LMFDB - Embedded newform 75.2.g.c.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(16,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("75.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.g (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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.3
Root			$1.97423 - 1.43436i$ of defining polynomial
Character	$\chi$	$=$	75.31
Dual form			75.2.g.c.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.754089 + 2.32085i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-3.19965 + 2.32468i) q^{4} +(0.824264 - 2.07860i) q^{5} +(1.97423 + 1.43436i) q^{6} -3.44028 q^{7} +(-3.85959 - 2.80415i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.754089 + 2.32085i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-3.19965 + 2.32468i) q^{4} +(0.824264 - 2.07860i) q^{5} +(1.97423 + 1.43436i) q^{6} -3.44028 q^{7} +(-3.85959 - 2.80415i) q^{8} +(0.309017 - 0.951057i) q^{9} +(5.44569 + 0.345540i) q^{10} +(-1.00942 - 3.10669i) q^{11} +(-1.22216 + 3.76141i) q^{12} +(-0.998755 + 3.07385i) q^{13} +(-2.59428 - 7.98437i) q^{14} +(-0.554928 - 2.16612i) q^{15} +(1.15323 - 3.54927i) q^{16} +(4.08826 + 2.97030i) q^{17} +2.44028 q^{18} +(2.49274 + 1.81108i) q^{19} +(2.19473 + 8.56695i) q^{20} +(-2.78325 + 2.02215i) q^{21} +(6.44895 - 4.68544i) q^{22} +(0.478250 + 1.47190i) q^{23} -4.77071 q^{24} +(-3.64118 - 3.42664i) q^{25} -7.88709 q^{26} +(-0.309017 - 0.951057i) q^{27} +(11.0077 - 7.99756i) q^{28} +(2.52590 - 1.83517i) q^{29} +(4.60876 - 2.92135i) q^{30} +(-6.02080 - 4.37437i) q^{31} -0.434479 q^{32} +(-2.64270 - 1.92004i) q^{33} +(-3.81069 + 11.7281i) q^{34} +(-2.83570 + 7.15098i) q^{35} +(1.22216 + 3.76141i) q^{36} +(-1.77944 + 5.47655i) q^{37} +(-2.32349 + 7.15098i) q^{38} +(0.998755 + 3.07385i) q^{39} +(-9.01004 + 5.71118i) q^{40} +(1.67476 - 5.15437i) q^{41} +(-6.79191 - 4.93461i) q^{42} +2.53106 q^{43} +(10.4519 + 7.59371i) q^{44} +(-1.72216 - 1.42625i) q^{45} +(-3.05541 + 2.21989i) q^{46} +(-5.72106 + 4.15659i) q^{47} +(-1.15323 - 3.54927i) q^{48} +4.83555 q^{49} +(5.20693 - 11.0346i) q^{50} +5.05337 q^{51} +(-3.95006 - 12.1570i) q^{52} +(8.21277 - 5.96693i) q^{53} +(1.97423 - 1.43436i) q^{54} +(-7.28960 - 0.462540i) q^{55} +(13.2781 + 9.64708i) q^{56} +3.08119 q^{57} +(6.16391 + 4.47834i) q^{58} +(0.534773 - 1.64586i) q^{59} +(6.81110 + 5.64078i) q^{60} +(2.42149 + 7.45259i) q^{61} +(5.61202 - 17.2720i) q^{62} +(-1.06311 + 3.27190i) q^{63} +(-2.63409 - 8.10689i) q^{64} +(5.56608 + 4.60968i) q^{65} +(2.46328 - 7.58119i) q^{66} +(1.49595 + 1.08687i) q^{67} -19.9860 q^{68} +(1.25207 + 0.909685i) q^{69} +(-18.7347 - 1.18876i) q^{70} +(0.577613 - 0.419660i) q^{71} +(-3.85959 + 2.80415i) q^{72} +(-0.581036 - 1.78825i) q^{73} -14.0521 q^{74} +(-4.95990 - 0.631977i) q^{75} -12.1861 q^{76} +(3.47270 + 10.6879i) q^{77} +(-6.38079 + 4.63591i) q^{78} +(10.7868 - 7.83708i) q^{79} +(-6.42695 - 5.32263i) q^{80} +(-0.809017 - 0.587785i) q^{81} +13.2254 q^{82} +(-3.20166 - 2.32614i) q^{83} +(4.20457 - 12.9403i) q^{84} +(9.54388 - 6.04956i) q^{85} +(1.90864 + 5.87419i) q^{86} +(0.964807 - 2.96937i) q^{87} +(-4.81567 + 14.8211i) q^{88} +(2.63713 + 8.11624i) q^{89} +(2.01144 - 5.07238i) q^{90} +(3.43600 - 10.5749i) q^{91} +(-4.95193 - 3.59779i) q^{92} -7.44212 q^{93} +(-13.9610 - 10.1433i) q^{94} +(5.81919 - 3.68860i) q^{95} +(-0.351501 + 0.255380i) q^{96} +(8.61831 - 6.26157i) q^{97} +(3.64643 + 11.2226i) q^{98} -3.26656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23} + 6 q^{24} + 4 q^{25} - 56 q^{26} + 3 q^{27} + q^{28} - q^{29} + 19 q^{30} + 13 q^{31} - 32 q^{32} - q^{33} - 25 q^{34} - 10 q^{35} + 8 q^{37} - 22 q^{38} + 2 q^{39} - 28 q^{40} + 8 q^{41} - 16 q^{42} - 4 q^{43} + 33 q^{44} - 6 q^{45} - 22 q^{46} - 13 q^{47} - 16 q^{48} - 28 q^{49} + 81 q^{50} + 26 q^{51} + 44 q^{52} + 44 q^{53} + 9 q^{55} + 45 q^{56} - 22 q^{57} + 41 q^{58} - 22 q^{59} + 14 q^{60} - 8 q^{61} + 41 q^{62} + 3 q^{63} + 49 q^{64} - 38 q^{65} - 3 q^{66} - 6 q^{67} - 100 q^{68} + 6 q^{69} - 45 q^{70} - 21 q^{71} + 9 q^{72} - 16 q^{73} - 44 q^{74} - 4 q^{75} - 52 q^{76} + q^{77} - 19 q^{78} + 10 q^{79} - 99 q^{80} - 3 q^{81} + 26 q^{82} - 10 q^{83} - 6 q^{84} + 23 q^{85} + 56 q^{86} - 4 q^{87} - 16 q^{88} + 57 q^{89} + 16 q^{90} - 7 q^{91} + 3 q^{92} + 22 q^{93} - 23 q^{94} + 21 q^{95} - 23 q^{96} + 4 q^{97} - 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.754089	+	2.32085i	0.533221	+	1.64109i	0.747461	+	0.664306i	$0.231273\pi$
$2$	0.754089	+	2.32085i	0.533221	+	1.64109i	−0.214240	+	0.976781i	$0.568727\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−3.19965	+	2.32468i	−1.59982	+	1.16234i
$5$	0.824264	−	2.07860i	0.368622	−	0.929579i
$5$	0.824264	−	2.07860i	0.368622	−	0.929579i
$6$	1.97423	+	1.43436i	0.805976	+	0.585576i
$7$	−3.44028			−1.30030			−0.650152	−	0.759804i	$-0.725295\pi$
$7$	−3.44028			−1.30030			−0.650152	+	0.759804i	$0.725295\pi$
$8$	−3.85959	−	2.80415i	−1.36457	−	0.991418i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	5.44569	+	0.345540i	1.72208	+	0.109269i
$11$	−1.00942	−	3.10669i	−0.304353	−	0.936701i	−0.979918	−	0.199401i	$-0.936100\pi$
$11$	−1.00942	−	3.10669i	−0.304353	−	0.936701i	0.675565	−	0.737300i	$-0.263900\pi$
$12$	−1.22216	+	3.76141i	−0.352806	+	1.08583i
$13$	−0.998755	+	3.07385i	−0.277005	+	0.852533i	0.711677	+	0.702506i	$0.247936\pi$
$13$	−0.998755	+	3.07385i	−0.277005	+	0.852533i	−0.988682	+	0.150026i	$0.952064\pi$
$14$	−2.59428	−	7.98437i	−0.693350	−	2.13391i
$15$	−0.554928	−	2.16612i	−0.143282	−	0.559289i
$16$	1.15323	−	3.54927i	0.288307	−	0.887317i
$17$	4.08826	+	2.97030i	0.991550	+	0.720403i	0.960260	−	0.279107i	$-0.0900386\pi$
$17$	4.08826	+	2.97030i	0.991550	+	0.720403i	0.0312897	+	0.999510i	$0.490039\pi$
$18$	2.44028			0.575180
$19$	2.49274	+	1.81108i	0.571873	+	0.415490i	0.835785	−	0.549056i	$-0.185013\pi$
$19$	2.49274	+	1.81108i	0.571873	+	0.415490i	−0.263912	+	0.964547i	$0.585013\pi$
$20$	2.19473	+	8.56695i	0.490757	+	1.91563i
$21$	−2.78325	+	2.02215i	−0.607354	+	0.441269i
$22$	6.44895	−	4.68544i	1.37492	−	0.998938i
$23$	0.478250	+	1.47190i	0.0997219	+	0.306913i	0.988455	−	0.151512i	$-0.0484141\pi$
$23$	0.478250	+	1.47190i	0.0997219	+	0.306913i	−0.888734	+	0.458424i	$0.848414\pi$
$24$	−4.77071			−0.973817
$25$	−3.64118	−	3.42664i	−0.728235	−	0.685327i
$26$	−7.88709			−1.54679
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	11.0077	−	7.99756i	2.08026	−	1.51140i
$29$	2.52590	−	1.83517i	0.469047	−	0.340783i	−0.328022	−	0.944670i	$-0.606382\pi$
$29$	2.52590	−	1.83517i	0.469047	−	0.340783i	0.797070	+	0.603887i	$0.206382\pi$
$30$	4.60876	−	2.92135i	0.841440	−	0.533363i
$31$	−6.02080	−	4.37437i	−1.08137	−	0.785659i	−0.103446	−	0.994635i	$-0.532987\pi$
$31$	−6.02080	−	4.37437i	−1.08137	−	0.785659i	−0.977921	+	0.208976i	$0.932987\pi$
$32$	−0.434479			−0.0768057
$33$	−2.64270	−	1.92004i	−0.460036	−	0.334236i
$34$	−3.81069	+	11.7281i	−0.653528	+	2.01135i
$35$	−2.83570	+	7.15098i	−0.479321	+	1.20874i
$36$	1.22216	+	3.76141i	0.203693	+	0.626902i
$37$	−1.77944	+	5.47655i	−0.292538	+	0.900339i	0.691499	+	0.722377i	$0.256950\pi$
$37$	−1.77944	+	5.47655i	−0.292538	+	0.900339i	−0.984037	+	0.177962i	$0.943050\pi$
$38$	−2.32349	+	7.15098i	−0.376921	+	1.16004i
$39$	0.998755	+	3.07385i	0.159929	+	0.492210i
$40$	−9.01004	+	5.71118i	−1.42461	+	0.903017i
$41$	1.67476	−	5.15437i	0.261553	−	0.804977i	−0.730915	−	0.682469i	$-0.760906\pi$
$41$	1.67476	−	5.15437i	0.261553	−	0.804977i	0.992468	−	0.122508i	$-0.0390938\pi$
$42$	−6.79191	−	4.93461i	−1.04801	−	0.761427i
$43$	2.53106			0.385982			0.192991	−	0.981201i	$-0.438181\pi$
$43$	2.53106			0.385982			0.192991	+	0.981201i	$0.438181\pi$
$44$	10.4519	+	7.59371i	1.57568	+	1.14480i
$45$	−1.72216	−	1.42625i	−0.256724	−	0.212612i
$46$	−3.05541	+	2.21989i	−0.450496	+	0.327305i
$47$	−5.72106	+	4.15659i	−0.834502	+	0.606301i	−0.920829	−	0.389966i	$-0.872487\pi$
$47$	−5.72106	+	4.15659i	−0.834502	+	0.606301i	0.0863273	+	0.996267i	$0.472487\pi$
$48$	−1.15323	−	3.54927i	−0.166454	−	0.512293i
$49$	4.83555			0.690793
$50$	5.20693	−	11.0346i	0.736371	−	1.56053i
$51$	5.05337			0.707614
$52$	−3.95006	−	12.1570i	−0.547774	−	1.68588i
$53$	8.21277	−	5.96693i	1.12811	−	0.819621i	0.142692	−	0.989767i	$-0.454424\pi$
$53$	8.21277	−	5.96693i	1.12811	−	0.819621i	0.985419	+	0.170147i	$0.0544241\pi$
$54$	1.97423	−	1.43436i	0.268659	−	0.195192i
$55$	−7.28960	−	0.462540i	−0.982929	−	0.0623689i
$56$	13.2781	+	9.64708i	1.77436	+	1.28915i
$57$	3.08119			0.408114
$58$	6.16391	+	4.47834i	0.809361	+	0.588035i
$59$	0.534773	−	1.64586i	0.0696215	−	0.214273i	−0.910192	−	0.414187i	$-0.864066\pi$
$59$	0.534773	−	1.64586i	0.0696215	−	0.214273i	0.979814	+	0.199913i	$0.0640661\pi$
$60$	6.81110	+	5.64078i	0.879309	+	0.728221i
$61$	2.42149	+	7.45259i	0.310040	+	0.954206i	0.977748	+	0.209783i	$0.0672756\pi$
$61$	2.42149	+	7.45259i	0.310040	+	0.954206i	−0.667708	+	0.744424i	$0.732724\pi$
$62$	5.61202	−	17.2720i	0.712727	−	2.19355i
$63$	−1.06311	+	3.27190i	−0.133939	+	0.412221i
$64$	−2.63409	−	8.10689i	−0.329261	−	1.01336i
$65$	5.56608	+	4.60968i	0.690387	+	0.571760i
$66$	2.46328	−	7.58119i	0.303209	−	0.933180i
