LMFDB - Embedded newform 750.2.m.a.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			91.1
Character	$\chi$	$=$	750.91
Dual form			750.2.m.a.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.15608 - 0.592736i) q^{5} +(0.968583 - 0.248690i) q^{6} +(1.47991 + 4.55470i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})$	\(q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.15608 - 0.592736i) q^{5} +(0.968583 - 0.248690i) q^{6} +(1.47991 + 4.55470i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(-1.16596 - 1.90802i) q^{10} +(-2.49938 - 2.34708i) q^{11} +(0.876307 + 0.481754i) q^{12} +(1.50453 + 3.19728i) q^{13} +(-2.03910 + 4.33330i) q^{14} +(-1.65575 + 1.50283i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(-0.230327 + 3.66094i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.36553 + 2.15173i) q^{19} +(0.456185 - 2.18904i) q^{20} +(4.63864 + 1.19100i) q^{21} +(-0.215287 - 3.42189i) q^{22} +(1.07979 + 5.66047i) q^{23} +(0.309017 + 0.951057i) q^{24} +(4.29733 + 2.55597i) q^{25} +(-1.09194 + 3.36064i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(-4.45279 + 1.76298i) q^{28} +(-8.22281 + 3.25564i) q^{29} +(-2.23575 - 0.0379198i) q^{30} +(0.249351 - 3.96331i) q^{31} +(-0.809017 - 0.587785i) q^{32} +(-3.32094 + 0.852672i) q^{33} +(-2.67399 + 2.51104i) q^{34} +(-0.491068 - 10.6975i) q^{35} +(0.876307 - 0.481754i) q^{36} +(6.09805 - 0.770363i) q^{37} +(-0.477533 + 2.50332i) q^{38} +(3.50572 + 0.442876i) q^{39} +(1.83105 - 1.28346i) q^{40} +(1.87371 - 9.82234i) q^{41} +(2.56613 + 4.04357i) q^{42} +(0.905649 - 0.657993i) q^{43} +(2.18551 - 2.64183i) q^{44} +(0.381689 + 2.20325i) q^{45} +(-3.08772 + 4.86547i) q^{46} +(5.66187 + 6.84402i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(-12.8920 + 9.36662i) q^{49} +(1.38294 + 4.80494i) q^{50} +(2.96762 + 2.15610i) q^{51} +(-3.09651 + 1.70232i) q^{52} +(-3.62418 - 0.930532i) q^{53} +(-0.637424 - 0.770513i) q^{54} +(3.99766 + 6.54195i) q^{55} +(-4.45279 - 1.76298i) q^{56} +2.54846 q^{57} +(-8.22281 - 3.25564i) q^{58} +(6.38483 + 3.51009i) q^{59} +(-1.60383 - 1.55812i) q^{60} +(0.724257 + 3.79669i) q^{61} +(2.89484 - 2.71844i) q^{62} +(3.49110 - 3.27836i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-1.34873 - 7.78538i) q^{65} +(-3.00456 - 1.65177i) q^{66} +(-7.01992 - 2.77938i) q^{67} -3.66818 q^{68} +(5.35787 + 2.12133i) q^{69} +(6.96496 - 8.13429i) q^{70} +(7.01543 + 8.48019i) q^{71} +(0.968583 + 0.248690i) q^{72} +(1.93446 - 1.06348i) q^{73} +(4.97264 + 3.61283i) q^{74} +(4.46070 - 2.25880i) q^{75} +(-2.06175 + 1.49795i) q^{76} +(6.99137 - 14.8574i) q^{77} +(2.25239 + 2.72268i) q^{78} +(6.10476 - 9.61956i) q^{79} +(2.21336 + 0.317834i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(8.08973 - 5.87753i) q^{82} +(-8.31496 - 13.1023i) q^{83} +(-0.897387 + 4.70427i) q^{84} +(2.66657 - 7.75674i) q^{85} +(1.11062 + 0.140304i) q^{86} +(-1.65717 + 8.68721i) q^{87} +(3.40162 - 0.429725i) q^{88} +(4.29841 - 2.36307i) q^{89} +(-1.22999 + 1.86738i) q^{90} +(-12.3361 + 11.5844i) q^{91} +(-5.58150 + 1.43308i) q^{92} +(-3.21273 - 2.33418i) q^{93} +(-0.557732 + 8.86489i) q^{94} +(-1.66878 - 5.44870i) q^{95} +(-0.929776 + 0.368125i) q^{96} +(-15.1122 + 5.98334i) q^{97} +(-15.8098 - 1.99724i) q^{98} +(-1.05951 + 3.26085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 20 q^{5} + 5 q^{7}+O(q^{10}) $ 100 * q - 20 * q^5 + 5 * q^7	$ 100 q - 20 q^{5} + 5 q^{7} - 20 q^{10} + 10 q^{11} + 10 q^{13} - 20 q^{14} - 20 q^{15} + 15 q^{17} - 25 q^{18} + 15 q^{19} + 5 q^{20} + 5 q^{21} + 10 q^{22} - 5 q^{23} - 25 q^{24} + 10 q^{26} + 5 q^{28} + 25 q^{29} + 5 q^{30} - 25 q^{31} - 25 q^{32} + 10 q^{33} - 10 q^{34} + 40 q^{35} + 30 q^{37} - 35 q^{38} + 10 q^{39} + 5 q^{40} - 15 q^{41} + 5 q^{42} + 35 q^{43} - 15 q^{44} + 5 q^{45} + 20 q^{46} - 110 q^{47} + 20 q^{49} + 15 q^{51} - 40 q^{52} + 45 q^{53} + 60 q^{55} + 5 q^{56} - 60 q^{57} + 25 q^{58} - 20 q^{60} + 25 q^{62} + 5 q^{63} + 70 q^{65} - 15 q^{66} - 45 q^{67} - 60 q^{68} + 20 q^{69} - 10 q^{70} + 10 q^{71} + 60 q^{73} + 30 q^{74} - 25 q^{75} + 15 q^{76} + 5 q^{77} + 10 q^{78} - 10 q^{79} + 5 q^{80} - 15 q^{82} - 5 q^{83} + 5 q^{84} - 10 q^{85} + 35 q^{86} + 25 q^{87} + 10 q^{88} + 5 q^{90} + 15 q^{91} - 55 q^{92} + 40 q^{94} - 125 q^{95} + 80 q^{97} - 5 q^{98} + 10 q^{99}+O(q^{100}) $ 100 * q - 20 * q^5 + 5 * q^7 - 20 * q^10 + 10 * q^11 + 10 * q^13 - 20 * q^14 - 20 * q^15 + 15 * q^17 - 25 * q^18 + 15 * q^19 + 5 * q^20 + 5 * q^21 + 10 * q^22 - 5 * q^23 - 25 * q^24 + 10 * q^26 + 5 * q^28 + 25 * q^29 + 5 * q^30 - 25 * q^31 - 25 * q^32 + 10 * q^33 - 10 * q^34 + 40 * q^35 + 30 * q^37 - 35 * q^38 + 10 * q^39 + 5 * q^40 - 15 * q^41 + 5 * q^42 + 35 * q^43 - 15 * q^44 + 5 * q^45 + 20 * q^46 - 110 * q^47 + 20 * q^49 + 15 * q^51 - 40 * q^52 + 45 * q^53 + 60 * q^55 + 5 * q^56 - 60 * q^57 + 25 * q^58 - 20 * q^60 + 25 * q^62 + 5 * q^63 + 70 * q^65 - 15 * q^66 - 45 * q^67 - 60 * q^68 + 20 * q^69 - 10 * q^70 + 10 * q^71 + 60 * q^73 + 30 * q^74 - 25 * q^75 + 15 * q^76 + 5 * q^77 + 10 * q^78 - 10 * q^79 + 5 * q^80 - 15 * q^82 - 5 * q^83 + 5 * q^84 - 10 * q^85 + 35 * q^86 + 25 * q^87 + 10 * q^88 + 5 * q^90 + 15 * q^91 - 55 * q^92 + 40 * q^94 - 125 * q^95 + 80 * q^97 - 5 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{6}{25}\right)$	$1$

