	17.6954i	0.669849	+	0.600966i
$868$	45.4777	+	55.8101i	1.54361	+	1.89432i
$869$	−12.6034	+	17.3470i	−0.427540	+	0.588458i
$870$	42.8266	+	19.1938i	1.45196	+	0.650732i
$871$	0.241150	−	0.541632i	0.00817106	−	0.0183525i
$872$	−14.2129	+	31.9228i	−0.481311	+	1.08104i
$873$	8.75820	−	19.8624i	0.296420	−	0.672239i
$874$		−	2.70313i		−	0.0914347i
$875$	7.37900	+	28.6453i	0.249456	+	0.968386i
$876$	−10.6124	+	102.739i	−0.358559	+	3.47124i
$877$	−3.79274	−	0.806172i	−0.128072	−	0.0272225i	0.143430	−	0.989660i	$-0.454187\pi$
$877$	−3.79274	−	0.806172i	−0.128072	−	0.0272225i	−0.271502	+	0.962438i	$0.587520\pi$
$878$	−13.9572	−	6.21413i	−0.471032	−	0.209717i
$879$	−28.5190	−	16.3974i	−0.961921	−	0.553071i
$880$	−30.4865	+	92.4892i	−1.02770	+	3.11781i
$881$	27.6575	+	20.0943i	0.931803	+	0.676995i	0.946434	−	0.322898i	$-0.104657\pi$
$881$	27.6575	+	20.0943i	0.931803	+	0.676995i	−0.0146303	+	0.999893i	$0.504657\pi$
$882$	−53.6234	−	23.2538i	−1.80559	−	0.782996i
$883$	−18.7257	−	13.6050i	−0.630169	−	0.457845i	0.226290	−	0.974060i	$-0.427340\pi$
$883$	−18.7257	−	13.6050i	−0.630169	−	0.457845i	−0.856459	+	0.516215i	$0.827340\pi$
$884$	−20.3453	+	18.3190i	−0.684285	+	0.616133i
$885$	39.7921	+	29.0603i	1.33760	+	0.976851i
$886$	11.2428	−	12.4864i	0.377708	−	0.419488i
$887$	−15.3757	−	17.0764i	−0.516265	−	0.573370i	0.427488	−	0.904021i	$-0.359398\pi$
$887$	−15.3757	−	17.0764i	−0.516265	−	0.573370i	−0.943753	+	0.330651i	$0.892732\pi$
$888$	−157.187	−	69.6470i	−5.27484	−	2.33720i
$889$	0.0260590	−	0.528171i	0.000873991	−	0.0177143i
$890$	−31.3935	+	34.5696i	−1.05231	+	1.15878i
$891$	−21.2161	+	7.06193i	−0.710766	+	0.236583i
$892$	−117.883	−	12.3900i	−3.94702	−	0.414849i
$893$	−0.530489	+	0.306278i	−0.0177521	+	0.0102492i
$894$	−85.0540	+	27.8042i	−2.84463	+	0.929912i
$895$	30.1276	−	33.1756i	1.00705	−	1.10894i
$896$	160.988	+	42.6087i	5.37822	+	1.42346i
$897$	−12.8341	+	7.44042i	−0.428517	+	0.248429i
$898$	−65.8794	−	14.0031i	−2.19842	−	0.467289i
$899$	10.3079	+	17.8538i	0.343787	+	0.595457i
$900$	43.4651	−	74.4365i	1.44884	−	2.48122i
$901$	1.31668	+	0.760184i	0.0438649	+	0.0253254i
$902$	14.5896	+	44.9020i	0.485779	+	1.49507i
$903$	5.19787	+	6.35553i	0.172974	+	0.211499i
$904$	69.9223	−	50.8015i	2.32558	−	1.68963i
$905$	−2.26440	+	1.63053i	−0.0752713	+	0.0542008i
$906$	95.1014	+	20.0365i	3.15953	+	0.665668i
$907$	1.89355	+	3.27972i	0.0628742	+	0.108901i	0.895749	−	0.444560i	$-0.146640\pi$
$907$	1.89355	+	3.27972i	0.0628742	+	0.108901i	−0.832875	+	0.553461i	$0.813307\pi$