$67$	1.49595	+	1.08687i	0.182760	+	0.132783i	0.675404	−	0.737448i	$-0.263969\pi$
$67$	1.49595	+	1.08687i	0.182760	+	0.132783i	−0.492644	+	0.870231i	$0.663969\pi$
$68$	−19.9860			−2.42366
$69$	1.25207	+	0.909685i	0.150732	+	0.109513i
$70$	−18.7347	−	1.18876i	−2.23923	−	0.142084i
$71$	0.577613	−	0.419660i	0.0685500	−	0.0498045i	−0.552982	−	0.833193i	$-0.686510\pi$
$71$	0.577613	−	0.419660i	0.0685500	−	0.0498045i	0.621533	+	0.783388i	$0.286510\pi$
$72$	−3.85959	+	2.80415i	−0.454857	+	0.330473i
$73$	−0.581036	−	1.78825i	−0.0680052	−	0.209298i	0.911279	−	0.411790i	$-0.135096\pi$
$73$	−0.581036	−	1.78825i	−0.0680052	−	0.209298i	−0.979284	+	0.202491i	$0.935096\pi$
$74$	−14.0521			−1.63352
$75$	−4.95990	−	0.631977i	−0.572720	−	0.0729744i
$76$	−12.1861			−1.39784
$77$	3.47270	+	10.6879i	0.395751	+	1.21800i
$78$	−6.38079	+	4.63591i	−0.722482	+	0.524914i
$79$	10.7868	−	7.83708i	1.21361	−	0.881740i	0.218058	−	0.975936i	$-0.430028\pi$
$79$	10.7868	−	7.83708i	1.21361	−	0.881740i	0.995554	+	0.0941957i	$0.0300279\pi$
$80$	−6.42695	−	5.32263i	−0.718555	−	0.595089i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	13.2254			1.46050
$83$	−3.20166	−	2.32614i	−0.351428	−	0.255328i	0.398040	−	0.917368i	$-0.369691\pi$
$83$	−3.20166	−	2.32614i	−0.351428	−	0.255328i	−0.749468	+	0.662041i	$0.769691\pi$
$84$	4.20457	−	12.9403i	0.458756	−	1.41190i
$85$	9.54388	−	6.04956i	1.03518	−	0.656167i
$86$	1.90864	+	5.87419i	0.205814	+	0.633430i
$87$	0.964807	−	2.96937i	0.103438	−	0.318350i
$88$	−4.81567	+	14.8211i	−0.513352	+	1.57993i
$89$	2.63713	+	8.11624i	0.279535	+	0.860320i	0.987984	+	0.154558i	$0.0493952\pi$
$89$	2.63713	+	8.11624i	0.279535	+	0.860320i	−0.708449	+	0.705762i	$0.750605\pi$
$90$	2.01144	−	5.07238i	0.212024	−	0.534676i
$91$	3.43600	−	10.5749i	0.360191	−	1.10855i
$92$	−4.95193	−	3.59779i	−0.516274	−	0.375095i
$93$	−7.44212			−0.771712
$94$	−13.9610	−	10.1433i	−1.43997	−	1.04620i
$95$	5.81919	−	3.68860i	0.597037	−	0.378443i
$96$	−0.351501	+	0.255380i	−0.0358749	+	0.0260646i
$97$	8.61831	−	6.26157i	0.875057	−	0.635766i	−0.0568823	−	0.998381i	$-0.518116\pi$
$97$	8.61831	−	6.26157i	0.875057	−	0.635766i	0.931939	+	0.362615i	$0.118116\pi$
$98$	3.64643	+	11.2226i	0.368345	+	1.13365i
$99$	−3.26656			−0.328302
$100$	19.6163	+	2.49946i	1.96163	+	0.249946i
$101$	1.76173			0.175299			0.0876496	−	0.996151i	$-0.472064\pi$
$101$	1.76173			0.175299			0.0876496	+	0.996151i	$0.472064\pi$
$102$	3.81069	+	11.7281i	0.377315	+	1.16126i
$103$	−12.8749	+	9.35416i	−1.26860	+	0.921693i	−0.999146	−	0.0413198i	$-0.986844\pi$
$103$	−12.8749	+	9.35416i	−1.26860	+	0.921693i	−0.269456	+	0.963013i	$0.586844\pi$
$104$	12.4743	−	9.06313i	1.22321	−	0.888713i
$105$	1.90911	+	7.45205i	0.186310	+	0.727246i
$106$	20.0415	+	14.5610i	1.94660	+	1.41429i
$107$	−15.7807			−1.52558			−0.762788	−	0.646649i	$-0.776170\pi$
$107$	−15.7807			−1.52558			−0.762788	+	0.646649i	$0.776170\pi$
$108$	3.19965	+	2.32468i	0.307886	+	0.223692i
$109$	−3.06539	+	9.43429i	−0.293611	+	0.903641i	0.690074	+	0.723739i	$0.257578\pi$
$109$	−3.06539	+	9.43429i	−0.293611	+	0.903641i	−0.983685	+	0.179902i	$0.942422\pi$
$110$	−4.42352	−	17.2668i	−0.421766	−	1.64633i
$111$	1.77944	+	5.47655i	0.168897	+	0.519811i
$112$	−3.96743	+	12.2105i	−0.374887	+	1.15378i
$113$	1.70388	−	5.24399i	0.160287	−	0.493313i	−0.838371	−	0.545100i	$-0.816492\pi$
$113$	1.70388	−	5.24399i	0.160287	−	0.493313i	0.998658	+	0.0517868i	$0.0164916\pi$
$114$	2.32349	+	7.15098i	0.217615	+	0.669751i
$115$	3.45370	+	0.219145i	0.322059	+	0.0204353i
$116$	−3.81580	+	11.7438i	−0.354288	+	1.09039i
$117$	2.61477	+	1.89974i	0.241736	+	0.175631i
$118$	4.22306			0.388764
$119$	−14.0648	−	10.2187i	−1.28932	−	0.936743i
$120$	−3.93233	+	9.91641i	−0.358971	+	0.905240i
$121$	0.266626	−	0.193715i	0.0242387	−	0.0176105i
$122$	−15.4703	+	11.2398i	−1.40061	+	1.01761i
$123$	−1.67476	−	5.15437i	−0.151008	−	0.464754i
$124$	29.4334			2.64320
$125$	−10.1239	+	4.74410i	−0.905510	+	0.424326i
$126$	−8.39527			−0.747910
$127$	−0.306572	−	0.943532i	−0.0272039	−	0.0837250i	0.936533	−	0.350580i	$-0.114016\pi$
$127$	−0.306572	−	0.943532i	−0.0272039	−	0.0837250i	−0.963737	+	0.266855i	$0.914016\pi$
$128$	16.1255	−	11.7159i	1.42531	−	1.03555i
$129$	2.04767	−	1.48772i	0.180287	−	0.130986i
$130$	−6.50105	+	16.3941i	−0.570179	+	1.43786i
$131$	10.2029	+	7.41286i	0.891434	+	0.647665i	0.936252	−	0.351330i	$-0.114271\pi$
$131$	10.2029	+	7.41286i	0.891434	+	0.647665i	−0.0448175	+	0.998995i	$0.514271\pi$
$132$	12.9192			1.12447
$133$	−8.57573	−	6.23063i	−0.743610	−	0.540264i
$134$	−1.39438	+	4.29147i	−0.120456	+	0.370727i
$135$	−2.23158	−	0.141599i	−0.192064	−	0.0121869i
$136$	−7.44984	−	22.9282i	−0.638818	−	1.96608i
$137$	2.54650	−	7.83732i	0.217562	−	0.669588i	−0.781400	−	0.624031i	$-0.785494\pi$
$137$	2.54650	−	7.83732i	0.217562	−	0.669588i	0.998962	−	0.0455566i	$-0.0145061\pi$
$138$	−1.16706	+	3.59186i	−0.0993471	+	0.305759i
$139$	2.49182	+	7.66904i	0.211354	+	0.650479i	0.999392	+	0.0348539i	$0.0110966\pi$
$139$	2.49182	+	7.66904i	0.211354	+	0.650479i	−0.788039	+	0.615626i	$0.788903\pi$
$140$	−7.55049	−	29.4727i	−0.638133	−	2.49090i
$141$	−2.18525	+	6.72551i	−0.184031	+	0.566390i
$142$	1.40954	+	1.02409i	0.118286	+	0.0859397i
$143$	10.5577			0.882875
$144$	−3.01919	−	2.19357i	−0.251599	−	0.182797i
$145$	−1.73259	−	6.76301i	−0.143883	−	0.561637i
$146$	3.71209	−	2.69699i	0.307215	−	0.223205i
$147$	3.91204	−	2.84226i	0.322660	−	0.234426i
$148$	−7.03765	−	21.6597i	−0.578491	−	1.78041i
$149$	−19.1101			−1.56556			−0.782781	−	0.622298i	$-0.786199\pi$
$149$	−19.1101			−1.56556			−0.782781	+	0.622298i	$0.786199\pi$
$150$	−2.27348	−	11.9877i	−0.185629	−	0.978795i
$151$	1.58550			0.129026			0.0645132	−	0.997917i	$-0.479451\pi$
$151$	1.58550			0.129026			0.0645132	+	0.997917i	$0.479451\pi$
$152$	−4.54239	−	13.9800i	−0.368437	−	1.13393i
$153$	4.08826	−	2.97030i	0.330517	−	0.240134i
$154$	−22.1862	+	16.1192i	−1.78782	+	1.29892i
$155$	−14.0553	+	8.90921i	−1.12895	+	0.715605i
$156$	−10.3414	−	7.51345i	−0.827973	−	0.601558i
$157$	−21.8510			−1.74390			−0.871948	−	0.489599i	$-0.837143\pi$
$157$	−21.8510			−1.74390			−0.871948	+	0.489599i	$0.837143\pi$
$158$	26.3229	+	19.1247i	2.09414	+	1.52148i
$159$	3.13700	−	9.65469i	0.248780	−	0.765667i
$160$	−0.358125	+	0.903108i	−0.0283123	+	0.0713970i
$161$	−1.64531	−	5.06376i	−0.129669	−	0.399080i
$162$	0.754089	−	2.32085i	0.0592468	−	0.182343i
$163$	3.13153	−	9.63786i	0.245280	−	0.754896i	−0.750310	−	0.661087i	$-0.770096\pi$
$163$	3.13153	−	9.63786i	0.245280	−	0.754896i	0.995590	−	0.0938092i	$-0.0299044\pi$
$164$	6.62363	+	20.3854i	0.517219	+	1.59184i
$165$	−6.16928	+	3.91051i	−0.480278	+	0.304433i
$166$	2.98429	−	9.18469i	0.231626	−	0.712870i
$167$	1.22250	+	0.888195i	0.0945996	+	0.0687306i	0.634080	−	0.773268i	$-0.281379\pi$
$167$	1.22250	+	0.888195i	0.0945996	+	0.0687306i	−0.539480	+	0.841998i	$0.681379\pi$
$168$	16.4126			1.26626
$169$	2.06617	+	1.50116i	0.158936	+	0.115474i
$170$	21.2370	+	17.5880i	1.62881	+	1.34894i
$171$	2.49274	−	1.81108i	0.190624	−	0.138497i
$172$	−8.09848	+	5.88389i	−0.617504	+	0.448643i
$173$	−4.28153	−	13.1772i	−0.325518	−	1.00184i	−0.971206	−	0.238241i	$-0.923429\pi$
$173$	−4.28153	−	13.1772i	−0.325518	−	1.00184i	0.645688	−	0.763602i	$-0.276571\pi$
$174$	7.61901			0.577595
$175$	12.5267	+	11.7886i	0.946928	+	0.891134i
$176$	−12.1906			−0.918897
$177$	−0.534773	−	1.64586i	−0.0401960	−	0.123711i
$178$	−16.8479	+	12.2407i	−1.26281	+	0.917482i
$179$	−11.6949	+	8.49685i	−0.874119	+	0.635085i	−0.931689	−	0.363257i	$-0.881665\pi$
$179$	−11.6949	+	8.49685i	−0.874119	+	0.635085i	0.0575701	+	0.998341i	$0.481665\pi$
$180$	8.82586	+	0.560020i	0.657841	+	0.0417414i
$181$	−13.9068	−	10.1039i	−1.03369	−	0.751017i	−0.0646435	−	0.997908i	$-0.520591\pi$
$181$	−13.9068	−	10.1039i	−1.03369	−	0.751017i	−0.969043	+	0.246891i	$0.920591\pi$
$182$	27.1338			2.01129
$183$	6.33955	+	4.60595i	0.468633	+	0.340482i
$184$	2.28159	−	7.02201i	0.168201	−	0.517670i
$185$	9.91684	+	8.21287i	0.729101	+	0.603822i
$186$	−5.61202	−	17.2720i	−0.411493	−	1.26645i
$187$	5.10099	−	15.6992i	0.373021	−	1.14804i
$188$	8.64262	−	26.5993i	0.630328	−	1.93995i
$189$	1.06311	+	3.27190i	0.0773296	+	0.237996i
$190$	12.9489	+	10.7239i	0.939410	+	0.777995i
$191$	3.25778	−	10.0264i	0.235725	−	0.725486i	−0.761300	−	0.648400i	$-0.775438\pi$
$191$	3.25778	−	10.0264i	0.235725	−	0.725486i	0.997024	−	0.0770858i	$-0.0245615\pi$
$192$	−6.89613	−	5.01034i	−0.497686	−	0.361590i
$193$	−0.682908			−0.0491568			−0.0245784	−	0.999698i	$-0.507824\pi$
$193$	−0.682908			−0.0491568			−0.0245784	+	0.999698i	$0.507824\pi$
$194$	21.0311	+	15.2800i	1.50995	+	1.09704i
$195$	7.21255	+	0.457652i	0.516502	+	0.0327731i
$196$	−15.4721	+	11.2411i	−1.10515	+	0.802936i
$197$	18.8478	−	13.6937i	1.34285	−	0.975639i	0.343518	−	0.939146i	$-0.388381\pi$
$197$	18.8478	−	13.6937i	1.34285	−	0.975639i	0.999334	−	0.0364929i	$-0.0116186\pi$
$198$	−2.46328	−	7.58119i	−0.175058	−	0.538772i
$199$	10.1946			0.722679			0.361339	−	0.932434i	$-0.382320\pi$
$199$	10.1946			0.722679			0.361339	+	0.932434i	$0.382320\pi$