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 $

$2$	0.728969	+	0.684547i	0.515459	+	0.484048i
$2$	0.728969	+	0.684547i	0.515459	+	0.484048i
$3$	0.535827	−	0.844328i	0.309360	−	0.487473i
$3$	0.535827	−	0.844328i	0.309360	−	0.487473i
$4$	0.0627905	+	0.998027i	0.0313953	+	0.499013i
$5$	−2.15608	−	0.592736i	−0.964227	−	0.265080i
$5$	−2.15608	−	0.592736i	−0.964227	−	0.265080i
$6$	0.968583	−	0.248690i	0.395422	−	0.101527i
$7$	1.47991	+	4.55470i	0.559354	+	1.72152i	0.684158	+	0.729334i	$0.260170\pi$
$7$	1.47991	+	4.55470i	0.559354	+	1.72152i	−0.124804	+	0.992181i	$0.539830\pi$
$8$	−0.637424	+	0.770513i	−0.225363	+	0.272418i
$9$	−0.425779	−	0.904827i	−0.141926	−	0.301609i
$10$	−1.16596	−	1.90802i	−0.368708	−	0.603369i
$11$	−2.49938	−	2.34708i	−0.753592	−	0.707670i	0.209212	−	0.977870i	$-0.432910\pi$
$11$	−2.49938	−	2.34708i	−0.753592	−	0.707670i	−0.962804	+	0.270200i	$0.912910\pi$
$12$	0.876307	+	0.481754i	0.252968	+	0.139070i
$13$	1.50453	+	3.19728i	0.417281	+	0.886767i	0.997388	+	0.0722271i	$0.0230106\pi$
$13$	1.50453	+	3.19728i	0.417281	+	0.886767i	−0.580107	+	0.814540i	$0.696989\pi$
$14$	−2.03910	+	4.33330i	−0.544972	+	1.15812i
$15$	−1.65575	+	1.50283i	−0.427512	+	0.388029i
$16$	−0.992115	+	0.125333i	−0.248029	+	0.0313333i
$17$	−0.230327	+	3.66094i	−0.0558625	+	0.887908i	0.865916	+	0.500190i	$0.166737\pi$
$17$	−0.230327	+	3.66094i	−0.0558625	+	0.887908i	−0.921778	+	0.387718i	$0.873263\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	1.36553	+	2.15173i	0.313274	+	0.493642i	0.964083	−	0.265600i	$-0.0855701\pi$
$19$	1.36553	+	2.15173i	0.313274	+	0.493642i	−0.650809	+	0.759242i	$0.725570\pi$
$20$	0.456185	−	2.18904i	0.102006	−	0.489484i
$21$	4.63864	+	1.19100i	1.01223	+	0.259897i
$22$	−0.215287	−	3.42189i	−0.0458994	−	0.729550i
$23$	1.07979	+	5.66047i	0.225152	+	1.18029i	0.897826	+	0.440350i	$0.145146\pi$
$23$	1.07979	+	5.66047i	0.225152	+	1.18029i	−0.672674	+	0.739939i	$0.734854\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	4.29733	+	2.55597i	0.859466	+	0.511194i
$26$	−1.09194	+	3.36064i	−0.214147	+	0.659076i
$27$	−0.992115	−	0.125333i	−0.190933	−	0.0241204i
$28$	−4.45279	+	1.76298i	−0.841498	+	0.333173i
$29$	−8.22281	+	3.25564i	−1.52694	+	0.604557i	−0.973572	−	0.228381i	$-0.926657\pi$
$29$	−8.22281	+	3.25564i	−1.52694	+	0.604557i	−0.553366	+	0.832938i	$0.686657\pi$
$30$	−2.23575	−	0.0379198i	−0.408190	−	0.00692317i
$31$	0.249351	−	3.96331i	0.0447847	−	0.711832i	−0.910014	−	0.414578i	$-0.863929\pi$
$31$	0.249351	−	3.96331i	0.0447847	−	0.711832i	0.954798	−	0.297254i	$-0.0960708\pi$
$32$	−0.809017	−	0.587785i	−0.143015	−	0.103907i
$33$	−3.32094	+	0.852672i	−0.578101	+	0.148431i
$34$	−2.67399	+	2.51104i	−0.458585	+	0.430640i
$35$	−0.491068	−	10.6975i	−0.0830056	−	1.80820i
$36$	0.876307	−	0.481754i	0.146051	−	0.0802923i
$37$	6.09805	−	0.770363i	1.00251	−	0.126647i	0.393097	−	0.919497i	$-0.371404\pi$
$37$	6.09805	−	0.770363i	1.00251	−	0.126647i	0.609417	+	0.792850i	$0.291404\pi$
$38$	−0.477533	+	2.50332i	−0.0774661	+	0.406092i
$39$	3.50572	+	0.442876i	0.561365	+	0.0709169i
$40$	1.83105	−	1.28346i	0.289514	−	0.202933i
$41$	1.87371	−	9.82234i	0.292625	−	1.53399i	−0.467370	−	0.884062i	$-0.654798\pi$
$41$	1.87371	−	9.82234i	0.292625	−	1.53399i	0.759994	−	0.649930i	$-0.225202\pi$
$42$	2.56613	+	4.04357i	0.395962	+	0.623936i
$43$	0.905649	−	0.657993i	0.138110	−	0.100343i	−0.516585	−	0.856236i	$-0.672797\pi$
$43$	0.905649	−	0.657993i	0.138110	−	0.100343i	0.654695	+	0.755893i	$0.272797\pi$
$44$	2.18551	−	2.64183i	0.329478	−	0.398270i
$45$	0.381689	+	2.20325i	0.0568988	+	0.328441i
$46$	−3.08772	+	4.86547i	−0.455260	+	0.717375i
$47$	5.66187	+	6.84402i	0.825868	+	0.998303i	0.999908	+	0.0135643i	$0.00431780\pi$
$47$	5.66187	+	6.84402i	0.825868	+	0.998303i	−0.174040	+	0.984739i	$0.555682\pi$
$48$	−0.425779	+	0.904827i	−0.0614559	+	0.130601i
$49$	−12.8920	+	9.36662i	−1.84172	+	1.33809i
$50$	1.38294	+	4.80494i	0.195577	+	0.679522i
$51$	2.96762	+	2.15610i	0.415550	+	0.301915i
$52$	−3.09651	+	1.70232i	−0.429408	+	0.236069i
$53$	−3.62418	−	0.930532i	−0.497820	−	0.127818i	−0.00857194	−	0.999963i	$-0.502729\pi$
$53$	−3.62418	−	0.930532i	−0.497820	−	0.127818i	−0.489248	+	0.872145i	$0.662729\pi$
$54$	−0.637424	−	0.770513i	−0.0867424	−	0.104854i
$55$	3.99766	+	6.54195i	0.539045	+	0.882117i
$56$	−4.45279	−	1.76298i	−0.595029	−	0.235589i
$57$	2.54846			0.337551
$58$	−8.22281	−	3.25564i	−1.07971	−	0.427487i
$59$	6.38483	+	3.51009i	0.831234	+	0.456975i	0.839740	−	0.542989i	$-0.182707\pi$
$59$	6.38483	+	3.51009i	0.831234	+	0.456975i	−0.00850549	+	0.999964i	$0.502707\pi$
$60$	−1.60383	−	1.55812i	−0.207054	−	0.201152i