$908$	47.0039	−	20.9275i	1.55988	−	0.694503i
$909$	−8.77200	+	15.3200i	−0.290949	+	0.508132i
$910$	56.1729	−	21.4863i	1.86211	−	0.712265i
$911$	33.0289	−	10.7317i	1.09430	−	0.355558i	0.294391	−	0.955685i	$-0.404883\pi$
$911$	33.0289	−	10.7317i	1.09430	−	0.355558i	0.799905	+	0.600127i	$0.204883\pi$
$912$	10.1601	−	7.40956i	0.336434	−	0.245355i
$913$	−3.78664	−	17.8147i	−0.125320	−	0.589582i
$914$	54.1981	+	48.8002i	1.79272	+	1.61417i
$915$	−28.7509	+	16.5053i	−0.950477	+	0.545649i
$916$	−114.019	−	37.0471i	−3.76730	−	1.22407i
$917$	−19.0575	+	1.05728i	−0.629335	+	0.0349145i
$918$	5.73279	−	17.9716i	0.189210	−	0.593153i
$919$	42.0257	−	18.7110i	1.38630	−	0.617220i	0.428208	−	0.903680i	$-0.359145\pi$
$919$	42.0257	−	18.7110i	1.38630	−	0.617220i	0.958092	+	0.286460i	$0.0924786\pi$
$920$	−22.0263	−	50.0429i	−0.726186	−	1.64987i
$921$	7.46308	−	12.9801i	0.245917	−	0.427707i
$922$	−97.5927	+	10.2574i	−3.21404	+	0.337810i
$923$	10.9914	+	33.8279i	0.361785	+	1.11346i
$924$	29.4197	−	58.4388i	0.967839	−	1.92249i
$925$	−4.57284	−	47.3759i	−0.150354	−	1.55771i
$926$	67.1894	+	38.7918i	2.20798	+	1.27478i
$927$	−12.1494	−	16.5969i	−0.399038	−	0.545113i
$928$	111.101	+	49.4651i	3.64705	+	1.62377i
$929$	4.78072	+	45.4855i	0.156850	+	1.49233i	0.735928	+	0.677060i	$0.236746\pi$
$929$	4.78072	+	45.4855i	0.156850	+	1.49233i	−0.579078	+	0.815272i	$0.696587\pi$
$930$	46.6810	−	20.6464i	1.53073	−	0.677023i
$931$	0.879005	−	2.76275i	0.0288082	−	0.0905454i
$932$		−	25.7052i		−	0.842002i
$933$	7.60345	−	2.48557i	0.248926	−	0.0813740i
$934$	−6.43488	−	30.2737i	−0.210556	−	0.990587i
$935$	−6.63235	+	2.91922i	−0.216901	+	0.0954687i
$936$	−104.547	−	46.0992i	−3.41721	−	1.50680i
$937$	−29.0983	−	9.45461i	−0.950600	−	0.308869i	−0.207640	−	0.978205i	$-0.566578\pi$
$937$	−29.0983	−	9.45461i	−0.950600	−	0.308869i	−0.742959	+	0.669337i	$0.766578\pi$
$938$	−0.931239	−	0.749393i	−0.0304060	−	0.0244686i
$939$	−13.5644	+	2.90859i	−0.442656	+	0.0949182i
$940$	−11.2357	+	15.3272i	−0.366467	+	0.499919i
$941$	11.4311	−	2.42975i	0.372642	−	0.0792075i	−0.0177840	−	0.999842i	$-0.505661\pi$
$941$	11.4311	−	2.42975i	0.372642	−	0.0792075i	0.390426	+	0.920634i	$0.372328\pi$
$942$	10.3013	−	48.8941i	0.335634	−	1.59305i
$943$	−13.8653	−	8.00515i	−0.451517	−	0.260684i
$944$	180.423	+	131.085i	5.87227	+	4.26645i
$945$	−19.2457	+	23.9709i	−0.626062	+	0.779773i
$946$	−10.0232	+	7.28226i	−0.325881	+	0.236767i
$947$	30.6567	−	3.22215i	0.996209	−	0.104706i	0.407632	−	0.913146i	$-0.366355\pi$