$200$	4.44462	+	23.4358i	0.314282	+	1.65716i
$201$	1.84910			0.130425
$202$	1.32850	+	4.08872i	0.0934733	+	0.287681i
$203$	−8.68980	+	6.31351i	−0.609905	+	0.443122i
$204$	−16.1690	+	11.7475i	−1.13206	+	0.822488i
$205$	−9.33344	−	7.72971i	−0.651876	−	0.539867i
$206$	−31.4184	−	22.8268i	−2.18902	−	1.59042i
$207$	1.54765			0.107569
$208$	9.75813	+	7.08969i	0.676604	+	0.491582i
$209$	3.11023	−	9.57230i	0.215139	−	0.662130i
$210$	−15.8554	+	10.0503i	−1.09413	+	0.693534i
$211$	5.64172	+	17.3634i	0.388392	+	1.19535i	0.933990	+	0.357300i	$0.116303\pi$
$211$	5.64172	+	17.3634i	0.388392	+	1.19535i	−0.545598	+	0.838047i	$0.683697\pi$
$212$	−12.4068	+	38.1841i	−0.852101	+	2.62250i
$213$	0.220629	−	0.679025i	0.0151172	−	0.0465260i
$214$	−11.9000	−	36.6245i	−0.813470	−	2.50360i
$215$	2.08626	−	5.26106i	0.142282	−	0.358801i
$216$	−1.47423	+	4.53722i	−0.100309	+	0.308718i
$217$	20.7133	+	15.0491i	1.40611	+	1.02160i
$218$	−24.2071			−1.63951
$219$	−1.52117	−	1.10520i	−0.102791	−	0.0746823i
$220$	24.3994	−	15.4660i	1.64501	−	1.04272i
$221$	−13.2134	+	9.60011i	−0.888831	+	0.645774i
$222$	−11.3684	+	8.25961i	−0.762996	+	0.554349i
$223$	5.32262	+	16.3813i	0.356429	+	1.09698i	0.955176	+	0.296037i	$0.0956653\pi$
$223$	5.32262	+	16.3813i	0.356429	+	1.09698i	−0.598748	+	0.800938i	$0.704335\pi$
$224$	1.49473			0.0998708
$225$	−4.38411	+	2.40408i	−0.292274	+	0.160272i
$226$	13.4554			0.895039
$227$	−1.33767	−	4.11692i	−0.0887842	−	0.273250i	0.896800	−	0.442437i	$-0.145886\pi$
$227$	−1.33767	−	4.11692i	−0.0887842	−	0.273250i	−0.985584	+	0.169187i	$0.945886\pi$
$228$	−9.85874	+	7.16279i	−0.652911	+	0.474367i
$229$	−16.4349	+	11.9407i	−1.08605	+	0.789062i	−0.978728	−	0.205163i	$-0.934228\pi$
$229$	−16.4349	+	11.9407i	−1.08605	+	0.789062i	−0.107322	+	0.994224i	$0.534228\pi$
$230$	2.09580	+	8.18077i	0.138193	+	0.539424i
$231$	9.09165	+	6.60547i	0.598187	+	0.434608i
$232$	−14.8950			−0.977906
$233$	0.275839	+	0.200409i	0.0180708	+	0.0131292i	0.596784	−	0.802402i	$-0.296445\pi$
$233$	0.275839	+	0.200409i	0.0180708	+	0.0131292i	−0.578713	+	0.815531i	$0.696445\pi$
$234$	−2.43724	+	7.50107i	−0.159328	+	0.490360i
$235$	3.92424	+	15.3179i	0.255989	+	0.999232i
$236$	2.11502	+	6.50936i	0.137676	+	0.423723i
$237$	4.12020	−	12.6807i	0.267635	−	0.823697i
$238$	13.1099	−	40.3480i	0.849786	−	2.61537i
$239$	−2.21407	−	6.81421i	−0.143216	−	0.440774i	0.853561	−	0.520993i	$-0.174438\pi$
$239$	−2.21407	−	6.81421i	−0.143216	−	0.440774i	−0.996777	+	0.0802185i	$0.974438\pi$
$240$	−8.32808	−	0.528434i	−0.537575	−	0.0341103i
$241$	−3.88194	+	11.9474i	−0.250058	+	0.769599i	0.744705	+	0.667393i	$0.232590\pi$
$241$	−3.88194	+	11.9474i	−0.250058	+	0.769599i	−0.994763	+	0.102206i	$0.967410\pi$
$242$	0.650643	+	0.472720i	0.0418249	+	0.0303876i
$243$	−1.00000			−0.0641500
$244$	−25.0728	−	18.2165i	−1.60512	−	1.16619i
$245$	3.98577	−	10.0512i	0.254642	−	0.642147i
$246$	10.6996	−	7.77370i	0.682181	−	0.495633i
$247$	−8.05662	+	5.85348i	−0.512631	+	0.372448i
$248$	10.9714	+	33.7665i	0.696684	+	2.14417i
$249$	−3.95747			−0.250795
$250$	−18.6447	−	19.9186i	−1.17919	−	1.25976i
$251$	17.0160			1.07404			0.537022	−	0.843568i	$-0.319549\pi$
$251$	17.0160			1.07404			0.537022	+	0.843568i	$0.319549\pi$
$252$	−4.20457	−	12.9403i	−0.264863	−	0.815164i
$253$	4.08998	−	2.97154i	0.257135	−	0.186819i
$254$	1.95861	−	1.42301i	0.122894	−	0.0892879i
$255$	4.16531	−	10.5040i	0.260842	−	0.657783i
$256$	25.5586	+	18.5694i	1.59741	+	1.16059i
$257$	4.13200			0.257747			0.128874	−	0.991661i	$-0.458864\pi$
$257$	4.13200			0.257747			0.128874	+	0.991661i	$0.458864\pi$
$258$	4.99689	+	3.63045i	0.311093	+	0.226022i
$259$	6.12177	−	18.8409i	0.380388	−	1.17072i
$260$	−28.5255	−	1.81000i	−1.76908	−	0.112252i
$261$	−0.964807	−	2.96937i	−0.0597201	−	0.183799i
$262$	−9.51020	+	29.2694i	−0.587542	+	1.80827i
$263$	−0.320676	+	0.986940i	−0.0197737	+	0.0608573i	−0.960456	−	0.278430i	$-0.910186\pi$
$263$	−0.320676	+	0.986940i	−0.0197737	+	0.0608573i	0.940683	+	0.339287i	$0.110186\pi$
$264$	4.81567	+	14.8211i	0.296384	+	0.912176i
$265$	−5.63338	−	21.9894i	−0.346056	−	1.35080i
$266$	7.99348	−	24.6014i	0.490112	−	1.50841i
$267$	6.90408	+	5.01611i	0.422523	+	0.306981i
$268$	−7.31315			−0.446722
$269$	12.7741	+	9.28093i	0.778851	+	0.565869i	0.904634	−	0.426189i	$-0.140144\pi$
$269$	12.7741	+	9.28093i	0.778851	+	0.565869i	−0.125783	+	0.992058i	$0.540144\pi$
$270$	−1.35418	−	5.28593i	−0.0824129	−	0.321692i
$271$	11.0838	−	8.05286i	0.673294	−	0.489176i	−0.197832	−	0.980236i	$-0.563390\pi$
$271$	11.0838	−	8.05286i	0.673294	−	0.489176i	0.871126	+	0.491059i	$0.163390\pi$
$272$	15.2571	−	11.0849i	0.925096	−	0.672122i
$273$	−3.43600	−	10.5749i	−0.207956	−	0.640023i
$274$	20.1095			1.21486
$275$	−6.96999	+	14.7709i	−0.420306	+	0.890720i
$276$	−6.12092			−0.368436
$277$	2.15691	+	6.63827i	0.129596	+	0.398855i	0.994710	−	0.102719i	$-0.0327543\pi$
$277$	2.15691	+	6.63827i	0.129596	+	0.398855i	−0.865114	+	0.501574i	$0.832754\pi$
$278$	−15.9196	+	11.5663i	−0.954795	+	0.693699i
$279$	−6.02080	+	4.37437i	−0.360456	+	0.261886i
$280$	30.9971	−	19.6481i	1.85243	−	1.17420i
$281$	−6.43834	−	4.67773i	−0.384079	−	0.279050i	0.378946	−	0.925419i	$-0.376287\pi$
$281$	−6.43834	−	4.67773i	−0.384079	−	0.279050i	−0.763025	+	0.646369i	$0.776287\pi$
$282$	−17.2567			−1.02762
$283$	22.4868	+	16.3376i	1.33670	+	0.971169i	0.999558	+	0.0297149i	$0.00945992\pi$
$283$	22.4868	+	16.3376i	1.33670	+	0.971169i	0.337141	+	0.941454i	$0.390540\pi$
$284$	−0.872582	+	2.68553i	−0.0517782	+	0.159357i
$285$	2.53972	−	6.40458i	0.150440	−	0.379374i
$286$	7.96141	+	24.5027i	0.470768	+	1.44888i
$287$	−5.76163	+	17.7325i	−0.340099	+	1.04672i
$288$	−0.134261	+	0.413214i	−0.00791142	+	0.0243488i
$289$	2.63794	+	8.11876i	0.155173	+	0.477574i
$290$	14.3894	−	9.12098i	0.844973	−	0.535602i
$291$	3.29190	−	10.1314i	0.192975	−	0.593915i
$292$	6.01621	+	4.37103i	0.352072	+	0.255795i
$293$	−14.2098			−0.830146			−0.415073	−	0.909788i	$-0.636244\pi$
$293$	−14.2098			−0.830146			−0.415073	+	0.909788i	$0.636244\pi$
$294$	9.54649	+	6.93593i	0.556763	+	0.404512i
$295$	−2.98030	−	2.46821i	−0.173520	−	0.143705i
$296$	22.2250	−	16.1474i	1.29180	−	0.938548i
$297$	−2.64270	+	1.92004i	−0.153345	+	0.111412i
$298$	−14.4107	−	44.3517i	−0.834791	−	2.56922i
$299$	−5.00206			−0.289276
$300$	17.3391	−	9.50808i	1.00107	−	0.548949i
$301$	−8.70755			−0.501895
$302$	1.19561	+	3.67971i	0.0687997	+	0.211744i
$303$	1.42527	−	1.03552i	0.0818798	−	0.0594892i
$304$	9.30270	−	6.75881i	0.533547	−	0.387644i
$305$	17.4869	+	1.10958i	1.00130	+	0.0635345i
$306$	9.97652	+	7.24837i	0.570320	+	0.414362i
$307$	−23.2911			−1.32930			−0.664648	−	0.747157i	$-0.731418\pi$
$307$	−23.2911			−1.32930			−0.664648	+	0.747157i	$0.731418\pi$
$308$	−35.9573	−	26.1245i	−2.04886	−	1.48858i
$309$	−4.91777	+	15.1354i	−0.279762	+	0.861020i
$310$	−31.2759	−	25.9019i	−1.77635	−	1.47113i
$311$	−2.33284	−	7.17976i	−0.132283	−	0.407127i	0.862874	−	0.505419i	$-0.168662\pi$
$311$	−2.33284	−	7.17976i	−0.132283	−	0.407127i	−0.995158	+	0.0982923i	$0.968662\pi$
$312$	4.76477	−	14.6645i	0.269752	−	0.830211i
$313$	−9.78241	+	30.1072i	−0.552934	+	1.70176i	0.148402	+	0.988927i	$0.452587\pi$
$313$	−9.78241	+	30.1072i	−0.552934	+	1.70176i	−0.701337	+	0.712830i	$0.747413\pi$
$314$	−16.4776	−	50.7127i	−0.929883	−	2.86188i
$315$	5.92471	+	4.90669i	0.333819	+	0.276461i
$316$	−16.2953	+	50.1518i	−0.916682	+	2.82126i
$317$	−20.9019	−	15.1861i	−1.17397	−	0.852938i	−0.182490	−	0.983208i	$-0.558416\pi$
$317$	−20.9019	−	15.1861i	−1.17397	−	0.852938i	−0.991479	+	0.130270i	$0.958416\pi$
$318$	24.7726			1.38918
$319$	−8.25100	−	5.99471i	−0.461968	−	0.335639i
$320$	−19.0222	−	1.20700i	−1.06337	−	0.0674733i
$321$	−12.7668	+	9.27565i	−0.712575	+	0.517716i
$322$	10.5115	−	7.63705i	0.585783	−	0.425596i
$323$	4.81152	+	14.8083i	0.267720	+	0.823959i
$324$	3.95498			0.219721
$325$	14.1696	−	7.77006i	0.785988	−	0.431006i
$326$	24.7295			1.36964
$327$	3.06539	+	9.43429i	0.169516	+	0.521717i
$328$	−20.9175	+	15.1975i	−1.15498	+	0.839139i
$329$	19.6821	−	14.2999i	1.08511	−	0.788376i
$330$	−13.7279	−	11.3691i	−0.755696	−	0.625848i
$331$	−16.2679	−	11.8193i	−0.894166	−	0.649650i	0.0427948	−	0.999084i	$-0.486374\pi$
$331$	−16.2679	−	11.8193i	−0.894166	−	0.649650i	−0.936961	+	0.349434i	$0.886374\pi$
$332$	15.6517			0.859001
$333$	4.65863	+	3.38469i	0.255291	+	0.185480i
$334$	−1.13949	+	3.50700i	−0.0623504	+	0.191895i
$335$	3.49224	−	2.21362i	0.190801	−	0.120943i
$336$	3.96743	+	12.2105i	0.216441	+	0.666137i
$337$	1.04564	−	3.21816i	0.0569599	−	0.175304i	−0.918529	−	0.395354i	$-0.870622\pi$
$337$	1.04564	−	3.21816i	0.0569599	−	0.175304i	0.975489	+	0.220050i	$0.0706219\pi$
$338$	−1.92589	+	5.92729i	−0.104755	+	0.322402i
$339$	−1.70388	−	5.24399i	−0.0925419	−	0.284815i
$340$	−16.4737	+	41.5429i	−0.893414	+	2.25298i
$341$	−7.51225	+	23.1203i	−0.406811	+	1.25204i
$342$	6.08299	+	4.41955i	0.328930	+	0.238982i
$343$	7.44633			0.402064
$344$	−9.76882	−	7.09747i	−0.526700	−	0.382670i
$345$	2.92291	−	1.85274i	0.157364	−	0.0997483i
$346$	27.3536	−	19.8735i	1.47054	−	1.06841i
$347$	23.6204	−	17.1612i	1.26801	−	0.921262i	0.268887	−	0.963172i	$-0.413344\pi$