$61$	0.724257	+	3.79669i	0.0927316	+	0.486116i	0.998107	+	0.0615036i	$0.0195896\pi$
$61$	0.724257	+	3.79669i	0.0927316	+	0.486116i	−0.905375	+	0.424612i	$0.860410\pi$
$62$	2.89484	−	2.71844i	0.367646	−	0.345242i
$63$	3.49110	−	3.27836i	0.439837	−	0.413035i
$64$	−0.187381	−	0.982287i	−0.0234227	−	0.122786i
$65$	−1.34873	−	7.78538i	−0.167290	−	0.965657i
$66$	−3.00456	−	1.65177i	−0.369835	−	0.203319i
$67$	−7.01992	−	2.77938i	−0.857620	−	0.339556i	−0.102174	−	0.994767i	$-0.532580\pi$
$67$	−7.01992	−	2.77938i	−0.857620	−	0.339556i	−0.755446	+	0.655211i	$0.772580\pi$
$68$	−3.66818			−0.444832
$69$	5.35787	+	2.12133i	0.645012	+	0.255378i
$70$	6.96496	−	8.13429i	0.832471	−	0.972233i
$71$	7.01543	+	8.48019i	0.832578	+	1.00641i	0.999790	+	0.0204929i	$0.00652354\pi$
$71$	7.01543	+	8.48019i	0.832578	+	1.00641i	−0.167212	+	0.985921i	$0.553476\pi$
$72$	0.968583	+	0.248690i	0.114149	+	0.0293084i
$73$	1.93446	−	1.06348i	0.226412	−	0.124471i	−0.364511	−	0.931199i	$-0.618764\pi$
$73$	1.93446	−	1.06348i	0.226412	−	0.124471i	0.590923	+	0.806728i	$0.298764\pi$
$74$	4.97264	+	3.61283i	0.578057	+	0.419983i
$75$	4.46070	−	2.25880i	0.515077	−	0.260824i
$76$	−2.06175	+	1.49795i	−0.236498	+	0.171826i
$77$	6.99137	−	14.8574i	0.796740	−	1.69316i
$78$	2.25239	+	2.72268i	0.255033	+	0.308282i
$79$	6.10476	−	9.61956i	0.686839	−	1.08228i	−0.304697	−	0.952449i	$-0.598555\pi$
$79$	6.10476	−	9.61956i	0.686839	−	1.08228i	0.991536	−	0.129835i	$-0.0414449\pi$
$80$	2.21336	+	0.317834i	0.247462	+	0.0355349i
$81$	−0.637424	+	0.770513i	−0.0708249	+	0.0856126i
$82$	8.08973	−	5.87753i	0.893362	−	0.649065i
$83$	−8.31496	−	13.1023i	−0.912685	−	1.43816i	−0.898849	−	0.438258i	$-0.855596\pi$
$83$	−8.31496	−	13.1023i	−0.912685	−	1.43816i	−0.0138358	−	0.999904i	$-0.504404\pi$
$84$	−0.897387	+	4.70427i	−0.0979130	+	0.513278i
$85$	2.66657	−	7.75674i	0.289230	−	0.841337i
$86$	1.11062	+	0.140304i	0.119761	+	0.0151293i
$87$	−1.65717	+	8.68721i	−0.177668	+	0.931366i
$88$	3.40162	−	0.429725i	0.362614	−	0.0458088i
$89$	4.29841	−	2.36307i	0.455631	−	0.250485i	−0.237374	−	0.971418i	$-0.576287\pi$
$89$	4.29841	−	2.36307i	0.455631	−	0.250485i	0.693005	+	0.720933i	$0.256287\pi$
$90$	−1.22999	+	1.86738i	−0.129652	+	0.196840i
$91$	−12.3361	+	11.5844i	−1.29318	+	1.21437i
$92$	−5.58150	+	1.43308i	−0.581911	+	0.149409i
$93$	−3.21273	−	2.33418i	−0.333144	−	0.242044i
$94$	−0.557732	+	8.86489i	−0.0575256	+	0.914344i
$95$	−1.66878	−	5.44870i	−0.171213	−	0.559025i
$96$	−0.929776	+	0.368125i	−0.0948949	+	0.0375716i
$97$	−15.1122	+	5.98334i	−1.53441	+	0.607516i	−0.975164	−	0.221484i	$-0.928910\pi$
$97$	−15.1122	+	5.98334i	−1.53441	+	0.607516i	−0.559247	+	0.829001i	$0.688910\pi$
$98$	−15.8098	−	1.99724i	−1.59703	−	0.201752i
$99$	−1.05951	+	3.26085i	−0.106485	+	0.327727i
$100$	−2.28109	+	4.44934i	−0.228109	+	0.444934i
$101$	−2.70065	−	8.31173i	−0.268724	−	0.827048i	−0.990812	−	0.135247i	$-0.956817\pi$
$101$	−2.70065	−	8.31173i	−0.268724	−	0.827048i	0.722088	−	0.691802i	$-0.243183\pi$
$102$	0.687348	+	3.60320i	0.0680576	+	0.356770i
$103$	−0.585514	−	9.30647i	−0.0576924	−	0.916994i	−0.915321	−	0.402725i	$-0.868063\pi$
$103$	−0.585514	−	9.30647i	−0.0576924	−	0.916994i	0.857629	−	0.514269i	$-0.171937\pi$
$104$	−3.42257	−	0.878767i	−0.335611	−	0.0861702i
$105$	−9.29531	−	5.31737i	−0.907129	−	0.518923i
$106$	−2.00492	−	3.15925i	−0.194735	−	0.306854i
$107$	4.31526	−	13.2810i	0.417172	−	1.28392i	−0.493122	−	0.869960i	$-0.664144\pi$
$107$	4.31526	−	13.2810i	0.417172	−	1.28392i	0.910294	−	0.413963i	$-0.135856\pi$
$108$	0.0627905	−	0.998027i	0.00604202	−	0.0960352i
$109$	8.25792	−	1.04322i	0.790965	−	0.0999222i	0.280538	−	0.959843i	$-0.409487\pi$
$109$	8.25792	−	1.04322i	0.790965	−	0.0999222i	0.510428	+	0.859921i	$0.329487\pi$
$110$	−1.56410	+	7.50547i	−0.149131	+	0.715618i
$111$	2.61706	−	5.56154i	0.248400	−	0.527878i
$112$	−2.03910	−	4.33330i	−0.192677	−	0.409459i
$113$	8.96924	+	4.93088i	0.843755	+	0.463858i	0.844128	−	0.536142i	$-0.180119\pi$
$113$	8.96924	+	4.93088i	0.843755	+	0.463858i	−0.000373155		1.00000i	$0.500119\pi$
$114$	1.85775	+	1.74454i	0.173994	+	0.163391i
$115$	1.02705	−	12.8444i	0.0957728	−	1.19775i
$116$	−3.76553	−	8.00216i	−0.349621	−	0.742982i
$117$	2.25239	−	2.72268i	0.208234	−	0.251711i
$118$	2.25152	+	6.92947i	0.207269	+	0.637909i
$119$	−17.0154	+	4.36880i	−1.55979	+	0.400487i
$120$	−0.102539	−	2.23372i	−0.00936046	−	0.203909i
$121$	0.0474501	+	0.754198i	0.00431365	+	0.0685634i
$122$	−2.07105	+	3.26345i	−0.187504	+	0.295459i
$123$	−7.28929	−	6.84510i	−0.657253	−	0.617202i
$124$	3.97115			0.356620
$125$	−7.75035	−	8.05804i	−0.693213	−	0.720733i
$126$	4.78910			0.426647
$127$	−5.47047	−	5.13711i	−0.485426	−	0.455845i	0.402776	−	0.915299i	$-0.368045\pi$
$127$	−5.47047	−	5.13711i	−0.485426	−	0.455845i	−0.888202	+	0.459453i	$0.848045\pi$
$128$	0.535827	−	0.844328i	0.0473608	−	0.0746288i
$129$	−0.0702905	−	1.11724i	−0.00618873	−	0.0983671i
$130$	4.34627	−	6.59857i	0.381194	−	0.578732i