$947$	30.6567	−	3.22215i	0.996209	−	0.104706i	0.588578	+	0.808441i	$0.299688\pi$
$948$	63.7329	−	57.5923i	2.06995	−	1.87051i
$949$	18.9512	+	32.8245i	0.615183	+	1.06553i
$950$	5.24533	+	2.38897i	0.170181	+	0.0775084i
$951$	−3.73718	+	36.1800i	−0.121186	+	1.17322i
$952$	16.4350	+	32.0128i	0.532661	+	1.03754i
$953$	12.7601	+	17.5628i	0.413340	+	0.568914i	0.964029	−	0.265797i	$-0.0856350\pi$
$953$	12.7601	+	17.5628i	0.413340	+	0.568914i	−0.550689	+	0.834710i	$0.685635\pi$
$954$	−0.982659	+	9.68282i	−0.0318148	+	0.313493i
$955$	31.2184	−	13.7407i	1.01020	−	0.444640i
$956$	34.7156	+	3.64876i	1.12278	+	0.118009i
$957$	10.9852	−	15.1769i	0.355101	−	0.490600i
$958$	49.7257	−	68.4415i	1.60656	−	2.21124i
$959$	−8.63486	+	55.6199i	−0.278834	+	1.79606i
$960$	83.0152	−	142.974i	2.67931	−	4.61447i
$961$	−8.39049	−	1.78345i	−0.270661	−	0.0575308i
$962$	−94.6561	+	20.1198i	−3.05183	+	0.648688i
$963$	0.0152658	+	4.26277i	0.000491933	+	0.137366i
$964$	7.40160	−	34.8218i	0.238389	−	1.12153i
$965$	−5.70725	−	27.4228i	−0.183723	−	0.882770i
$966$	7.88098	+	28.8515i	0.253566	+	0.928282i
$967$	−31.0324	−	22.5463i	−0.997934	−	0.725042i	−0.0362899	−	0.999341i	$-0.511554\pi$
$967$	−31.0324	−	22.5463i	−0.997934	−	0.725042i	−0.961644	+	0.274300i	$0.911554\pi$
$968$	−43.5921	−	25.1679i	−1.40110	−	0.808927i
$969$	0.915602	+	0.192904i	0.0294134	+	0.00619698i
$970$	44.8056	−	4.51692i	1.43862	−	0.145030i
$971$	5.39104	+	51.2923i	0.173007	+	1.64605i	0.644809	+	0.764344i	$0.276937\pi$
$971$	5.39104	+	51.2923i	0.173007	+	1.64605i	−0.471802	+	0.881705i	$0.656396\pi$
$972$	89.0009	−	10.1608i	2.85471	−	0.325907i
$973$	25.3532	+	1.25088i	0.812787	+	0.0401015i
$974$		−	73.3134i		−	2.34911i
$975$	−3.09541	−	31.4798i	−0.0991325	−	1.00816i
$976$	−129.944	+	75.0231i	−4.15940	+	2.40143i
$977$	7.60065	+	6.84366i	0.243166	+	0.218948i	0.781698	−	0.623657i	$-0.214354\pi$
$977$	7.60065	+	6.84366i	0.243166	+	0.218948i	−0.538531	+	0.842605i	$0.681021\pi$
$978$	−33.7586	+	0.0604478i	−1.07948	+	0.00193291i
$979$	10.9575	+	15.0816i	0.350202	+	0.482012i
$980$	−9.56978	−	89.4364i	−0.305695	−	2.85694i
$981$	−6.75375	−	7.44700i	−0.215631	−	0.237764i
$982$	16.8529	−	29.1900i	0.537797	−	0.931492i
$983$	2.73571	−	26.0285i	0.0872555	−	0.830181i	−0.860128	−	0.510079i	$-0.829616\pi$
$983$	2.73571	−	26.0285i	0.0872555	−	0.830181i	0.947383	−	0.320102i	$-0.103717\pi$
$984$	−13.1092	−	122.613i	−0.417906	−	3.90877i
$985$	1.68061	+	5.24815i	0.0535488	+	0.167220i