$347$	23.6204	−	17.1612i	1.26801	−	0.921262i	0.999121	+	0.0419100i	$0.0133443\pi$
$348$	3.81580	+	11.7438i	0.204548	+	0.629534i
$349$	−20.3979			−1.09187			−0.545937	−	0.837826i	$-0.683826\pi$
$349$	−20.3979			−1.09187			−0.545937	+	0.837826i	$0.683826\pi$
$350$	−17.9133	+	37.9622i	−0.957506	+	2.02916i
$351$	3.23204			0.172513
$352$	0.438573	+	1.34979i	0.0233760	+	0.0719440i
$353$	1.50757	−	1.09532i	0.0802400	−	0.0582978i	−0.546942	−	0.837170i	$-0.684208\pi$
$353$	1.50757	−	1.09532i	0.0802400	−	0.0582978i	0.627182	+	0.778873i	$0.284208\pi$
$354$	3.41653	−	2.48225i	0.181586	−	0.131930i
$355$	−0.396201	−	1.54654i	−0.0210282	−	0.0820818i
$356$	−27.3055	−	19.8386i	−1.44719	−	1.05145i
$357$	−17.3850			−0.920113
$358$	−28.5389	−	20.7347i	−1.50833	−	1.09586i
$359$	1.18599	−	3.65011i	0.0625943	−	0.192645i	−0.914869	−	0.403751i	$-0.867706\pi$
$359$	1.18599	−	3.65011i	0.0625943	−	0.192645i	0.977463	+	0.211105i	$0.0677063\pi$
$360$	2.64740	+	10.3339i	0.139530	+	0.544645i
$361$	−2.93759	−	9.04097i	−0.154610	−	0.475841i
$362$	12.9626	−	39.8949i	0.681301	−	2.09683i
$363$	0.101842	−	0.313438i	0.00534532	−	0.0164512i
$364$	13.5893	+	41.8236i	0.712274	+	2.19215i
$365$	−4.19598	−	0.266244i	−0.219628	−	0.0139358i
$366$	−5.90913	+	18.1864i	−0.308875	+	0.950620i
$367$	−20.7335	−	15.0638i	−1.08228	−	0.786324i	−0.104203	−	0.994556i	$-0.533229\pi$
$367$	−20.7335	−	15.0638i	−1.08228	−	0.786324i	−0.978079	+	0.208232i	$0.933229\pi$
$368$	5.77570			0.301079
$369$	−4.38457	−	3.18557i	−0.228251	−	0.165834i
$370$	−11.5826	+	29.2087i	−0.602153	+	1.51849i
$371$	−28.2543	+	20.5279i	−1.46689	+	1.06576i
$372$	23.8122	−	17.3005i	1.23460	−	0.896991i
$373$	6.62437	+	20.3877i	0.342997	+	1.05564i	0.962648	+	0.270758i	$0.0872742\pi$
$373$	6.62437	+	20.3877i	0.342997	+	1.05564i	−0.619651	+	0.784878i	$0.712726\pi$
$374$	40.2821			2.08294
$375$	−5.40190	+	9.78874i	−0.278953	+	0.505489i
$376$	33.7366			1.73983
$377$	3.11829	+	9.59712i	0.160600	+	0.494277i
$378$	−6.79191	+	4.93461i	−0.349338	+	0.253809i
$379$	20.9304	−	15.2068i	1.07512	−	0.781120i	0.0982945	−	0.995157i	$-0.468661\pi$
$379$	20.9304	−	15.2068i	1.07512	−	0.781120i	0.976826	+	0.214037i	$0.0686613\pi$
$380$	−10.0445	+	25.3300i	−0.515274	+	1.29940i
$381$	−0.802617	−	0.583135i	−0.0411193	−	0.0298749i
$382$	25.7264			1.31628
$383$	11.7579	+	8.54263i	0.600802	+	0.436508i	0.846163	−	0.532924i	$-0.178907\pi$
$383$	11.7579	+	8.54263i	0.600802	+	0.436508i	−0.245362	+	0.969432i	$0.578907\pi$
$384$	6.15940	−	18.9567i	0.314321	−	0.967379i
$385$	25.0783	+	1.59127i	1.27811	+	0.0810986i
$386$	−0.514974	−	1.58493i	−0.0262115	−	0.0806706i
$387$	0.782139	−	2.40718i	0.0397584	−	0.122364i
$388$	−13.0194	+	40.0696i	−0.660960	+	2.03423i
$389$	7.13973	+	21.9738i	0.361999	+	1.11412i	0.951839	+	0.306598i	$0.0991907\pi$
$389$	7.13973	+	21.9738i	0.361999	+	1.11412i	−0.589840	+	0.807520i	$0.700809\pi$
$390$	4.37677	+	17.0843i	0.221626	+	0.865099i
$391$	−2.41677	+	7.43806i	−0.122221	+	0.376159i
$392$	−18.6632	−	13.5596i	−0.942635	−	0.684864i
$393$	12.6115			0.636167
$394$	45.9940	+	33.4166i	2.31715	+	1.68350i
$395$	−7.39898	−	28.8813i	−0.372283	−	1.45318i
$396$	10.4519	−	7.59371i	0.525225	−	0.381598i
$397$	−11.2733	+	8.19052i	−0.565790	+	0.411070i	−0.833573	−	0.552409i	$-0.813709\pi$
$397$	−11.2733	+	8.19052i	−0.565790	+	0.411070i	0.267784	+	0.963479i	$0.413709\pi$
$398$	7.68766	+	23.6602i	0.385348	+	1.18598i
$399$	−10.6002			−0.530673
$400$	−16.3611	+	8.97182i	−0.818057	+	0.448591i
$401$	−27.5822			−1.37739			−0.688694	−	0.725052i	$-0.741816\pi$
$401$	−27.5822			−1.37739			−0.688694	+	0.725052i	$0.741816\pi$
$402$	1.39438	+	4.29147i	0.0695456	+	0.214039i
$403$	19.4594	−	14.1381i	0.969344	−	0.704270i
$404$	−5.63693	+	4.09547i	−0.280448	+	0.203757i
$405$	−1.88862	+	1.19713i	−0.0938461	+	0.0594861i
$406$	−21.2056	−	15.4068i	−1.05242	−	0.764625i
$407$	18.8101			0.932383
$408$	−19.5039	−	14.1704i	−0.965588	−	0.701541i
$409$	4.08288	−	12.5658i	0.201886	−	0.621340i	−0.797941	−	0.602735i	$-0.794078\pi$
$409$	4.08288	−	12.5658i	0.201886	−	0.621340i	0.999827	−	0.0186048i	$-0.00592242\pi$
$410$	10.9012	−	27.4904i	0.538374	−	1.35765i
$411$	−2.54650	−	7.83732i	−0.125610	−	0.386587i
$412$	19.4497	−	59.8601i	0.958218	−	2.94909i
$413$	−1.83977	+	5.66223i	−0.0905292	+	0.278620i
$414$	1.16706	+	3.59186i	0.0573581	+	0.176530i
$415$	−7.47415	+	4.73763i	−0.366891	+	0.232561i
$416$	0.433937	−	1.33552i	0.0212755	−	0.0654794i
$417$	6.52367	+	4.73973i	0.319466	+	0.232105i
$418$	24.5612			1.20133
$419$	7.15797	+	5.20057i	0.349690	+	0.254064i	0.748739	−	0.662865i	$-0.230660\pi$
$419$	7.15797	+	5.20057i	0.349690	+	0.254064i	−0.399049	+	0.916930i	$0.630660\pi$
$420$	−23.4321	−	19.4059i	−1.14337	−	0.946909i
$421$	30.3192	−	22.0282i	1.47767	−	1.07359i	0.499367	−	0.866390i	$-0.333566\pi$
$421$	30.3192	−	22.0282i	1.47767	−	1.07359i	0.978299	−	0.207197i	$-0.0664341\pi$
$422$	−36.0435	+	26.1871i	−1.75457	+	1.27477i
$423$	2.18525	+	6.72551i	0.106250	+	0.327005i
$424$	−48.4301			−2.35197
$425$	−4.70796	−	24.8244i	−0.228370	−	1.20416i
$426$	1.74229			0.0844140
$427$	−8.33062	−	25.6390i	−0.403147	−	1.24076i
$428$	50.4926	−	36.6850i	2.44065	−	1.77324i
$429$	8.54132	−	6.20563i	0.412379	−	0.299611i
$430$	13.7833	+	0.874582i	0.664691	+	0.0421761i
$431$	21.5397	+	15.6495i	1.03753	+	0.753809i	0.969802	−	0.243895i	$-0.0784252\pi$
$431$	21.5397	+	15.6495i	1.03753	+	0.753809i	0.0677274	+	0.997704i	$0.478425\pi$
$432$	−3.73192			−0.179552
$433$	−28.3133	−	20.5708i	−1.36065	−	0.988571i	−0.998403	−	0.0564887i	$-0.982010\pi$
$433$	−28.3133	−	20.5708i	−1.36065	−	0.988571i	−0.362248	−	0.932082i	$-0.617990\pi$
$434$	−19.3069	+	59.4206i	−0.926762	+	2.85228i
$435$	−5.37689	−	4.45300i	−0.257802	−	0.213505i
$436$	−12.1235	−	37.3124i	−0.580613	−	1.78694i
$437$	−1.47358	+	4.53521i	−0.0704909	+	0.216949i
$438$	1.41789	−	4.36383i	0.0677496	−	0.208512i
$439$	6.19701	+	19.0724i	0.295767	+	0.910277i	0.982963	+	0.183805i	$0.0588415\pi$
$439$	6.19701	+	19.0724i	0.295767	+	0.910277i	−0.687196	+	0.726472i	$0.741159\pi$
$440$	26.8378	+	22.2264i	1.27944	+	1.05960i
$441$	1.49427	−	4.59888i	0.0711556	−	0.218994i
$442$	−32.2445	−	23.4270i	−1.53371	−	1.11431i
$443$	4.14871			0.197111			0.0985556	−	0.995132i	$-0.468578\pi$
$443$	4.14871			0.197111			0.0985556	+	0.995132i	$0.468578\pi$
$444$	−18.4248	−	13.3864i	−0.874402	−	0.635291i
$445$	19.0441	+	1.20839i	0.902778	+	0.0572832i
$446$	−34.0048	+	24.7060i	−1.61018	+	1.16986i
$447$	−15.4604	+	11.2326i	−0.731252	+	0.531286i
$448$	9.06201	+	27.8900i	0.428140	+	1.31768i
$449$	−8.34804			−0.393969			−0.196984	−	0.980407i	$-0.563115\pi$
$449$	−8.34804			−0.393969			−0.196984	+	0.980407i	$0.563115\pi$
$450$	−8.88550	−	8.36196i	−0.418867	−	0.394187i
$451$	−17.7035			−0.833627
$452$	6.73880	+	20.7399i	0.316967	+	0.975523i
$453$	1.28270	−	0.931936i	0.0602665	−	0.0437862i
$454$	8.54602	−	6.20905i	0.401085	−	0.291405i
$455$	−19.1489	−	15.8586i	−0.897713	−	0.743463i
$456$	−11.8921	−	8.64014i	−0.556900	−	0.404612i
$457$	20.5774			0.962571			0.481285	−	0.876564i	$-0.340170\pi$
$457$	20.5774			0.962571			0.481285	+	0.876564i	$0.340170\pi$
$458$	−40.1059	−	29.1386i	−1.87402	−	1.36156i
$459$	1.56158	−	4.80604i	0.0728882	−	0.224327i
$460$	−11.5601	+	7.32757i	−0.538991	+	0.341650i
$461$	8.86541	+	27.2849i	0.412903	+	1.27079i	0.914113	+	0.405460i	$0.132889\pi$
$461$	8.86541	+	27.2849i	0.412903	+	1.27079i	−0.501210	+	0.865326i	$0.667111\pi$
$462$	−8.47438	+	26.0815i	−0.394264	+	1.21342i
$463$	12.3853	−	38.1181i	0.575594	−	1.77150i	−0.0585520	−	0.998284i	$-0.518648\pi$
$463$	12.3853	−	38.1181i	0.575594	−	1.77150i	0.634146	−	0.773213i	$-0.281352\pi$
$464$	−3.60058	−	11.0815i	−0.167153	−	0.514444i
$465$	−6.13427	+	15.4692i	−0.284470	+	0.717367i
$466$	−0.257111	+	0.791307i	−0.0119105	+	0.0366566i
$467$	6.58694	+	4.78569i	0.304807	+	0.221456i	0.729665	−	0.683805i	$-0.239676\pi$
$467$	6.58694	+	4.78569i	0.304807	+	0.221456i	−0.424858	+	0.905260i	$0.639676\pi$
$468$	−12.7827			−0.590878
$469$	−5.14650	−	3.73915i	−0.237643	−	0.172658i
$470$	−32.5914	+	20.6586i	−1.50333	+	0.952912i
$471$	−17.6778	+	12.8437i	−0.814550	+	0.591805i
$472$	−6.67925	+	4.85276i	−0.307438	+	0.223366i
$473$	−2.55491	−	7.86319i	−0.117475	−	0.361550i
$474$	32.5369			1.49447
$475$	−2.87059	−	15.1362i	−0.131712	−	0.694495i
$476$	68.7575			3.15149
$477$	−3.13700	−	9.65469i	−0.143633	−	0.442058i
$478$	14.1451	−	10.2770i	0.646983	−	0.470061i
$479$	22.7027	−	16.4945i	1.03731	−	0.753652i	0.0675535	−	0.997716i	$-0.478481\pi$
$479$	22.7027	−	16.4945i	1.03731	−	0.753652i	0.969759	+	0.244064i	$0.0784807\pi$
$480$	0.241104	+	0.941131i	0.0110049	+	0.0429565i
$481$	−15.0569	−	10.9395i	−0.686534	−	0.498796i
$482$	−30.6554			−1.39631
$483$	−4.30749	−	3.12957i	−0.195998	−	0.142401i
$484$	−0.402784	+	1.23964i	−0.0183084	+	0.0563473i
$485$	−5.91155	−	23.0752i	−0.268429	−	1.04779i
$486$	−0.754089	−	2.32085i	−0.0342062	−	0.105276i
$487$	−4.70239	+	14.4725i	−0.213086	+	0.655810i	0.786198	+	0.617974i	$0.212046\pi$
$487$	−4.70239	+	14.4725i	−0.213086	+	0.655810i	−0.999284	+	0.0378360i	$0.987954\pi$
$488$	11.5522	−	35.5541i	0.522945	−	1.60946i