$131$	1.56348	−	0.401434i	0.136602	−	0.0350735i	−0.179770	−	0.983709i	$-0.557535\pi$
$131$	1.56348	−	0.401434i	0.136602	−	0.0350735i	0.316372	+	0.948635i	$0.397535\pi$
$132$	−1.05951	−	3.26085i	−0.0922188	−	0.283820i
$133$	−7.77964	+	9.40397i	−0.674580	+	0.815427i
$134$	−3.21468	−	6.83155i	−0.277706	−	0.590156i
$135$	2.06479	+	0.858290i	0.177708	+	0.0738698i
$136$	−2.67399	−	2.51104i	−0.229292	−	0.215320i
$137$	18.8394	+	10.3571i	1.60956	+	0.884863i	0.995413	+	0.0956709i	$0.0304996\pi$
$137$	18.8394	+	10.3571i	1.60956	+	0.884863i	0.614147	+	0.789192i	$0.289500\pi$
$138$	2.45357	+	5.21410i	0.208862	+	0.443854i
$139$	−1.17259	+	2.49187i	−0.0994574	+	0.211358i	−0.948363	−	0.317186i	$-0.897262\pi$
$139$	−1.17259	+	2.49187i	−0.0994574	+	0.211358i	0.848906	+	0.528544i	$0.177262\pi$
$140$	10.6455	−	1.16180i	0.899712	−	0.0981899i
$141$	8.81238	−	1.11326i	0.742136	−	0.0937536i
$142$	−0.691066	+	10.9842i	−0.0579930	+	0.921772i
$143$	3.74388	−	11.5225i	0.313079	−	0.963559i
$144$	0.535827	+	0.844328i	0.0446522	+	0.0703607i
$145$	19.6587	−	2.14545i	1.63257	−	0.178170i
$146$	2.13817	+	0.548988i	0.176956	+	0.0454346i
$147$	1.00059	+	15.9040i	0.0825277	+	1.31174i
$148$	1.15174	+	6.03765i	0.0946727	+	0.496291i
$149$	−0.890662	−	2.74118i	−0.0729659	−	0.224566i	0.907922	−	0.419139i	$-0.137668\pi$
$149$	−0.890662	−	2.74118i	−0.0729659	−	0.224566i	−0.980888	+	0.194573i	$0.937668\pi$
$150$	4.79796	+	1.40697i	0.391752	+	0.114878i
$151$	−3.80439	+	11.7087i	−0.309597	+	0.952842i	0.668324	+	0.743870i	$0.267012\pi$
$151$	−3.80439	+	11.7087i	−0.309597	+	0.952842i	−0.977922	+	0.208972i	$0.932988\pi$
$152$	−2.52836	−	0.319406i	−0.205077	−	0.0259073i
$153$	3.41059	−	1.35035i	0.275730	−	0.109169i
$154$	15.2671	−	6.04467i	1.23026	−	0.487093i
$155$	−2.88682	+	8.39741i	−0.231875	+	0.674496i
$156$	−0.221876	+	3.52661i	−0.0177643	+	0.282355i
$157$	2.68609	+	1.95156i	0.214373	+	0.155751i	0.689790	−	0.724009i	$-0.257703\pi$
$157$	2.68609	+	1.95156i	0.214373	+	0.155751i	−0.475417	+	0.879761i	$0.657703\pi$
$158$	11.0352	−	2.83336i	0.877915	−	0.225410i
$159$	−2.72761	+	2.56139i	−0.216313	+	0.203132i
$160$	1.39590	+	1.74684i	0.110356	+	0.138100i
$161$	−24.1837	+	13.2951i	−1.90595	+	1.04780i
$162$	−0.992115	+	0.125333i	−0.0779479	+	0.00984711i
$163$	3.81586	−	20.0034i	0.298881	−	1.56679i	−0.443164	−	0.896440i	$-0.646144\pi$
$163$	3.81586	−	20.0034i	0.298881	−	1.56679i	0.742045	−	0.670350i	$-0.233856\pi$
$164$	9.92061	+	1.25326i	0.774670	+	0.0978635i
$165$	7.66561	+	0.130014i	0.596767	+	0.0101216i
$166$	2.90778	−	15.2431i	0.225688	−	1.18310i
$167$	2.37784	+	3.74688i	0.184003	+	0.289942i	0.923790	−	0.382898i	$-0.125074\pi$
$167$	2.37784	+	3.74688i	0.184003	+	0.289942i	−0.739788	+	0.672840i	$0.765074\pi$
$168$	−3.87446	+	2.81496i	−0.298921	+	0.217179i
$169$	0.327486	−	0.395863i	0.0251913	−	0.0304510i
$170$	7.25370	−	3.82903i	0.556334	−	0.293673i
$171$	1.36553	−	2.15173i	0.104425	−	0.164547i
$172$	0.713560	+	0.862546i	0.0544085	+	0.0657685i
$173$	−2.82765	+	6.00905i	−0.214982	+	0.456860i	−0.983009	−	0.183558i	$-0.941239\pi$
$173$	−2.82765	+	6.00905i	−0.214982	+	0.456860i	0.768027	+	0.640417i	$0.221239\pi$
$174$	−7.15483	+	5.19829i	−0.542406	+	0.394081i
$175$	−5.28200	+	23.3557i	−0.399282	+	1.76552i
$176$	2.77384	+	2.01531i	0.209086	+	0.151910i
$177$	6.38483	−	3.51009i	0.479913	−	0.263835i
$178$	4.75104	+	1.21986i	0.356106	+	0.0914324i
$179$	−3.46148	−	4.18421i	−0.258723	−	0.312743i	0.625117	−	0.780531i	$-0.285051\pi$
$179$	−3.46148	−	4.18421i	−0.258723	−	0.312743i	−0.883841	+	0.467788i	$0.845051\pi$
$180$	−2.17494	+	0.519279i	−0.162110	+	0.0387048i
$181$	15.0381	+	5.95399i	1.11777	+	0.442557i	0.853082	−	0.521777i	$-0.174731\pi$
$181$	15.0381	+	5.95399i	1.11777	+	0.442557i	0.264689	+	0.964334i	$0.414731\pi$
$182$	−16.9227			−1.25439
$183$	3.59372	+	1.42286i	0.265656	+	0.105181i
$184$	−5.04975	−	2.77612i	−0.372273	−	0.204659i
$185$	−13.6045	−	1.95357i	−1.00022	−	0.143630i
$186$	−0.744119	−	3.90081i	−0.0545615	−	0.286021i
$187$	9.16818	−	8.60950i	0.670444	−	0.629589i
$188$	−6.47500	+	6.08043i	−0.472238	+	0.443461i
$189$	−0.897387	−	4.70427i	−0.0652753	−	0.342185i
$190$	2.51340	−	5.11429i	0.182342	−	0.371030i
$191$	3.09514	+	1.70157i	0.223956	+	0.123121i	0.589782	−	0.807562i	$-0.299214\pi$
$191$	3.09514	+	1.70157i	0.223956	+	0.123121i	−0.365826	+	0.930683i	$0.619214\pi$
$192$	−0.929776	−	0.368125i	−0.0671008	−	0.0265671i
$193$	10.0726			0.725040			0.362520	−	0.931976i	$-0.381916\pi$
$193$	10.0726			0.725040			0.362520	+	0.931976i	$0.381916\pi$
$194$	−15.1122	−	5.98334i	−1.08499	−	0.429579i
$195$	−7.29610	−	3.03284i	−0.522484	−	0.217186i
$196$	−10.1576	−	12.2785i	−0.725545	−	0.877034i
$197$	21.1478	+	5.42984i	1.50672	+	0.386860i	0.909666	−	0.415341i	$-0.136338\pi$
$197$	21.1478	+	5.42984i	1.50672	+	0.386860i	0.597054	+	0.802201i	$0.296338\pi$
$198$	−3.00456	+	1.65177i	−0.213524	+	0.117386i
$199$	7.74084	+	5.62405i	0.548733	+	0.398678i	0.827318	−	0.561734i	$-0.189865\pi$
$199$	7.74084	+	5.62405i	0.548733	+	0.398678i	−0.278585	+	0.960412i	$0.589865\pi$