$986$	4.88419	+	15.0320i	0.155544	+	0.478716i
$987$	4.76915	−	4.81566i	0.151804	−	0.153284i
$988$	2.68632	−	8.26765i	0.0854633	−	0.263029i
$989$	0.873506	−	4.10952i	0.0277759	−	0.130675i
$990$	−34.4518	−	31.0621i	−1.09495	−	0.987219i
$991$	30.1044	−	6.39890i	0.956299	−	0.203268i	0.296772	−	0.954948i	$-0.404090\pi$
$991$	30.1044	−	6.39890i	0.956299	−	0.203268i	0.659527	+	0.751681i	$0.270757\pi$
$992$	120.835	−	53.7992i	3.83651	−	1.70813i
$993$	−4.84307	−	0.500261i	−0.153690	−	0.0158753i
$994$	71.5999	−	3.97224i	2.27101	−	0.125992i
$995$	−21.4073	+	4.45530i	−0.678656	+	0.141242i
$996$	0.130645	+	72.9623i	0.00413966	+	2.31190i
$997$	0.523630	−	1.17609i	0.0165835	−	0.0372472i	−0.905064	−	0.425276i	$-0.860177\pi$
$997$	0.523630	−	1.17609i	0.0165835	−	0.0372472i	0.921647	+	0.388029i	$0.126844\pi$
$998$	−70.9561	−	63.8892i	−2.24608	−	2.02238i
$999$	36.5800	−	33.2944i	1.15734	−	1.05339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bm.a.131.1	✓	608
3.2	odd	2	inner	525.2.bm.a.131.76	yes	608
7.3	odd	6	inner	525.2.bm.a.206.1	yes	608
21.17	even	6	inner	525.2.bm.a.206.76	yes	608
25.21	even	5	inner	525.2.bm.a.446.76	yes	608
75.71	odd	10	inner	525.2.bm.a.446.1	yes	608
175.171	odd	30	inner	525.2.bm.a.521.76	yes	608
525.521	even	30	inner	525.2.bm.a.521.1	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bm.a.131.1	✓	608	1.1	even	1	trivial
525.2.bm.a.131.76	yes	608	3.2	odd	2	inner
525.2.bm.a.206.1	yes	608	7.3	odd	6	inner
525.2.bm.a.206.76	yes	608	21.17	even	6	inner
525.2.bm.a.446.1	yes	608	75.71	odd	10	inner
525.2.bm.a.446.76	yes	608	25.21	even	5	inner
525.2.bm.a.521.1	yes	608	525.521	even	30	inner
525.2.bm.a.521.76	yes	608	175.171	odd	30	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.578671 + 2.72243i) q^{2} +(1.50155 + 0.863338i) q^{3} +(-5.24969 - 2.33731i) q^{4} +(2.12367 + 0.700010i) q^{5} +(-3.21928 + 3.58828i) q^{6} +(2.47291 + 0.940586i) q^{7} +(6.12911 - 8.43599i) q^{8} +(1.50929 + 2.59269i) q^{9} +O(q^{10})\)	\(q+(-0.578671 + 2.72243i) q^{2} +(1.50155 + 0.863338i) q^{3} +(-5.24969 - 2.33731i) q^{4} +(2.12367 + 0.700010i) q^{5} +(-3.21928 + 3.58828i) q^{6} +(2.47291 + 0.940586i) q^{7} +(6.12911 - 8.43599i) q^{8} +(1.50929 + 2.59269i) q^{9} +(-3.13464 + 5.37648i) q^{10} +(1.84635 + 1.66246i) q^{11} +(-5.86477 - 8.04184i) q^{12} +(-3.47374 - 1.12869i) q^{13} +(-3.99168 + 6.18805i) q^{14} +(2.58445 + 2.88455i) q^{15} +(11.7294 + 13.0268i) q^{16} +(-0.136342 + 1.29721i) q^{17} +(-7.93180 + 2.60864i) q^{18} +(-0.168459 - 0.378366i) q^{19} +(-9.51248 - 8.63852i) q^{20} +(2.90115 + 3.54730i) q^{21} +(-5.59436 + 4.06454i) q^{22} +(0.487541 - 2.29370i) q^{23} +(16.4863 - 7.37556i) q^{24} +(4.01997 + 2.97318i) q^{25} +(5.08292 - 8.80388i) q^{26} +(0.0279123 + 5.19608i) q^{27} +(-10.7836 - 10.7178i) q^{28} +(-2.55906 - 3.52224i) q^{29} +(-9.34853 + 5.36679i) q^{30} +(-4.70925 - 0.494963i) q^{31} +(-24.1911 + 13.9667i) q^{32} +(1.33712 + 4.09028i) q^{33} +(-3.45267 - 1.12184i) q^{34} +(4.59324 + 3.72856i) q^{35} +(-1.86341 - 17.1385i) q^{36} +(-6.36959 - 7.07415i) q^{37} +(1.12756 - 0.239670i) q^{38} +(-4.24155 - 4.69379i) q^{39} +(18.9215 - 13.6248i) q^{40} +(2.10984 - 6.49342i) q^{41} +(-11.3361 + 5.84548i) q^{42} +1.79166 q^{43} +(-5.80706 - 13.0429i) q^{44} +(1.39034 + 6.56254i) q^{45} +(5.96232 + 2.65460i) q^{46} +(-0.154596 - 1.47088i) q^{47} +(6.36569 + 29.6867i) q^{48} +(5.23060 + 4.65197i) q^{49} +(-10.4205 + 9.22361i) q^{50} +(-1.32465 + 1.83011i) q^{51} +(15.5979 + 14.0445i) q^{52} +(0.474096 - 1.06484i) q^{53} +(-14.1621 - 2.93083i) q^{54} +(2.75730 + 4.82298i) q^{55} +(23.0915 - 15.0965i) q^{56} +(0.0737078 - 0.713572i) q^{57} +(11.0699 - 4.92865i) q^{58} +(12.4444 - 2.64515i) q^{59} +(-6.82548 - 21.1836i) q^{60} +(-1.77967 + 8.37271i) q^{61} +(4.07261 - 12.5342i) q^{62} +(1.29371 + 7.83111i) q^{63} +(-13.1911 - 40.5981i) q^{64} +(-6.58699 - 4.82861i) q^{65} +(-11.9093 + 1.27328i) q^{66} +(-0.0169675 + 0.161435i) q^{67} +(3.74774 - 6.49127i) q^{68} +(2.71231 - 3.02319i) q^{69} +(-12.8087 + 10.3472i) q^{70} +(-5.72396 - 7.87836i) q^{71} +(31.1225 + 3.15846i) q^{72} +(-7.71171 - 6.94365i) q^{73} +(22.9448 - 13.2472i) q^{74} +(3.46932 + 7.93497i) q^{75} +2.38004i q^{76} +(3.00217 + 5.84776i) q^{77} +(15.2330 - 8.83117i) q^{78} +(0.902116 + 8.58306i) q^{79} +(15.7905 + 35.8753i) q^{80} +(-4.44406 + 7.82626i) q^{81} +(16.4570 + 9.50145i) q^{82} +(-5.93052 - 4.30878i) q^{83} +(-6.93902 - 25.4031i) q^{84} +(-1.19761 + 2.65941i) q^{85} +(-1.03678 + 4.87766i) q^{86} +(-0.801664 - 7.49815i) q^{87} +(25.3409 - 5.38638i) q^{88} +(7.33932 + 1.56002i) q^{89} +(-18.6706 - 0.0124439i) q^{90} +(-7.52862 - 6.05849i) q^{91} +(-7.92053 + 10.9017i) q^{92} +(-6.64385 - 4.80889i) q^{93} +(4.09384 + 0.430280i) q^{94} +(-0.0928926 - 0.921448i) q^{95} +(-48.3821 + 0.0866324i) q^{96} +(-4.25313 - 5.85393i) q^{97} +(-15.6915 + 11.5480i) q^{98} +(-1.52355 + 7.29614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Introduction

L-functions

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