$489$	−3.13153	−	9.63786i	−0.141613	−	0.435839i
$490$	26.3329	+	1.67088i	1.18960	+	0.0754826i
$491$	2.56246	−	7.88645i	0.115642	−	0.355910i	−0.876438	−	0.481514i	$-0.840087\pi$
$491$	2.56246	−	7.88645i	0.115642	−	0.355910i	0.992080	+	0.125604i	$0.0400869\pi$
$492$	17.3409	+	12.5989i	0.781788	+	0.568002i
$493$	15.7775			0.710585
$494$	−19.6604	−	14.2842i	−0.884565	−	0.642674i
$495$	−2.69251	+	6.78989i	−0.121019	+	0.305183i
$496$	−22.4691	+	16.3248i	−1.00889	+	0.733005i
$497$	−1.98715	+	1.44375i	−0.0891360	+	0.0647611i
$498$	−2.98429	−	9.18469i	−0.133729	−	0.411576i
$499$	−24.4006			−1.09232			−0.546160	−	0.837681i	$-0.683911\pi$
$499$	−24.4006			−1.09232			−0.546160	+	0.837681i	$0.683911\pi$
$500$	21.3644	−	38.7143i	0.955445	−	1.73136i
$501$	1.51109			0.0675104
$502$	12.8316	+	39.4916i	0.572703	+	1.76260i
$503$	−8.47295	+	6.15596i	−0.377790	+	0.274481i	−0.760434	−	0.649415i	$-0.775014\pi$
$503$	−8.47295	+	6.15596i	−0.377790	+	0.274481i	0.382644	+	0.923896i	$0.375014\pi$
$504$	13.2781	−	9.64708i	0.591452	−	0.429715i
$505$	1.45214	−	3.66195i	0.0646192	−	0.162954i
$506$	9.98070	+	7.25141i	0.443696	+	0.322364i
$507$	2.55393			0.113424
$508$	3.17433	+	2.30629i	0.140838	+	0.102325i
$509$	−3.41769	+	10.5186i	−0.151486	+	0.466227i	−0.997788	−	0.0664770i	$-0.978824\pi$
$509$	−3.41769	+	10.5186i	−0.151486	+	0.466227i	0.846302	+	0.532704i	$0.178824\pi$
$510$	27.5191	+	1.74614i	1.21857	+	0.0773206i
$511$	1.99893	+	6.15207i	0.0884274	+	0.272152i
$512$	−11.5045	+	35.4071i	−0.508431	+	1.56479i
$513$	0.952141	−	2.93039i	0.0420381	−	0.129380i
$514$	3.11590	+	9.58974i	0.137436	+	0.422985i
$515$	8.83126	+	34.4721i	0.389152	+	1.51902i
$516$	−3.09335	+	9.52034i	−0.136177	+	0.419110i
$517$	18.6882	+	13.5778i	0.821906	+	0.597150i
$518$	48.3432			2.12408
$519$	−11.2092	−	8.14395i	−0.492029	−	0.357480i
$520$	−8.55650	−	33.3996i	−0.375227	−	1.46467i
$521$	33.5105	−	24.3468i	1.46812	−	1.06665i	0.486967	−	0.873420i	$-0.338103\pi$
$521$	33.5105	−	24.3468i	1.46812	−	1.06665i	0.981153	−	0.193231i	$-0.0618968\pi$
$522$	6.16391	−	4.47834i	0.269787	−	0.196012i
$523$	4.21576	+	12.9748i	0.184342	+	0.567347i	0.999936	−	0.0112775i	$-0.00358982\pi$
$523$	4.21576	+	12.9748i	0.184342	+	0.567347i	−0.815594	+	0.578624i	$0.803590\pi$
$524$	−49.8783			−2.17894
$525$	17.0635	+	2.17418i	0.744710	+	0.0948890i
$526$	−2.53235			−0.110416
$527$	−11.6214	−	35.7671i	−0.506238	−	1.55804i
$528$	−9.86236	+	7.16543i	−0.429204	+	0.311835i
$529$	16.6696	−	12.1112i	0.724766	−	0.526573i
$530$	46.7860	−	29.6562i	2.03225	−	1.28818i
$531$	−1.40005	−	1.01720i	−0.0607572	−	0.0441427i
$532$	41.9235			1.81762
$533$	14.1711	+	10.2959i	0.613818	+	0.445965i
$534$	−6.43533	+	19.8059i	−0.278484	+	0.857086i
$535$	−13.0075	+	32.8018i	−0.562361	+	1.41814i
$536$	−2.72600	−	8.38976i	−0.117745	−	0.362382i
$537$	−4.46706	+	13.7482i	−0.192768	+	0.593278i
$538$	−11.9068	+	36.6454i	−0.513339	+	1.57990i
$539$	−4.88112	−	15.0225i	−0.210245	−	0.647066i
$540$	7.46944	−	4.73464i	0.321434	−	0.203747i
$541$	4.53011	−	13.9423i	0.194765	−	0.599424i	−0.805214	−	0.592984i	$-0.797950\pi$
$541$	4.53011	−	13.9423i	0.194765	−	0.599424i	0.999979	−	0.00644072i	$-0.00205016\pi$
$542$	27.0476	+	19.6513i	1.16180	+	0.844094i
$543$	−17.1898			−0.737685
$544$	−1.77626	−	1.29053i	−0.0761566	−	0.0553310i
$545$	17.0834	+	14.1481i	0.731775	+	0.606037i
$546$	21.9517	−	15.9489i	0.939447	−	0.682548i
$547$	−21.5298	+	15.6423i	−0.920549	+	0.668818i	−0.943661	−	0.330915i	$-0.892643\pi$
$547$	−21.5298	+	15.6423i	−0.920549	+	0.668818i	0.0231115	+	0.999733i	$0.492643\pi$
$548$	10.0714	+	30.9965i	0.430227	+	1.32410i
$549$	7.83611			0.334437
$550$	−39.5370	−	5.03770i	−1.68586	−	0.214808i
$551$	9.62005			0.409828
$552$	−2.28159	−	7.02201i	−0.0971109	−	0.298877i
$553$	−37.1097	+	26.9618i	−1.57806	+	1.14653i
$554$	−13.7799	+	10.0117i	−0.585453	+	0.425356i
$555$	12.8503	+	0.815379i	0.545465	+	0.0346109i
$556$	−25.8010	−	18.7455i	−1.09421	−	0.794988i
$557$	−10.3141			−0.437020			−0.218510	−	0.975835i	$-0.570120\pi$
$557$	−10.3141			−0.437020			−0.218510	+	0.975835i	$0.570120\pi$
$558$	−14.6925	−	10.6747i	−0.621981	−	0.451896i
$559$	−2.52790	+	7.78008i	−0.106919	+	0.329063i
$560$	22.1105	+	18.3114i	0.934341	+	0.773797i
$561$	−5.10099	−	15.6992i	−0.215364	−	0.662822i
$562$	6.00121	−	18.4698i	0.253146	−	0.779103i
$563$	−10.6311	+	32.7193i	−0.448049	+	1.37895i	0.431056	+	0.902325i	$0.358141\pi$
$563$	−10.6311	+	32.7193i	−0.448049	+	1.37895i	−0.879105	+	0.476628i	$0.841859\pi$
$564$	−8.64262	−	26.5993i	−0.363920	−	1.12003i
$565$	−9.49573	−	7.86412i	−0.399488	−	0.330846i
$566$	−20.9600	+	64.5083i	−0.881016	+	2.71149i
$567$	2.78325	+	2.02215i	0.116885	+	0.0849222i
$568$	−3.40614			−0.142918
$569$	9.87387	+	7.17378i	0.413934	+	0.300741i	0.775193	−	0.631725i	$-0.217653\pi$
$569$	9.87387	+	7.17378i	0.413934	+	0.300741i	−0.361259	+	0.932466i	$0.617653\pi$
$570$	16.7792	+	1.06468i	0.702804	+	0.0445944i
$571$	−34.0308	+	24.7248i	−1.42415	+	1.03470i	−0.433076	+	0.901357i	$0.642572\pi$
$571$	−34.0308	+	24.7248i	−1.42415	+	1.03470i	−0.991070	+	0.133345i	$0.957428\pi$
$572$	−33.7808	+	24.5432i	−1.41245	+	1.02620i
$573$	−3.25778	−	10.0264i	−0.136096	−	0.418859i
$574$	−45.4992			−1.89910
$575$	3.30228	−	6.99824i	0.137715	−	0.291847i
$576$	−8.52409			−0.355170
$577$	5.41863	+	16.6768i	0.225581	+	0.694266i	0.998232	+	0.0594353i	$0.0189300\pi$
$577$	5.41863	+	16.6768i	0.225581	+	0.694266i	−0.772652	+	0.634830i	$0.781070\pi$
$578$	−16.8532	+	12.2445i	−0.700999	+	0.509305i
$579$	−0.552485	+	0.401404i	−0.0229605	+	0.0166818i
$580$	21.2655	+	17.6115i	0.883001	+	0.731279i
$581$	11.0146	+	8.00260i	0.456964	+	0.332004i
$582$	25.9959			1.07756
$583$	−26.8275	−	19.4913i	−1.11108	−	0.807249i
$584$	−2.77196	+	8.53120i	−0.114704	+	0.353024i
$585$	6.10408	−	3.86918i	0.252373	−	0.159971i
$586$	−10.7155	−	32.9788i	−0.442651	−	1.36234i
$587$	−6.77115	+	20.8395i	−0.279475	+	0.860137i	0.708525	+	0.705686i	$0.249361\pi$
$587$	−6.77115	+	20.8395i	−0.279475	+	0.860137i	−0.988000	+	0.154451i	$0.950639\pi$
$588$	−5.90980	+	18.1885i	−0.243716	+	0.750081i
$589$	−7.08595	−	21.8083i	−0.291971	−	0.898595i
$590$	3.48092	−	8.77807i	0.143307	−	0.361387i
$591$	7.19923	−	22.1569i	0.296137	−	0.911415i
$592$	17.3856	+	12.6314i	0.714545	+	0.519148i
$593$	−38.0061			−1.56072			−0.780361	−	0.625330i	$-0.784965\pi$
$593$	−38.0061			−1.56072			−0.780361	+	0.625330i	$0.784965\pi$
$594$	−6.44895	−	4.68544i	−0.264604	−	0.192246i
$595$	−32.8336	+	20.8122i	−1.34605	+	0.853218i
$596$	61.1456	−	44.4249i	2.50462	−	1.81971i
$597$	8.24764	−	5.99226i	0.337553	−	0.245247i
$598$	−3.77200	−	11.6090i	−0.154248	−	0.474728i
$599$	16.3154			0.666629			0.333314	−	0.942816i	$-0.391833\pi$
$599$	16.3154			0.666629			0.333314	+	0.942816i	$0.391833\pi$
$600$	17.3710	+	16.3475i	0.709168	+	0.667383i
$601$	2.31871			0.0945822			0.0472911	−	0.998881i	$-0.484941\pi$
$601$	2.31871			0.0945822			0.0472911	+	0.998881i	$0.484941\pi$
$602$	−6.56626	−	20.2089i	−0.267621	−	0.823653i
$603$	1.49595	−	1.08687i	0.0609199	−	0.0442609i
$604$	−5.07305	+	3.68579i	−0.206420	+	0.149973i
$605$	−0.182887	−	0.713882i	−0.00743539	−	0.0290234i
$606$	3.47807	+	2.52697i	0.141287	+	0.102651i
$607$	32.2134			1.30750			0.653752	−	0.756709i	$-0.273194\pi$
$607$	32.2134			1.30750			0.653752	+	0.756709i	$0.273194\pi$
$608$	−1.08304	−	0.786876i	−0.0439231	−	0.0319120i
$609$	−3.31921	+	10.2155i	−0.134501	+	0.413952i
$610$	10.6115	+	41.4212i	0.429648	+	1.67709i
$611$	−7.06281	−	21.7371i	−0.285731	−	0.879389i
$612$	−6.17601	+	19.0078i	−0.249651	+	0.768345i
$613$	8.01843	−	24.6782i	0.323861	−	0.996742i	−0.648091	−	0.761563i	$-0.724432\pi$
$613$	8.01843	−	24.6782i	0.323861	−	0.996742i	0.971952	−	0.235179i	$-0.0755677\pi$
$614$	−17.5636	−	54.0552i	−0.708809	−	2.18149i
$615$	−12.0943	−	0.767411i	−0.487690	−	0.0309450i
$616$	16.5673	−	50.9888i	0.667514	−	2.05440i
$617$	−1.54016	−	1.11899i	−0.0620043	−	0.0450488i	0.556351	−	0.830947i	$-0.312201\pi$
$617$	−1.54016	−	1.11899i	−0.0620043	−	0.0450488i	−0.618356	+	0.785898i	$0.712201\pi$
$618$	−38.8353			−1.56218
$619$	16.0829	+	11.6849i	0.646425	+	0.469655i	0.862052	−	0.506821i	$-0.169179\pi$
$619$	16.0829	+	11.6849i	0.646425	+	0.469655i	−0.215627	+	0.976476i	$0.569179\pi$
$620$	24.2609	−	61.1804i	0.974343	−	2.45706i
$621$	1.25207	−	0.909685i	0.0502440	−	0.0365044i
$622$	14.9039	−	10.8283i	0.597594	−	0.434177i
$623$	−9.07246	−	27.9222i	−0.363480	−	1.11868i
$624$	12.0617			0.482855
$625$	1.51633	+	24.9540i	0.0606533	+	0.998159i
$626$	−77.2509			−3.08757
$627$	−3.11023	−	9.57230i	−0.124211	−	0.382281i
$628$	69.9154	−	50.7965i	2.78993	−	2.02700i
$629$	−23.5418	+	17.1041i	−0.938673	+	0.681986i
$630$	−6.91992	+	17.4504i	−0.275696	+	0.695241i
$631$	26.6152	+	19.3371i	1.05953	+	0.769796i	0.974002	−	0.226539i	$-0.0727412\pi$
$631$	26.6152	+	19.3371i	1.05953	+	0.769796i	0.0855315	+	0.996335i	$0.472741\pi$
$632$	−63.6090			−2.53023
$633$	14.7702	+	10.7312i	0.587063	+	0.426526i
$634$	19.4828	−	59.9618i	0.773760	−	2.38139i
$635$	−2.21393	−	0.140478i	−0.0878570	−	0.00557471i
$636$	12.4068	+	38.1841i	0.491961	+	1.51410i
$637$	−4.82953	+	14.8638i	−0.191353	+	0.588923i