$200$	−4.70863	+	1.68191i	−0.332950	+	0.118929i
$201$	−6.10817	+	4.43785i	−0.430837	+	0.313022i
$202$	3.72109	−	7.90771i	0.261815	−	0.556385i
$203$	−26.9975	−	32.6344i	−1.89485	−	2.29048i
$204$	−1.96551	+	3.09715i	−0.137613	+	0.216844i
$205$	−9.86192	+	20.0671i	−0.688786	+	1.40155i
$206$	5.94390	−	7.18494i	0.414131	−	0.500598i
$207$	4.66199	−	3.38713i	0.324031	−	0.235422i
$208$	−1.89339	−	2.98351i	−0.131283	−	0.206869i
$209$	1.63730	−	8.58302i	0.113254	−	0.593700i
$210$	−3.13600	−	10.2393i	−0.216404	−	0.706577i
$211$	−15.1020	−	1.90783i	−1.03966	−	0.131340i	−0.413081	−	0.910694i	$-0.635547\pi$
$211$	−15.1020	−	1.90783i	−1.03966	−	0.131340i	−0.626584	+	0.779354i	$0.715547\pi$
$212$	0.701131	−	3.67546i	0.0481539	−	0.252432i
$213$	10.9191	−	1.37941i	0.748166	−	0.0945153i
$214$	12.2372	−	6.72744i	0.836515	−	0.459878i
$215$	−2.34266	+	0.881871i	−0.159768	+	0.0601431i
$216$	0.728969	−	0.684547i	0.0496000	−	0.0465775i
$217$	18.4207	−	4.72964i	1.25048	−	0.321069i
$218$	6.73390	+	4.89246i	0.456077	+	0.331359i
$219$	0.138611	−	2.20316i	0.00936649	−	0.148876i
$220$	−6.27803	+	4.40055i	−0.423265	+	0.296685i
$221$	−12.0516	+	4.77157i	−0.810678	+	0.320970i
$222$	5.71489	−	2.26268i	0.383558	−	0.151861i
$223$	−11.5859	−	1.46365i	−0.775852	−	0.0980129i	−0.272571	−	0.962136i	$-0.587874\pi$
$223$	−11.5859	−	1.46365i	−0.775852	−	0.0980129i	−0.503281	+	0.864123i	$0.667874\pi$
$224$	1.47991	−	4.55470i	0.0988808	−	0.304324i
$225$	0.482996	−	4.97662i	0.0321997	−	0.331774i
$226$	3.16287	+	9.73432i	0.210391	+	0.647517i
$227$	3.61299	+	18.9399i	0.239802	+	1.25709i	0.874766	+	0.484546i	$0.161015\pi$
$227$	3.61299	+	18.9399i	0.239802	+	1.25709i	−0.634964	+	0.772542i	$0.718985\pi$
$228$	0.160019	+	2.54343i	0.0105975	+	0.168443i
$229$	7.64096	+	1.96187i	0.504929	+	0.129644i	0.492558	−	0.870280i	$-0.336062\pi$
$229$	7.64096	+	1.96187i	0.504929	+	0.129644i	0.0123711	+	0.999923i	$0.496062\pi$
$230$	9.54130	−	8.66012i	0.629135	−	0.571032i
$231$	−8.79837	−	13.8640i	−0.578890	−	0.912185i
$232$	2.73290	−	8.41101i	0.179424	−	0.552210i
$233$	−1.28636	+	20.4462i	−0.0842725	+	1.33947i	0.697803	+	0.716290i	$0.254161\pi$
$233$	−1.28636	+	20.4462i	−0.0842725	+	1.33947i	−0.782075	+	0.623184i	$0.785839\pi$
$234$	3.50572	−	0.442876i	0.229176	−	0.0289517i
$235$	−8.15072	−	18.1122i	−0.531694	−	1.18151i
$236$	−3.10226	+	6.59263i	−0.201940	+	0.429144i
$237$	−4.85097	−	10.3088i	−0.315104	−	0.669631i
$238$	−15.3943	−	8.46309i	−0.997865	−	0.548581i
$239$	−19.8922	−	18.6800i	−1.28672	−	1.20831i	−0.965231	−	0.261397i	$-0.915817\pi$
$239$	−19.8922	−	18.6800i	−1.28672	−	1.20831i	−0.321489	−	0.946913i	$-0.604183\pi$
$240$	1.45434	−	1.69850i	0.0938770	−	0.109638i
$241$	10.5904	+	22.5057i	0.682186	+	1.44972i	0.882656	+	0.470020i	$0.155753\pi$
$241$	10.5904	+	22.5057i	0.682186	+	1.44972i	−0.200469	+	0.979700i	$0.564247\pi$
$242$	−0.481694	+	0.582268i	−0.0309645	+	0.0374296i
$243$	0.309017	+	0.951057i	0.0198234	+	0.0610103i
$244$	−3.74372	+	0.961223i	−0.239667	+	0.0615360i
$245$	33.3482	−	12.5536i	2.13054	−	0.802018i
$246$	−0.627871	−	9.97973i	−0.0400316	−	0.636284i
$247$	−4.82522	+	7.60334i	−0.307022	+	0.483789i
$248$	2.89484	+	2.71844i	0.183823	+	0.172621i
$249$	−15.5180			−0.983413
$250$	−0.133654	−	11.1795i	−0.00845303	−	0.707056i
$251$	−14.5298			−0.917115			−0.458557	−	0.888665i	$-0.651634\pi$
$251$	−14.5298			−0.917115			−0.458557	+	0.888665i	$0.651634\pi$
$252$	3.49110	+	3.27836i	0.219919	+	0.206517i
$253$	10.5867	−	16.6820i	0.665583	−	1.04879i
$254$	−0.471205	−	7.48959i	−0.0295660	−	0.469939i
$255$	−5.12041	−	6.40773i	−0.320653	−	0.401268i
$256$	0.968583	−	0.248690i	0.0605364	−	0.0155431i
$257$	−5.13048	−	15.7900i	−0.320030	−	0.984952i	−0.973634	−	0.228115i	$-0.926744\pi$
$257$	−5.13048	−	15.7900i	−0.320030	−	0.984952i	0.653604	−	0.756837i	$-0.273256\pi$
$258$	0.713560	−	0.862546i	0.0444243	−	0.0536998i
$259$	12.5334	+	26.6347i	0.778785	+	1.65500i
$260$	7.68533	−	1.83492i	0.476624	−	0.113797i
$261$	6.44689	+	6.05404i	0.399053	+	0.374735i
$262$	1.41453	+	0.777645i	0.0873900	+	0.0480430i
$263$	8.14371	+	17.3063i	0.502163	+	1.06715i	0.981841	+	0.189706i	$0.0607535\pi$
$263$	8.14371	+	17.3063i	0.502163	+	1.06715i	−0.479678	+	0.877445i	$0.659247\pi$
$264$	1.45985	−	3.10234i	0.0898476	−	0.190936i
$265$	7.26245	+	4.15448i	0.446129	+	0.255208i
$266$	−12.1086	+	1.52967i	−0.742424	+	0.0937900i
$267$	0.307997	−	4.89547i	0.0188491	−	0.299598i
$268$	2.33311	−	7.18059i	0.142518	−	0.438624i
$269$	1.67283	+	2.63595i	0.101994	+	0.160717i	0.891492	−	0.453036i	$-0.149659\pi$
$269$	1.67283	+	2.63595i	0.101994	+	0.160717i	−0.789498	+	0.613753i	$0.789659\pi$
$270$	0.917624	+	2.03911i	0.0558448	+	0.124096i
$271$	−15.7186	−	4.03585i	−0.954837	−	0.245160i	−0.261038	−	0.965329i	$-0.584065\pi$
$271$	−15.7186	−	4.03585i	−0.954837	−	0.245160i	−0.693800	+	0.720168i	$0.744065\pi$
$272$	−0.230327	−	3.66094i	−0.0139656	−	0.221977i
$273$	3.17100	+	16.6229i	0.191917	+	1.00607i