$638$	7.69080	−	23.6699i	0.304482	−	0.937099i
$639$	−0.220629	−	0.679025i	−0.00872793	−	0.0268618i
$640$	−11.0610	−	43.1755i	−0.437223	−	1.70666i
$641$	−12.5963	+	38.7673i	−0.497523	+	1.53122i	0.315465	+	0.948937i	$0.397839\pi$
$641$	−12.5963	+	38.7673i	−0.497523	+	1.53122i	−0.812988	+	0.582280i	$0.802161\pi$
$642$	−31.1547	−	22.6352i	−1.22958	−	0.893341i
$643$	24.9947			0.985695			0.492847	−	0.870116i	$-0.335956\pi$
$643$	24.9947			0.985695			0.492847	+	0.870116i	$0.335956\pi$
$644$	17.0360	+	12.3774i	0.671314	+	0.487738i
$645$	−1.40455	−	5.48256i	−0.0553042	−	0.215875i
$646$	−30.7396	+	22.3336i	−1.20943	+	0.878705i
$647$	25.9073	−	18.8228i	1.01852	−	0.739999i	0.0525420	−	0.998619i	$-0.483268\pi$
$647$	25.9073	−	18.8228i	1.01852	−	0.739999i	0.965979	+	0.258620i	$0.0832677\pi$
$648$	1.47423	+	4.53722i	0.0579132	+	0.178239i
$649$	−5.65299			−0.221899
$650$	28.7183	+	27.0262i	1.12642	+	1.06005i
$651$	25.6030			1.00346
$652$	12.3852	+	38.1176i	0.485040	+	1.49280i
$653$	36.1446	−	26.2606i	1.41445	−	1.02766i	0.421791	−	0.906693i	$-0.361401\pi$
$653$	36.1446	−	26.2606i	1.41445	−	1.02766i	0.992657	−	0.120964i	$-0.0385985\pi$
$654$	−19.5840	+	14.2286i	−0.765794	+	0.556382i
$655$	23.8183	−	15.0977i	0.930658	−	0.589915i
$656$	−16.3629	−	11.8883i	−0.638862	−	0.464161i
$657$	−1.88027			−0.0733564
$658$	48.0298	+	34.8957i	1.87240	+	1.36038i
$659$	−7.42307	+	22.8458i	−0.289162	+	0.889948i	0.695959	+	0.718082i	$0.254980\pi$
$659$	−7.42307	+	22.8458i	−0.289162	+	0.889948i	−0.985120	+	0.171866i	$0.945020\pi$
$660$	10.6488	−	26.8539i	0.414505	−	1.04529i
$661$	11.7095	+	36.0382i	0.455447	+	1.40172i	0.870610	+	0.491974i	$0.163725\pi$
$661$	11.7095	+	36.0382i	0.455447	+	1.40172i	−0.415163	+	0.909747i	$0.636275\pi$
$662$	15.1634	−	46.6682i	0.589343	−	1.81381i
$663$	−5.04708	+	15.5333i	−0.196012	+	0.603264i
$664$	5.83423	+	17.9559i	0.226412	+	0.696824i
$665$	−20.0197	+	12.6898i	−0.776329	+	0.492091i
$666$	−4.34233	+	13.3643i	−0.168262	+	0.517857i
$667$	3.90920	+	2.84020i	0.151365	+	0.109973i
$668$	−5.97633			−0.231231
$669$	13.9348	+	10.1242i	0.538750	+	0.391425i
$670$	7.77093	+	6.43568i	0.300217	+	0.248632i
$671$	20.7085	−	15.0456i	0.799444	−	0.580830i
$672$	1.20926	−	0.878580i	0.0466483	−	0.0338920i
$673$	−5.69418	−	17.5249i	−0.219494	−	0.675534i	−0.998804	−	0.0488951i	$-0.984430\pi$
$673$	−5.69418	−	17.5249i	−0.219494	−	0.675534i	0.779310	−	0.626639i	$-0.215570\pi$
$674$	8.25737			0.318062
$675$	−2.13374	+	4.52185i	−0.0821277	+	0.174046i
$676$	−10.1008			−0.388491
$677$	−7.05064	−	21.6996i	−0.270978	−	0.833985i	−0.990256	−	0.139262i	$-0.955527\pi$
$677$	−7.05064	−	21.6996i	−0.270978	−	0.833985i	0.719277	−	0.694723i	$-0.244473\pi$
$678$	10.8856	−	7.90887i	0.418060	−	0.303738i
$679$	−29.6494	+	21.5416i	−1.13784	+	0.826690i
$680$	−53.7993	−	3.41368i	−2.06311	−	0.130909i
$681$	−3.50206	−	2.54440i	−0.134199	−	0.0975015i
$682$	−59.3236			−2.27162
$683$	−26.0555	−	18.9304i	−0.996987	−	0.724353i	−0.0355465	−	0.999368i	$-0.511317\pi$
$683$	−26.0555	−	18.9304i	−0.996987	−	0.724353i	−0.961440	+	0.275015i	$0.911317\pi$
$684$	−3.76570	+	11.5896i	−0.143985	+	0.443141i
$685$	−14.1917	−	11.7532i	−0.542237	−	0.449066i
$686$	5.61519	+	17.2818i	0.214389	+	0.659822i
$687$	−6.27758	+	19.3204i	−0.239505	+	0.737120i
$688$	2.91888	−	8.98339i	0.111281	−	0.342489i
$689$	10.1389	+	31.2043i	0.386261	+	1.18879i
$690$	6.50407	+	5.38650i	0.247606	+	0.205061i
$691$	7.59466	−	23.3740i	0.288915	−	0.889188i	−0.696283	−	0.717767i	$-0.745164\pi$
$691$	7.59466	−	23.3740i	0.288915	−	0.889188i	0.985198	−	0.171421i	$-0.0548358\pi$
$692$	44.3321	+	32.2092i	1.68525	+	1.22441i
$693$	11.2379			0.426893
$694$	57.6404	+	41.8782i	2.18800	+	1.58967i
$695$	17.9948	+	1.14181i	0.682582	+	0.0433113i
$696$	−12.0503	+	8.75508i	−0.456767	+	0.331860i
$697$	22.1568	−	16.0979i	0.839251	−	0.609751i
$698$	−15.3818	−	47.3404i	−0.582211	−	1.79186i
$699$	0.340956			0.0128961
$700$	−67.4857	−	8.59884i	−2.55072	−	0.325006i
$701$	−3.66355			−0.138370			−0.0691852	−	0.997604i	$-0.522040\pi$
$701$	−3.66355			−0.138370			−0.0691852	+	0.997604i	$0.522040\pi$
$702$	2.43724	+	7.50107i	0.0919879	+	0.283109i
$703$	−14.3541	+	10.4289i	−0.541377	+	0.393333i
$704$	−22.5267	+	16.3666i	−0.849005	+	0.616838i
$705$	12.1784	+	10.0859i	0.458666	+	0.379856i
$706$	3.67890	+	2.67288i	0.138457	+	0.100595i
$707$	−6.06087			−0.227942
$708$	5.53719	+	4.02300i	0.208100	+	0.151194i
$709$	−8.24980	+	25.3903i	−0.309828	+	0.953552i	0.668003	+	0.744158i	$0.267149\pi$
$709$	−8.24980	+	25.3903i	−0.309828	+	0.953552i	−0.977831	+	0.209394i	$0.932851\pi$
$710$	3.29051	−	2.08575i	0.123491	−	0.0782768i
$711$	−4.12020	−	12.6807i	−0.154519	−	0.475562i
$712$	12.5810	−	38.7202i	0.471492	−	1.45110i
$713$	3.55919	−	10.9541i	0.133293	−	0.410233i
$714$	−13.1099	−	40.3480i	−0.490624	−	1.50999i
$715$	8.70230	−	21.9452i	0.325447	−	0.820703i
$716$	17.6671	−	54.3739i	0.660252	−	2.03205i
$717$	−5.79651	−	4.21141i	−0.216475	−	0.157278i
$718$	9.36569			0.349524
$719$	−14.4570	−	10.5036i	−0.539156	−	0.391720i	0.284616	−	0.958642i	$-0.408134\pi$
$719$	−14.4570	−	10.5036i	−0.539156	−	0.391720i	−0.823771	+	0.566922i	$0.808134\pi$
$720$	−7.04816	+	4.46761i	−0.262670	+	0.166498i
$721$	44.2933	−	32.1810i	1.64957	−	1.19848i
$722$	18.7675	−	13.6354i	0.698455	−	0.507457i
$723$	3.88194	+	11.9474i	0.144371	+	0.444328i
$724$	67.9853			2.52665
$725$	−15.4857	−	1.97315i	−0.575125	−	0.0732808i
$726$	0.804239			0.0298481
$727$	−10.5290	−	32.4050i	−0.390500	−	1.20184i	−0.932411	−	0.361400i	$-0.882299\pi$
$727$	−10.5290	−	32.4050i	−0.390500	−	1.20184i	0.541910	−	0.840436i	$-0.317701\pi$
$728$	−42.9152	+	31.1797i	−1.59054	+	1.15560i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.54623	−	9.93900i	−0.0942402	−	0.367859i
$731$	10.3476	+	7.51799i	0.382721	+	0.278063i
$732$	−30.9917			−1.14549
$733$	32.5068	+	23.6176i	1.20067	+	0.872335i	0.994350	−	0.106150i	$-0.0338525\pi$
$733$	32.5068	+	23.6176i	1.20067	+	0.872335i	0.206316	+	0.978485i	$0.433853\pi$
$734$	19.3258	−	59.4788i	0.713330	−	2.19540i
$735$	−2.68338	−	10.4744i	−0.0989780	−	0.386352i
$736$	−0.207789	−	0.639509i	−0.00765921	−	0.0235726i
$737$	1.86652	−	5.74457i	0.0687542	−	0.211604i
$738$	4.08688	−	12.5781i	0.150440	−	0.463007i
$739$	4.78203	+	14.7176i	0.175910	+	0.541395i	0.999674	−	0.0255381i	$-0.00812990\pi$
$739$	4.78203	+	14.7176i	0.175910	+	0.541395i	−0.823764	+	0.566933i	$0.808130\pi$
$740$	−50.8227	−	3.22481i	−1.86828	−	0.118546i
$741$	−3.07736	+	9.47113i	−0.113050	+	0.347931i
$742$	−68.9484	−	50.0939i	−2.53118	−	1.83901i
$743$	−17.1140			−0.627853			−0.313926	−	0.949447i	$-0.601645\pi$
$743$	−17.1140			−0.627853			−0.313926	+	0.949447i	$0.601645\pi$
$744$	28.7235	+	20.8688i	1.05305	+	0.765089i
$745$	−15.7518	+	39.7223i	−0.577101	+	1.45531i
$746$	−42.3214	+	30.7483i	−1.54950	+	1.12577i
$747$	−3.20166	+	2.32614i	−0.117143	+	0.0851092i
$748$	20.1743	+	62.0902i	0.737647	+	2.27024i
$749$	54.2900			1.98371
$750$	−26.7917	−	5.15539i	−0.978294	−	0.188248i
$751$	−11.1559			−0.407086			−0.203543	−	0.979066i	$-0.565246\pi$
$751$	−11.1559			−0.407086			−0.203543	+	0.979066i	$0.565246\pi$
$752$	8.15518	+	25.0991i	0.297389	+	0.915268i
$753$	13.7663	−	10.0018i	0.501671	−	0.364485i
$754$	−19.9220	+	14.4742i	−0.725516	+	0.527118i
$755$	1.30687	−	3.29563i	0.0475620	−	0.119940i
$756$	−11.0077	−	7.99756i	−0.400346	−	0.290868i
$757$	24.6773			0.896911			0.448456	−	0.893805i	$-0.351974\pi$
$757$	24.6773			0.896911			0.448456	+	0.893805i	$0.351974\pi$
$758$	51.0760	+	37.1089i	1.85516	+	1.34786i
$759$	1.56223	−	4.80806i	0.0567054	−	0.174521i
$760$	−32.8031	−	2.08143i	−1.18989	−	0.0755012i
$761$	−12.4372	−	38.2779i	−0.450850	−	1.38757i	−0.875939	−	0.482422i	$-0.839757\pi$
$761$	−12.4372	−	38.2779i	−0.450850	−	1.38757i	0.425089	−	0.905151i	$-0.360243\pi$
$762$	0.748123	−	2.30249i	0.0271016	−	0.0834103i
$763$	10.5458	−	32.4566i	0.381784	−	1.17501i
$764$	12.8845	+	39.6543i	0.466143	+	1.43464i
$765$	−2.80426	−	10.9462i	−0.101388	−	0.395760i
$766$	−10.9596	+	33.7302i	−0.395987	+	1.21872i
$767$	4.52503	+	3.28763i	0.163389	+	0.118709i
$768$	31.5921			1.13998
$769$	−17.8801	−	12.9907i	−0.644773	−	0.468455i	0.216714	−	0.976235i	$-0.430466\pi$
$769$	−17.8801	−	12.9907i	−0.644773	−	0.468455i	−0.861487	+	0.507780i	$0.830466\pi$
$770$	15.2182	+	59.4028i	0.548424	+	2.14073i
$771$	3.34286	−	2.42873i	0.120390	−	0.0874685i
$772$	2.18507	−	1.58754i	0.0786423	−	0.0571370i
$773$	1.51429	+	4.66049i	0.0544651	+	0.167626i	0.974589	−	0.224002i	$-0.0719121\pi$
$773$	1.51429	+	4.66049i	0.0544651	+	0.167626i	−0.920124	+	0.391628i	$0.871912\pi$
$774$	6.17649			0.222009
$775$	6.93343	+	36.5589i	0.249056	+	1.31324i
$776$	−50.8215			−1.82439
$777$	−6.12177	−	18.8409i	−0.219617	−	0.675913i
$778$	−45.6139	+	33.1405i	−1.63534	+	1.18814i
$779$	13.5097	−	9.81537i	0.484035	−	0.351672i
$780$	−24.1415	+	15.3026i	−0.864405	+	0.547919i
$781$	−1.88681	−	1.37085i	−0.0675153	−	0.0490528i
$782$	−19.0851			−0.682481
$783$	−2.52590	−	1.83517i	−0.0902682	−	0.0655837i
$784$	5.57648	−	17.1627i	0.199160	−	0.612952i
$785$	−18.0110	+	45.4194i	−0.642839	+	1.62109i
$786$	9.51020	+	29.2694i	0.339218	+	1.04400i