$274$	6.64345	+	20.4464i	0.401345	+	1.23521i
$275$	−4.74162	−	16.4745i	−0.285930	−	0.993450i
$276$	−1.78072	+	5.48050i	−0.107187	+	0.329887i
$277$	28.0850	+	3.54796i	1.68746	+	0.213176i	0.909667	−	0.415339i	$-0.136337\pi$
$277$	28.0850	+	3.54796i	1.68746	+	0.213176i	0.777797	+	0.628515i	$0.216337\pi$
$278$	−2.56058	+	1.01381i	−0.153573	+	0.0608040i
$279$	−3.69228	+	1.46188i	−0.221051	+	0.0875203i
$280$	8.55557	+	6.44046i	0.511293	+	0.384891i
$281$	−0.544814	+	8.65957i	−0.0325009	+	0.516586i	0.947773	+	0.318944i	$0.103328\pi$
$281$	−0.544814	+	8.65957i	−0.0325009	+	0.516586i	−0.980274	+	0.197642i	$0.936672\pi$
$282$	7.18603	+	5.22095i	0.427922	+	0.310903i
$283$	10.9189	−	2.80350i	0.649061	−	0.166651i	0.0902156	−	0.995922i	$-0.471244\pi$
$283$	10.9189	−	2.80350i	0.649061	−	0.166651i	0.558846	+	0.829272i	$0.311244\pi$
$284$	−8.02296	+	7.53406i	−0.476075	+	0.447064i
$285$	−5.49467	−	1.51056i	−0.325476	−	0.0894780i
$286$	10.6169	−	5.83667i	0.627788	−	0.345129i
$287$	47.5108	−	6.00201i	2.80447	−	0.354287i
$288$	−0.187381	+	0.982287i	−0.0110415	+	0.0578818i
$289$	3.51652	+	0.444240i	0.206854	+	0.0261317i
$290$	15.7993	+	11.8934i	0.927765	+	0.698402i
$291$	−3.04562	+	15.9657i	−0.178537	+	0.935925i
$292$	1.18285	+	1.86387i	0.0692210	+	0.109075i
$293$	2.84444	−	2.06661i	0.166174	−	0.120732i	−0.501590	−	0.865105i	$-0.667251\pi$
$293$	2.84444	−	2.06661i	0.166174	−	0.120732i	0.667764	+	0.744373i	$0.267251\pi$
$294$	−10.1576	+	12.2785i	−0.592405	+	0.716095i
$295$	−11.6856	−	11.3525i	−0.680364	−	0.660971i
$296$	−3.29347	+	5.18968i	−0.191429	+	0.301644i
$297$	2.18551	+	2.64183i	0.126816	+	0.153294i
$298$	1.22720	−	2.60793i	0.0710898	−	0.151073i
$299$	−16.4735	+	11.9687i	−0.952690	+	0.692170i
$300$	2.53443	+	4.31007i	0.146325	+	0.248842i
$301$	4.33724	+	3.15119i	0.249994	+	0.181632i
$302$	−10.7885	+	5.93100i	−0.620806	+	0.341291i
$303$	−8.46491	−	2.17342i	−0.486296	−	0.124860i
$304$	−1.62445	−	1.96362i	−0.0931685	−	0.112621i
$305$	0.688880	−	8.61524i	0.0394452	−	0.493307i
$306$	3.41059	+	1.35035i	0.194970	+	0.0771942i
$307$	−22.6647			−1.29354			−0.646772	−	0.762683i	$-0.723881\pi$
$307$	−22.6647			−1.29354			−0.646772	+	0.762683i	$0.723881\pi$
$308$	15.2671	+	6.04467i	0.869923	+	0.344427i
$309$	−8.17145	−	4.49229i	−0.464857	−	0.255558i
$310$	−7.85282	+	4.14528i	−0.446010	+	0.235436i
$311$	1.96868	+	10.3202i	0.111634	+	0.585205i	0.993512	+	0.113727i	$0.0362790\pi$
$311$	1.96868	+	10.3202i	0.111634	+	0.585205i	−0.881878	+	0.471477i	$0.843721\pi$
$312$	−2.57587	+	2.41891i	−0.145830	+	0.136944i
$313$	2.91865	−	2.74080i	0.164972	−	0.154919i	−0.597665	−	0.801746i	$-0.703905\pi$
$313$	2.91865	−	2.74080i	0.164972	−	0.154919i	0.762637	+	0.646827i	$0.223905\pi$
$314$	0.622141	+	3.26138i	0.0351094	+	0.184050i
$315$	−9.47028	+	4.99910i	−0.533590	+	0.281667i
$316$	9.98390	+	5.48869i	0.561638	+	0.308763i
$317$	−1.51488	−	0.599785i	−0.0850844	−	0.0336873i	0.325197	−	0.945646i	$-0.394569\pi$
$317$	−1.51488	−	0.599785i	−0.0850844	−	0.0336873i	−0.410281	+	0.911959i	$0.634569\pi$
$318$	−3.74173			−0.209826
$319$	28.1932	+	11.1625i	1.57852	+	0.624979i
$320$	−0.178229	+	2.22895i	−0.00996328	+	0.124602i
$321$	−8.90129	−	10.7598i	−0.496822	−	0.600554i
$322$	−26.7303	−	6.86318i	−1.48962	−	0.382470i
$323$	−8.19189	+	4.50353i	−0.455809	+	0.250583i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−1.70671	+	17.5853i	−0.0946710	+	0.975457i
$326$	16.4749	−	11.9697i	0.912462	−	0.662943i
$327$	3.54400	−	7.53138i	0.195983	−	0.416486i
$328$	6.37390	+	7.70472i	0.351939	+	0.425422i
$329$	−22.7934	+	35.9167i	−1.25664	+	1.98015i
$330$	5.49899	+	5.34225i	0.302709	+	0.294081i
$331$	2.26403	−	2.73674i	0.124442	−	0.150425i	−0.704612	−	0.709592i	$-0.748879\pi$
$331$	2.26403	−	2.73674i	0.124442	−	0.150425i	0.829055	+	0.559167i	$0.188879\pi$
$332$	12.5543	−	9.12125i	0.689008	−	0.500594i
$333$	−3.29347	−	5.18968i	−0.180481	−	0.284393i
$334$	−0.831543	+	4.35910i	−0.0455000	+	0.238519i
$335$	13.4880	+	10.1535i	0.736930	+	0.554746i
$336$	−4.75133	−	0.600233i	−0.259206	−	0.0327454i
$337$	−4.10226	+	21.5048i	−0.223464	+	1.17144i	0.676823	+	0.736145i	$0.263356\pi$
$337$	−4.10226	+	21.5048i	−0.223464	+	1.17144i	−0.900288	+	0.435295i	$0.856644\pi$
$338$	0.509714	−	0.0643919i	0.0277248	−	0.00350246i
$339$	8.96924	−	4.93088i	0.487142	−	0.267809i
$340$	7.90887	+	2.17426i	0.428919	+	0.117916i
$341$	−9.92543	+	9.32060i	−0.537492	+	0.504739i
$342$	2.46839	−	0.633776i	0.133475	−	0.0342707i
$343$	−34.6200	−	25.1529i	−1.86931	−	1.35813i
$344$	−0.0702905	+	1.11724i	−0.00378981	+	0.0602373i
$345$	−10.2946	−	7.74956i	−0.554242	−	0.417222i
$346$	−6.17474	+	2.44475i	−0.331956	+	0.131431i
$347$	24.1434	−	9.55906i	1.29609	−	0.513157i	0.384068	−	0.923305i	$-0.374523\pi$
$347$	24.1434	−	9.55906i	1.29609	−	0.513157i	0.912019	+	0.410147i	$0.134523\pi$
$348$	−8.77412	−	1.10843i	−0.470342	−	0.0594180i
$349$	7.82868	−	24.0942i	0.419060	−	1.28973i	−0.489510	−	0.871998i	$-0.662824\pi$
$349$	7.82868	−	24.0942i	0.419060	−	1.28973i	0.908569	−	0.417735i	$-0.137176\pi$
$350$	−19.8385	+	13.4098i	−1.06041	+	0.716782i
$351$	−1.09194	−	3.36064i	−0.0582834	−	0.179378i
$352$	0.642466	+	3.36793i	0.0342436	+	0.179511i
$353$	1.49188	+	23.7127i	0.0794047	+	1.26210i	0.812899	+	0.582405i	$0.197888\pi$
$353$	1.49188	+	23.7127i	0.0794047	+	1.26210i	−0.733494	+	0.679696i	$0.762112\pi$
$354$	7.05717	+	1.81197i	0.375084	+	0.0963052i
$355$	−10.0993	−	22.4422i	−0.536014	−	1.19111i
$356$	2.62831	+	4.14155i	0.139300	+	0.219502i
$357$	−5.42858	+	16.7075i	−0.287311	+	0.884252i
$358$	0.340979	−	5.41971i	0.0180213	−	0.286441i
$359$	9.95310	−	1.25737i	0.525305	−	0.0663614i	0.141791	−	0.989897i	$-0.454714\pi$
$359$	9.95310	−	1.25737i	0.525305	−	0.0663614i	0.383514	+	0.923535i	$0.374714\pi$
$360$	−1.94093	−	1.11031i	−0.102296	−	0.0585184i
$361$	5.32453	−	11.3152i	0.280238	−	0.595536i
$362$	6.88649	+	14.6345i	0.361946	+	0.769174i
$363$	0.662215	+	0.364056i	0.0347573	+	0.0191080i
$364$	−12.3361	−	11.5844i	−0.646588	−	0.607186i
$365$	−4.80122	+	1.14632i	−0.251307	+	0.0600011i
$366$	1.64570	+	3.49729i	0.0860221	+	0.182806i
$367$	−21.7808	+	26.3285i	−1.13695	+	1.37433i	−0.219918	+	0.975518i	$0.570579\pi$
$367$	−21.7808	+	26.3285i	−1.13695	+	1.37433i	−0.917031	+	0.398816i	$0.869421\pi$
$368$	−1.78072	−	5.48050i	−0.0928266	−	0.285691i
$369$	−9.68531	+	2.48676i	−0.504197	+	0.129456i
$370$	−8.57993	−	10.7370i	−0.446049	−	0.558190i
$371$	−1.12518	−	17.8842i	−0.0584163	−	0.928500i
$372$	2.12785	−	3.35295i	0.110324	−	0.173843i
$373$	−20.3133	−	19.0755i	−1.05179	−	0.987692i	−0.0518452	−	0.998655i	$-0.516510\pi$
$373$	−20.3133	−	19.0755i	−1.05179	−	0.987692i	−0.999940	+	0.0109632i	$0.996510\pi$
$374$	12.5769			0.650337
$375$	−10.9565	+	2.22612i	−0.565790	+	0.114957i
$376$	−8.88242			−0.458076
$377$	−22.7807	−	21.3925i	−1.17326	−	1.10177i
$378$	2.56613	−	4.04357i	0.131987	−	0.207979i
$379$	0.314432	+	4.99775i	0.0161513	+	0.256717i	0.997814	+	0.0660896i	$0.0210523\pi$
$379$	0.314432	+	4.99775i	0.0161513	+	0.256717i	−0.981662	+	0.190628i	$0.938948\pi$
$380$	5.33317	−	2.00761i	0.273586	−	0.102988i
$381$	−7.26863	+	1.86627i	−0.372383	+	0.0956118i
$382$	1.09146	+	3.35916i	0.0558437	+	0.171869i
$383$	11.8584	−	14.3343i	0.605935	−	0.732450i	−0.374948	−	0.927046i	$-0.622340\pi$
$383$	11.8584	−	14.3343i	0.605935	−	0.732450i	0.980883	+	0.194596i	$0.0623396\pi$
$384$	−0.425779	−	0.904827i	−0.0217280	−	0.0461743i
$385$	−23.8804	+	27.8897i	−1.21706	+	1.42139i
$386$	7.34259	+	6.89515i	0.373728	+	0.350954i
$387$	−0.980976	−	0.539296i	−0.0498658	−	0.0274140i
$388$	−6.92044	−	14.7067i	−0.351332	−	0.746619i
$389$	−0.767176	+	1.63033i	−0.0388974	+	0.0826611i	−0.923331	−	0.384004i	$-0.874545\pi$
$389$	−0.767176	+	1.63033i	−0.0388974	+	0.0826611i	0.884434	+	0.466665i	$0.154545\pi$
$390$	−3.24250	−	7.20537i	−0.164191	−	0.364858i
$391$	−20.9713	+	2.64930i	−1.06057	+	0.133981i
$392$	1.00059	−	15.9040i	0.0505377	−	0.803273i
$393$	0.498814	−	1.53519i	0.0251618	−	0.0774401i
$394$	11.6991	+	18.4349i	0.589393	+	0.928735i
$395$	−18.8642	+	17.1220i	−0.949160	+	0.861501i
$396$	−3.32094	−	0.852672i	−0.166883	−	0.0428484i
$397$	1.03832	+	16.5037i	0.0521120	+	0.828296i	0.934097	+	0.357019i	$0.116207\pi$
$397$	1.03832	+	16.5037i	0.0521120	+	0.828296i	−0.881985	+	0.471277i	$0.843793\pi$
$398$	1.79290	+	9.39872i	0.0898700	+	0.471115i
$399$	3.77149	+	11.6075i	0.188811	+	0.581100i
$400$	−4.58379	−	1.99722i	−0.229190	−	0.0998608i
$401$	−7.94518	+	24.4528i	−0.396763	+	1.22111i	0.530816	+	0.847487i	$0.321885\pi$
$401$	−7.94518	+	24.4528i	−0.396763	+	1.22111i	−0.927580	+	0.373625i	$0.878115\pi$
$402$	−7.49058	−	0.946280i	−0.373596	−	0.0471962i
$403$	13.0470	−	5.16567i	0.649917	−	0.257320i
$404$	8.12576	−	3.21721i	0.404271	−	0.160062i
$405$	1.83105	−	1.28346i	0.0909854	−	0.0637757i
$406$	2.65943	−	42.2705i	0.131986	−	2.09785i
$407$	−17.0495	−	12.3872i	−0.845111	−	0.614009i
$408$	−3.55294	+	0.912239i	−0.175897	+	0.0451626i
$409$	−6.18670	+	5.80970i	−0.305913	+	0.287271i	−0.822265	−	0.569105i	$-0.807290\pi$
$409$	−6.18670	+	5.80970i	−0.305913	+	0.287271i	0.516352	+	0.856376i	$0.327290\pi$
$410$	−20.9259	+	7.87734i	−1.03346	+	0.389034i
$411$	18.8394	−	10.3571i	0.929280	−	0.510876i
$412$	9.25134	−	1.16872i	0.455781	−	0.0575785i
$413$	−6.53843	+	34.2756i	−0.321735	+	1.68659i
$414$	5.71710	+	0.722237i	0.280980	+	0.0354960i
$415$	10.1615	+	33.1781i	0.498808	+	1.62865i
$416$	0.662128	−	3.47100i	0.0324635	−	0.170180i
$417$	1.47565	+	2.32526i	0.0722631	+	0.113868i
$418$	7.06902	−	5.13594i	0.345757	−	0.251207i
$419$	14.3799	−	17.3824i	0.702506	−	0.849183i	−0.291719	−	0.956504i	$-0.594227\pi$
$419$	14.3799	−	17.3824i	0.702506	−	0.849183i	0.994224	+	0.107321i	$0.0342271\pi$
$420$	4.72322	−	9.61085i	0.230470	−	0.468961i
$421$	−6.06751	+	9.56086i	−0.295712	+	0.465968i	−0.959403	−	0.282039i	$-0.908989\pi$
$421$	−6.06751	+	9.56086i	−0.295712	+	0.465968i	0.663691	+	0.748007i	$0.268989\pi$
$422$	−9.70288	−	11.7288i	−0.472329	−	0.570948i
$423$	3.78195	−	8.03705i	0.183885	−	0.390775i