$787$	−1.15411	+	3.55198i	−0.0411395	+	0.126614i	−0.969517	−	0.245024i	$-0.921204\pi$
$787$	−1.15411	+	3.55198i	−0.0411395	+	0.126614i	0.928377	+	0.371639i	$0.121204\pi$
$788$	−28.4728	+	87.6303i	−1.01430	+	3.12170i
$789$	0.320676	+	0.986940i	0.0114164	+	0.0351360i
$790$	61.4496	−	38.9510i	2.18628	−	1.38581i
$791$	−5.86182	+	18.0408i	−0.208422	+	0.641458i
$792$	12.6076	+	9.15994i	0.447991	+	0.325484i
$793$	−25.3266			−0.899375
$794$	−27.5100	−	19.9872i	−0.976294	−	0.709319i
$795$	−17.4825	−	14.4786i	−0.620042	−	0.513503i
$796$	−32.6193	+	23.6993i	−1.15616	+	0.839998i
$797$	−2.70538	+	1.96557i	−0.0958295	+	0.0696242i	−0.634668	−	0.772785i	$-0.718863\pi$
$797$	−2.70538	+	1.96557i	−0.0958295	+	0.0696242i	0.538839	+	0.842409i	$0.318863\pi$
$798$	−7.99348	−	24.6014i	−0.282966	−	0.870880i
$799$	−35.7355			−1.26423
$800$	1.58201	+	1.48880i	0.0559326	+	0.0526370i
$801$	8.53392			0.301531
$802$	−20.7994	−	64.0140i	−0.734453	−	2.26041i
$803$	−4.96901	+	3.61019i	−0.175352	+	0.127401i
$804$	−5.91646	+	4.29856i	−0.208658	+	0.151599i
$805$	−11.8817	−	0.753920i	−0.418775	−	0.0265722i
$806$	47.4866	+	34.5010i	1.67264	+	1.21525i
$807$	15.7897			0.555823
$808$	−6.79957	−	4.94017i	−0.239208	−	0.173795i
$809$	10.5954	−	32.6094i	0.372516	−	1.14649i	−0.572624	−	0.819818i	$-0.694074\pi$
$809$	10.5954	−	32.6094i	0.372516	−	1.14649i	0.945140	−	0.326667i	$-0.105926\pi$
$810$	−4.20255	−	3.48044i	−0.147663	−	0.122290i
$811$	−1.07152	−	3.29778i	−0.0376260	−	0.115801i	0.930479	−	0.366344i	$-0.119391\pi$
$811$	−1.07152	−	3.29778i	−0.0376260	−	0.115801i	−0.968105	+	0.250543i	$0.919391\pi$
$812$	13.1274	−	40.4020i	0.460682	−	1.41783i
$813$	4.23364	−	13.0298i	0.148480	−	0.456975i
$814$	14.1845	+	43.6554i	0.497167	+	1.53012i
$815$	−17.4521	−	14.4534i	−0.611320	−	0.506279i
$816$	5.82768	−	17.9358i	0.204010	−	0.627877i
$817$	6.30926	+	4.58394i	0.220733	+	0.160372i
$818$	32.2422			1.12732
$819$	−8.99556	−	6.53566i	−0.314330	−	0.228374i
$820$	47.8328	+	3.03510i	1.67040	+	0.105990i
$821$	11.8771	−	8.62922i	0.414514	−	0.301162i	−0.360913	−	0.932600i	$-0.617535\pi$
$821$	11.8771	−	8.62922i	0.414514	−	0.301162i	0.775427	+	0.631438i	$0.217535\pi$
$822$	16.2689	−	11.8201i	0.567445	−	0.412273i
$823$	−6.44912	−	19.8483i	−0.224802	−	0.691870i	−0.998312	−	0.0580851i	$-0.981501\pi$
$823$	−6.44912	−	19.8483i	−0.224802	−	0.691870i	0.773510	−	0.633785i	$-0.218499\pi$
$824$	75.9223			2.64488
$825$	3.04329	+	16.0468i	0.105954	+	0.558677i
$826$	−14.5285			−0.505512
$827$	13.9946	+	43.0710i	0.486641	+	1.49773i	0.829590	+	0.558372i	$0.188574\pi$
$827$	13.9946	+	43.0710i	0.486641	+	1.49773i	−0.342950	+	0.939354i	$0.611426\pi$
$828$	−4.95193	+	3.59779i	−0.172091	+	0.125032i
$829$	7.81291	−	5.67641i	0.271354	−	0.197150i	−0.443784	−	0.896134i	$-0.646364\pi$
$829$	7.81291	−	5.67641i	0.271354	−	0.197150i	0.715137	+	0.698984i	$0.246364\pi$
$830$	−16.6315	−	13.7738i	−0.577287	−	0.478094i
$831$	5.64685	+	4.10268i	0.195887	+	0.142320i
$832$	27.5502			0.955131
$833$	19.7690	+	14.3630i	0.684955	+	0.497649i
$834$	−6.08075	+	18.7146i	−0.210559	+	0.648035i
$835$	2.85386	−	1.80897i	0.0987620	−	0.0626022i
$836$	12.3009	+	37.8583i	0.425436	+	1.30936i
$837$	−2.29974	+	7.07787i	−0.0794907	+	0.244647i
$838$	−6.67198	+	20.5342i	−0.230480	+	0.709344i
$839$	−7.77848	−	23.9397i	−0.268543	−	0.826490i	−0.990856	−	0.134924i	$-0.956921\pi$
$839$	−7.77848	−	23.9397i	−0.268543	−	0.826490i	0.722313	−	0.691566i	$-0.243079\pi$
$840$	13.5283	−	34.1153i	0.466771	−	1.17709i
$841$	−5.94919	+	18.3097i	−0.205144	+	0.631370i
$842$	73.9874	+	53.7550i	2.54977	+	1.85252i
$843$	−7.95823			−0.274096
$844$	−58.4159	−	42.4416i	−2.01076	−	1.46090i
$845$	4.82340	−	3.05740i	0.165930	−	0.105178i
$846$	−13.9610	+	10.1433i	−0.479989	+	0.348733i
$847$	−0.917269	+	0.666435i	−0.0315177	+	0.0228990i
$848$	−11.7070	−	36.0305i	−0.402021	−	1.23729i
$849$	27.7952			0.953928
$850$	54.0633	−	29.6462i	1.85436	−	1.01686i
$851$	−8.91196			−0.305498
$852$	0.872582	+	2.68553i	0.0298942	+	0.0920048i
$853$	2.59571	−	1.88589i	0.0888753	−	0.0645717i	−0.542460	−	0.840081i	$-0.682507\pi$
$853$	2.59571	−	1.88589i	0.0888753	−	0.0645717i	0.631336	+	0.775510i	$0.282507\pi$
$854$	53.2222	−	38.6682i	1.82123	−	1.32320i
$855$	−1.70984	−	6.67422i	−0.0584753	−	0.228254i
$856$	60.9069	+	44.2514i	2.08175	+	1.51248i
$857$	19.4569			0.664634			0.332317	−	0.943168i	$-0.392170\pi$
$857$	19.4569			0.664634			0.332317	+	0.943168i	$0.392170\pi$
$858$	20.8432	+	15.1435i	0.711577	+	0.516991i
$859$	5.20173	−	16.0093i	0.177481	−	0.546230i	−0.822257	−	0.569116i	$-0.807286\pi$
$859$	5.20173	−	16.0093i	0.177481	−	0.546230i	0.999738	+	0.0228862i	$0.00728553\pi$
$860$	5.55498	+	21.6834i	0.189423	+	0.739398i
$861$	5.76163	+	17.7325i	0.196356	+	0.604322i
$862$	−20.0772	+	61.7914i	−0.683833	+	2.10462i
$863$	1.17803	−	3.62560i	0.0401006	−	0.123417i	−0.929002	−	0.370074i	$-0.879332\pi$
$863$	1.17803	−	3.62560i	0.0401006	−	0.123417i	0.969103	+	0.246657i	$0.0793322\pi$
$864$	0.134261	+	0.413214i	0.00456766	+	0.0140578i
$865$	−30.9192	−	1.96189i	−1.05129	−	0.0667063i
$866$	26.3910	−	81.2231i	0.896802	−	2.76007i
$867$	6.90623	+	5.01767i	0.234548	+	0.170409i
$868$	−101.259			−3.43697
$869$	−35.2358	−	25.6003i	−1.19529	−	0.868431i
$870$	6.28008	−	15.8369i	0.212915	−	0.536921i
$871$	−4.83497	+	3.51281i	−0.163827	+	0.119027i
$872$	38.2863	−	27.8166i	1.29654	−	0.941990i
$873$	−3.29190	−	10.1314i	−0.111414	−	0.342897i
$874$	−11.6367			−0.393619
$875$	34.8291	−	16.3211i	1.17744	−	0.551753i
$876$	7.43645			0.251254
$877$	−7.95569	−	24.4851i	−0.268644	−	0.826803i	−0.990831	−	0.135105i	$-0.956863\pi$
$877$	−7.95569	−	24.4851i	−0.268644	−	0.826803i	0.722187	−	0.691698i	$-0.243137\pi$
$878$	−39.5911	+	28.7646i	−1.33613	+	0.970759i
$879$	−11.4960	+	8.35231i	−0.387749	+	0.281717i
$880$	−10.0482	+	25.3393i	−0.338726	+	0.854188i
$881$	−36.6110	−	26.5995i	−1.23346	−	0.896159i	−0.236313	−	0.971677i	$-0.575939\pi$
$881$	−36.6110	−	26.5995i	−1.23346	−	0.896159i	−0.997144	+	0.0755181i	$0.975939\pi$
$882$	11.8001			0.397330
$883$	−35.9186	−	26.0964i	−1.20876	−	0.878212i	−0.213639	−	0.976913i	$-0.568531\pi$
$883$	−35.9186	−	26.0964i	−1.20876	−	0.878212i	−0.995117	+	0.0987003i	$0.968531\pi$
$884$	19.9611	−	61.4340i	0.671365	−	2.06625i
$885$	−3.86189	−	0.245045i	−0.129816	−	0.00823710i
$886$	3.12850	+	9.62853i	0.105104	+	0.323477i
$887$	−12.0495	+	37.0844i	−0.404581	+	1.24517i	0.516664	+	0.856189i	$0.327174\pi$
$887$	−12.0495	+	37.0844i	−0.404581	+	1.24517i	−0.921245	+	0.388984i	$0.872826\pi$
$888$	8.48919	−	26.1270i	0.284878	−	0.876766i
$889$	1.05470	+	3.24602i	0.0353734	+	0.108868i
$890$	11.5565	+	45.1097i	0.387374	+	1.51208i
$891$	−1.00942	+	3.10669i	−0.0338170	+	0.104078i
$892$	−55.1119	−	40.0411i	−1.84528	−	1.34068i
$893$	−21.7890			−0.729142
$894$	−37.7278	−	27.4108i	−1.26181	−	0.916755i
$895$	8.02188	+	31.3127i	0.268142	+	1.04667i
$896$	−55.4764	+	40.3059i	−1.85334	+	1.34653i
$897$	−4.04675	+	2.94014i	−0.135117	+	0.0981683i
$898$	−6.29517	−	19.3745i	−0.210072	−	0.646537i
$899$	−23.2356			−0.774952
$900$	8.43890	−	17.8838i	0.281297	−	0.596128i
$901$	51.2995			1.70903
$902$	−13.3500	−	41.0872i	−0.444508	−	1.36805i
$903$	−7.04455	+	5.11817i	−0.234428	+	0.170322i
$904$	−21.2812	+	15.4617i	−0.707803	+	0.514249i
$905$	−32.4649	+	20.5785i	−1.07917	+	0.684052i
$906$	3.13015	+	2.27419i	0.103992	+	0.0755548i
$907$	11.0201			0.365915			0.182958	−	0.983121i	$-0.441433\pi$
$907$	11.0201			0.365915			0.182958	+	0.983121i	$0.441433\pi$
$908$	13.8506	+	10.0630i	0.459648	+	0.333954i
$909$	0.544406	−	1.67551i	0.0180568	−	0.0555731i
$910$	22.3654	−	56.4004i	0.741407	−	1.86966i
$911$	−16.3540	−	50.3325i	−0.541833	−	1.66759i	−0.728404	−	0.685148i	$-0.759737\pi$
$911$	−16.3540	−	50.3325i	−0.541833	−	1.66759i	0.186571	−	0.982441i	$-0.440263\pi$
$912$	3.55332	−	10.9360i	0.117662	−	0.362127i
$913$	−3.99477	+	12.2946i	−0.132207	+	0.406893i
$914$	15.5172	+	47.7570i	0.513263	+	1.57966i
$915$	14.7994	−	9.38088i	0.489253	−	0.310122i
$916$	24.8277	−	76.4119i	0.820331	−	2.52472i
$917$	−35.1010	−	25.5023i	−1.15914	−	0.842162i
$918$	12.3317			0.407005
$919$	38.5129	+	27.9812i	1.27042	+	0.923016i	0.999219	−	0.0395064i	$-0.0125786\pi$
$919$	38.5129	+	27.9812i	1.27042	+	0.923016i	0.271203	+	0.962522i	$0.412579\pi$
$920$	−12.7153	−	10.5305i	−0.419212	−	0.347181i
$921$	−18.8429	+	13.6902i	−0.620896	+	0.451107i
$922$	−56.6388	+	41.1505i	−1.86530	+	1.35522i
$923$	0.713080	+	2.19463i	0.0234713	+	0.0722372i
$924$	−44.4457			−1.46216
$925$	25.2454	−	13.8436i	0.830063	−	0.455175i
$926$	97.8059			3.21410
$927$	4.91777	+	15.1354i	0.161521	+	0.497110i
$928$	−1.09745	+	0.797343i	−0.0360255	+	0.0261741i
$929$	−17.5465	+	12.7483i	−0.575682	+	0.418258i	−0.837165	−	0.546951i	$-0.815789\pi$
$929$	−17.5465	+	12.7483i	−0.575682	+	0.418258i	0.261483	+	0.965208i	$0.415789\pi$
$930$	−40.5274	−	2.57155i	−1.32895	−	0.0843245i
$931$	12.0538	+	8.75757i	0.395046	+	0.287018i
$932$	−1.34848			−0.0441708
$933$	−6.10746	−	4.43733i	−0.199949	−	0.145272i
$934$	−6.13972	+	18.8961i	−0.200898	+	0.618300i
$935$	−28.4279	−	23.5433i	−0.929692	−	0.769947i
$936$	−4.76477	−	14.6645i	−0.155741	−	0.479323i
$937$	0.680112	−	2.09317i	0.0222183	−	0.0683809i	−0.939333	−	0.343008i	$-0.888554\pi$
$937$	0.680112	−	2.09317i	0.0222183	−	0.0683809i	0.961551	+	0.274627i	$0.0885543\pi$
$938$	4.79708	−	14.7639i	0.156630	−	0.482058i
$939$	9.78241	+	30.1072i	0.319237	+	0.982510i
$940$	−48.1655	−	39.8894i	−1.57098	−	1.30105i
$941$	−5.18833	+	15.9680i	−0.169135	+	0.520543i	−0.999317	−	0.0369489i	$-0.988236\pi$
$941$	−5.18833	+	15.9680i	−0.169135	+	0.520543i	0.830183	+	0.557492i	$0.188236\pi$
$942$	−43.1388	−	31.3422i	−1.40554	−	1.02118i
$943$	8.38767			0.273140
$944$	−5.22489	−	3.79611i	−0.170056	−	0.123553i
$945$	7.67727	+	0.487139i	0.249742	+	0.0158466i
$946$	16.3226	−	11.8591i	0.530695	−	0.385572i
$947$	−29.6207	+	21.5207i	−0.962544	+	0.699329i	−0.953740	−	0.300632i	$-0.902802\pi$
$947$	−29.6207	+	21.5207i	−0.962544	+	0.699329i	−0.00880418	+	0.999961i	$0.502802\pi$
$948$	16.2953	+	50.1518i	0.529247	+	1.62885i
$949$	6.07711			0.197271
$950$	32.9641	−	18.0762i	1.06950	−	0.586470i
$951$	−25.8362			−0.837796
$952$	25.6295	+	78.8796i	0.830658	+	2.55650i
$953$	−35.5383	+	25.8201i	−1.15120	+	0.836394i	−0.988640	−	0.150305i	$-0.951974\pi$
$953$	−35.5383	+	25.8201i	−1.15120	+	0.836394i	−0.162558	+	0.986699i	$0.551974\pi$
$954$	20.0415	−	14.5610i	0.648867	−	0.471430i
$955$	−18.1557	−	15.0360i	−0.587503	−	0.486555i
$956$	22.9251	+	16.6561i	0.741450	+	0.538695i
$957$	−10.1988			−0.329680
$958$	55.4010	+	40.2512i	1.78993	+	1.30046i
$959$	−8.76068	+	26.9626i	−0.282897	+	0.870668i
$960$	−16.0987	+	10.2045i	−0.519584	+	0.329348i
$961$	7.53541	+	23.1916i	0.243078	+	0.748116i
$962$	14.0346	−	43.1940i	0.452493	−	1.39263i
$963$	−4.87650	+	15.0083i	−0.157143	+	0.483636i
$964$	−15.3530	−	47.2517i	−0.494487	−	1.52188i
$965$	−0.562897	+	1.41950i	−0.0181203	+	0.0456952i
$966$	4.01503	−	12.3570i	0.129182	−	0.397580i
$967$	−19.8059	−	14.3899i	−0.636916	−	0.462747i	0.221873	−	0.975076i	$-0.428783\pi$
$967$	−19.8059	−	14.3899i	−0.636916	−	0.462747i	−0.858789	+	0.512329i	$0.828783\pi$
$968$	−1.57227			−0.0505348
$969$	12.5967	+	9.15206i	0.404665	+	0.294007i
$970$	49.0962	−	31.1206i	1.57639	−	0.999221i
$971$	15.8773	−	11.5355i	0.509526	−	0.370192i	−0.303118	−	0.952953i	$-0.598028\pi$
$971$	15.8773	−	11.5355i	0.509526	−	0.370192i	0.812644	+	0.582761i	$0.198028\pi$
$972$	3.19965	−	2.32468i	0.102629	−	0.0745642i
$973$	−8.57257	−	26.3837i	−0.274824	−	0.845822i
$974$	−37.1344			−1.18986
$975$	6.89632	−	14.6148i	0.220859	−	0.468048i
$976$	29.2438			0.936070
$977$	9.43236	+	29.0298i	0.301768	+	0.928746i	0.980864	+	0.194696i	$0.0623721\pi$
$977$	9.43236	+	29.0298i	0.301768	+	0.928746i	−0.679096	+	0.734050i	$0.737628\pi$
$978$	20.0066	−	14.5356i	0.639739	−	0.464798i
$979$	22.5526	−	16.3854i	0.720785	−	0.523681i
$980$	10.6127	+	41.4259i	0.339011	+	1.32330i
$981$	8.02529	+	5.83071i	0.256228	+	0.186160i
$982$	20.2356			0.645743
$983$	−8.38590	−	6.09271i	−0.267469	−	0.194327i	0.445964	−	0.895051i	$-0.352861\pi$
$983$	−8.38590	−	6.09271i	−0.267469	−	0.194327i	−0.713433	+	0.700723i	$0.752861\pi$
$984$	−7.98977	+	24.5900i	−0.254705	+	0.783901i
$985$	−12.9283	−	50.4644i	−0.411929	−	1.60793i
$986$	11.8977	+	36.6173i	0.378899	+	1.16613i
$987$	7.51788	−	23.1376i	0.239297	−	0.736479i
$988$	12.1709	−	37.4582i	0.387208	−	1.19170i
$989$	1.21048	+	3.72546i	0.0384909	+	0.118463i
$990$	−17.7887	−	1.12873i	−0.565361	−	0.0358734i
$991$	−3.12376	+	9.61395i	−0.0992295	+	0.305397i	−0.988333	−	0.152309i	$-0.951329\pi$
$991$	−3.12376	+	9.61395i	−0.0992295	+	0.305397i	0.889103	+	0.457707i	$0.151329\pi$
$992$	2.61591	+	1.90057i	0.0830552	+	0.0603431i
$993$	−20.1083			−0.638116
$994$	−4.84921	−	3.52316i	−0.153808	−	0.111748i
$995$	8.40308	−	21.1906i	0.266395	−	0.671787i
$996$	12.6625	−	9.19986i	0.401227	−	0.291509i
$997$	−17.2838	+	12.5574i	−0.547382	+	0.397697i	−0.826819	−	0.562467i	$-0.809852\pi$
$997$	−17.2838	+	12.5574i	−0.547382	+	0.397697i	0.279437	+	0.960164i	$0.409852\pi$
$998$	−18.4002	−	56.6300i	−0.582448	−	1.79259i
$999$	5.75838			0.182187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.g.c.31.3	✓	12
3.2	odd	2		225.2.h.d.181.1		12
5.2	odd	4		375.2.i.d.349.2		24
5.3	odd	4		375.2.i.d.349.5		24
5.4	even	2		375.2.g.c.151.1		12
25.2	odd	20		1875.2.b.f.1249.11		12
25.3	odd	20		375.2.i.d.274.2		24
25.4	even	10		375.2.g.c.226.1		12
25.11	even	5		1875.2.a.j.1.6		6
25.14	even	10		1875.2.a.k.1.1		6
25.21	even	5	inner	75.2.g.c.46.3	yes	12
25.22	odd	20		375.2.i.d.274.5		24
25.23	odd	20		1875.2.b.f.1249.2		12
75.11	odd	10		5625.2.a.p.1.1		6
75.14	odd	10		5625.2.a.q.1.6		6
75.71	odd	10		225.2.h.d.46.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.3	✓	12	1.1	even	1	trivial
75.2.g.c.46.3	yes	12	25.21	even	5	inner
225.2.h.d.46.1		12	75.71	odd	10
225.2.h.d.181.1		12	3.2	odd	2
375.2.g.c.151.1		12	5.4	even	2
375.2.g.c.226.1		12	25.4	even	10
375.2.i.d.274.2		24	25.3	odd	20
375.2.i.d.274.5		24	25.22	odd	20
375.2.i.d.349.2		24	5.2	odd	4
375.2.i.d.349.5		24	5.3	odd	4
1875.2.a.j.1.6		6	25.11	even	5
1875.2.a.k.1.1		6	25.14	even	10
1875.2.b.f.1249.2		12	25.23	odd	20
1875.2.b.f.1249.11		12	25.2	odd	20
5625.2.a.p.1.1		6	75.11	odd	10
5625.2.a.q.1.6		6	75.14	odd	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.754089 + 2.32085i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-3.19965 + 2.32468i) q^{4} +(0.824264 - 2.07860i) q^{5} +(1.97423 + 1.43436i) q^{6} -3.44028 q^{7} +(-3.85959 - 2.80415i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.754089 + 2.32085i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-3.19965 + 2.32468i) q^{4} +(0.824264 - 2.07860i) q^{5} +(1.97423 + 1.43436i) q^{6} -3.44028 q^{7} +(-3.85959 - 2.80415i) q^{8} +(0.309017 - 0.951057i) q^{9} +(5.44569 + 0.345540i) q^{10} +(-1.00942 - 3.10669i) q^{11} +(-1.22216 + 3.76141i) q^{12} +(-0.998755 + 3.07385i) q^{13} +(-2.59428 - 7.98437i) q^{14} +(-0.554928 - 2.16612i) q^{15} +(1.15323 - 3.54927i) q^{16} +(4.08826 + 2.97030i) q^{17} +2.44028 q^{18} +(2.49274 + 1.81108i) q^{19} +(2.19473 + 8.56695i) q^{20} +(-2.78325 + 2.02215i) q^{21} +(6.44895 - 4.68544i) q^{22} +(0.478250 + 1.47190i) q^{23} -4.77071 q^{24} +(-3.64118 - 3.42664i) q^{25} -7.88709 q^{26} +(-0.309017 - 0.951057i) q^{27} +(11.0077 - 7.99756i) q^{28} +(2.52590 - 1.83517i) q^{29} +(4.60876 - 2.92135i) q^{30} +(-6.02080 - 4.37437i) q^{31} -0.434479 q^{32} +(-2.64270 - 1.92004i) q^{33} +(-3.81069 + 11.7281i) q^{34} +(-2.83570 + 7.15098i) q^{35} +(1.22216 + 3.76141i) q^{36} +(-1.77944 + 5.47655i) q^{37} +(-2.32349 + 7.15098i) q^{38} +(0.998755 + 3.07385i) q^{39} +(-9.01004 + 5.71118i) q^{40} +(1.67476 - 5.15437i) q^{41} +(-6.79191 - 4.93461i) q^{42} +2.53106 q^{43} +(10.4519 + 7.59371i) q^{44} +(-1.72216 - 1.42625i) q^{45} +(-3.05541 + 2.21989i) q^{46} +(-5.72106 + 4.15659i) q^{47} +(-1.15323 - 3.54927i) q^{48} +4.83555 q^{49} +(5.20693 - 11.0346i) q^{50} +5.05337 q^{51} +(-3.95006 - 12.1570i) q^{52} +(8.21277 - 5.96693i) q^{53} +(1.97423 - 1.43436i) q^{54} +(-7.28960 - 0.462540i) q^{55} +(13.2781 + 9.64708i) q^{56} +3.08119 q^{57} +(6.16391 + 4.47834i) q^{58} +(0.534773 - 1.64586i) q^{59} +(6.81110 + 5.64078i) q^{60} +(2.42149 + 7.45259i) q^{61} +(5.61202 - 17.2720i) q^{62} +(-1.06311 + 3.27190i) q^{63} +(-2.63409 - 8.10689i) q^{64} +(5.56608 + 4.60968i) q^{65} +(2.46328 - 7.58119i) q^{66} +(1.49595 + 1.08687i) q^{67} -19.9860 q^{68} +(1.25207 + 0.909685i) q^{69} +(-18.7347 - 1.18876i) q^{70} +(0.577613 - 0.419660i) q^{71} +(-3.85959 + 2.80415i) q^{72} +(-0.581036 - 1.78825i) q^{73} -14.0521 q^{74} +(-4.95990 - 0.631977i) q^{75} -12.1861 q^{76} +(3.47270 + 10.6879i) q^{77} +(-6.38079 + 4.63591i) q^{78} +(10.7868 - 7.83708i) q^{79} +(-6.42695 - 5.32263i) q^{80} +(-0.809017 - 0.587785i) q^{81} +13.2254 q^{82} +(-3.20166 - 2.32614i) q^{83} +(4.20457 - 12.9403i) q^{84} +(9.54388 - 6.04956i) q^{85} +(1.90864 + 5.87419i) q^{86} +(0.964807 - 2.96937i) q^{87} +(-4.81567 + 14.8211i) q^{88} +(2.63713 + 8.11624i) q^{89} +(2.01144 - 5.07238i) q^{90} +(3.43600 - 10.5749i) q^{91} +(-4.95193 - 3.59779i) q^{92} -7.44212 q^{93} +(-13.9610 - 10.1433i) q^{94} +(5.81919 - 3.68860i) q^{95} +(-0.351501 + 0.255380i) q^{96} +(8.61831 - 6.26157i) q^{97} +(3.64643 + 11.2226i) q^{98} -3.26656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23} + 6 q^{24} + 4 q^{25} - 56 q^{26} + 3 q^{27} + q^{28} - q^{29} + 19 q^{30} + 13 q^{31} - 32 q^{32} - q^{33} - 25 q^{34} - 10 q^{35} + 8 q^{37} - 22 q^{38} + 2 q^{39} - 28 q^{40} + 8 q^{41} - 16 q^{42} - 4 q^{43} + 33 q^{44} - 6 q^{45} - 22 q^{46} - 13 q^{47} - 16 q^{48} - 28 q^{49} + 81 q^{50} + 26 q^{51} + 44 q^{52} + 44 q^{53} + 9 q^{55} + 45 q^{56} - 22 q^{57} + 41 q^{58} - 22 q^{59} + 14 q^{60} - 8 q^{61} + 41 q^{62} + 3 q^{63} + 49 q^{64} - 38 q^{65} - 3 q^{66} - 6 q^{67} - 100 q^{68} + 6 q^{69} - 45 q^{70} - 21 q^{71} + 9 q^{72} - 16 q^{73} - 44 q^{74} - 4 q^{75} - 52 q^{76} + q^{77} - 19 q^{78} + 10 q^{79} - 99 q^{80} - 3 q^{81} + 26 q^{82} - 10 q^{83} - 6 q^{84} + 23 q^{85} + 56 q^{86} - 4 q^{87} - 16 q^{88} + 57 q^{89} + 16 q^{90} - 7 q^{91} + 3 q^{92} + 22 q^{93} - 23 q^{94} + 21 q^{95} - 23 q^{96} + 4 q^{97} - 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more