$424$	3.02713	−	2.19934i	0.147010	−	0.106809i
$425$	−10.3470	+	15.1436i	−0.501905	+	0.734570i
$426$	8.90396	+	6.46911i	0.431398	+	0.313429i
$427$	−16.2209	+	8.91754i	−0.784986	+	0.431550i
$428$	13.5258	+	3.47282i	0.653792	+	0.167865i
$429$	−7.72268	−	9.33512i	−0.372855	−	0.450704i
$430$	−2.31141	−	0.960808i	−0.111466	−	0.0463343i
$431$	11.8742	+	4.70133i	0.571960	+	0.226455i	0.636259	−	0.771476i	$-0.280481\pi$
$431$	11.8742	+	4.70133i	0.571960	+	0.226455i	−0.0642986	+	0.997931i	$0.520481\pi$
$432$	1.00000			0.0481125
$433$	−17.8282	−	7.05869i	−0.856769	−	0.339219i	−0.101661	−	0.994819i	$-0.532416\pi$
$433$	−17.8282	−	7.05869i	−0.856769	−	0.339219i	−0.755108	+	0.655600i	$0.772416\pi$
$434$	16.6658	+	9.16210i	0.799984	+	0.439795i
$435$	8.72221	−	17.7480i	0.418198	−	0.850952i
$436$	1.55968	+	8.17612i	0.0746951	+	0.391565i
$437$	−10.7053	+	10.0530i	−0.512105	+	0.480899i
$438$	1.60921	−	1.51115i	0.0768912	−	0.0722056i
$439$	−5.26308	−	27.5901i	−0.251193	−	1.31680i	−0.854566	−	0.519342i	$-0.826177\pi$
$439$	−5.26308	−	27.5901i	−0.251193	−	1.31680i	0.603373	−	0.797459i	$-0.293823\pi$
$440$	−7.58887	−	1.08974i	−0.361785	−	0.0519515i
$441$	13.9643	+	7.67696i	0.664968	+	0.365570i
$442$	−12.0516	−	4.77157i	−0.573236	−	0.226960i
$443$	15.7889			0.750155			0.375077	−	0.926994i	$-0.377616\pi$
$443$	15.7889			0.750155			0.375077	+	0.926994i	$0.377616\pi$
$444$	5.71489	+	2.26268i	0.271217	+	0.107382i
$445$	−10.6684	+	2.54714i	−0.505730	+	0.120746i
$446$	−7.44386	−	8.99808i	−0.352477	−	0.426071i
$447$	−2.79169	−	0.716785i	−0.132043	−	0.0339028i
$448$	4.19672	−	2.30716i	0.198276	−	0.109003i
$449$	16.9199	+	12.2930i	0.798499	+	0.580144i	0.910473	−	0.413567i	$-0.135717\pi$
$449$	16.9199	+	12.2930i	0.798499	+	0.580144i	−0.111974	+	0.993711i	$0.535717\pi$
$450$	3.75882	−	3.29716i	0.177192	−	0.155430i
$451$	−27.7369	+	20.1521i	−1.30608	+	0.948923i
$452$	−4.35797	+	9.26115i	−0.204981	+	0.435608i
$453$	7.84750	+	9.48600i	0.368708	+	0.445691i
$454$	−10.3315	+	16.2799i	−0.484883	+	0.764053i
$455$	33.4641	−	17.6647i	1.56882	−	0.828136i
$456$	−1.62445	+	1.96362i	−0.0760717	+	0.0919549i
$457$	−19.9117	+	14.4667i	−0.931431	+	0.676724i	−0.946343	−	0.323165i	$-0.895253\pi$
$457$	−19.9117	+	14.4667i	−0.931431	+	0.676724i	0.0149121	+	0.999889i	$0.495253\pi$
$458$	4.22703	+	6.66073i	0.197516	+	0.311236i
$459$	0.687348	−	3.60320i	0.0320827	−	0.168183i
$460$	12.8836	+	0.218514i	0.600700	+	0.0101883i
$461$	−17.3467	−	2.19140i	−0.807916	−	0.102064i	−0.289484	−	0.957183i	$-0.593484\pi$
$461$	−17.3467	−	2.19140i	−0.807916	−	0.102064i	−0.518431	+	0.855119i	$0.673484\pi$
$462$	3.07683	−	16.1293i	0.143147	−	0.750404i
$463$	26.9677	−	3.40681i	1.25329	−	0.158328i	0.529480	−	0.848322i	$-0.322387\pi$
$463$	26.9677	−	3.40681i	1.25329	−	0.158328i	0.723815	+	0.689994i	$0.242387\pi$
$464$	7.74993	−	4.26056i	0.359781	−	0.197792i
$465$	5.54333	+	6.93698i	0.257066	+	0.321695i
$466$	−14.9341	+	14.0240i	−0.691808	+	0.649651i
$467$	−10.7686	+	2.76491i	−0.498312	+	0.127945i	−0.489477	−	0.872016i	$-0.662812\pi$
$467$	−10.7686	+	2.76491i	−0.498312	+	0.127945i	−0.00883518	+	0.999961i	$0.502812\pi$
$468$	2.85873	+	2.07699i	0.132145	+	0.0960089i
$469$	2.27039	−	36.0869i	0.104837	−	1.66634i
$470$	6.45705	−	18.7828i	0.297842	−	0.866385i
$471$	3.08703	−	1.22224i	0.142243	−	0.0563179i
$472$	−6.77442	+	2.68218i	−0.311818	+	0.123457i
$473$	−3.80792	−	0.481053i	−0.175089	−	0.0221188i
$474$	3.52068	−	10.8355i	0.161710	−	0.497693i
$475$	0.368376	+	12.7370i	0.0169022	+	0.584412i
$476$	−5.42858	−	16.7075i	−0.248819	−	0.765785i
$477$	0.701131	+	3.67546i	0.0321026	+	0.168288i
$478$	−1.71344	−	27.2343i	−0.0783708	−	1.24567i
$479$	−24.6431	−	6.32727i	−1.12597	−	0.289100i	−0.360620	−	0.932713i	$-0.617435\pi$
$479$	−24.6431	−	6.32727i	−1.12597	−	0.289100i	−0.765351	+	0.643613i	$0.777435\pi$
$480$	2.22287	−	0.242593i	0.101460	−	0.0110728i
$481$	11.6378	+	18.3382i	0.530636	+	0.836149i
$482$	−7.68616	+	23.6556i	−0.350095	+	1.07748i
$483$	−1.73285	+	27.5429i	−0.0788475	+	1.25324i
$484$	−0.749730	+	0.0947129i	−0.0340786	+	0.00430513i
$485$	36.1296	−	3.94300i	1.64056	−	0.179042i
$486$	−0.425779	+	0.904827i	−0.0193137	+	0.0410438i
$487$	−16.8119	−	35.7270i	−0.761818	−	1.61895i	−0.785218	−	0.619220i	$-0.787449\pi$
$487$	−16.8119	−	35.7270i	−0.761818	−	1.61895i	0.0233997	−	0.999726i	$-0.492551\pi$
$488$	−3.38706	−	1.86205i	−0.153325	−	0.0842910i
$489$	−14.8448	−	13.9402i	−0.671306	−	0.630398i
$490$	32.9033	+	13.6772i	1.48642	+	0.617875i
$491$	11.4137	+	24.2554i	0.515095	+	1.09463i	0.978073	+	0.208263i	$0.0667810\pi$
$491$	11.4137	+	24.2554i	0.515095	+	1.09463i	−0.462978	+	0.886370i	$0.653219\pi$
$492$	6.37390	−	7.70472i	0.287357	−	0.347355i
$493$	−10.0248	−	30.8531i	−0.451493	−	1.38955i
$494$	−8.72228	+	2.23950i	−0.392434	+	0.100760i
$495$	4.21721	−	6.40262i	0.189550	−	0.287776i
$496$	0.249351	+	3.96331i	0.0111962	+	0.177958i
$497$	−28.2425	+	44.5031i	−1.26685	+	1.99624i
$498$	−11.3121	−	10.6228i	−0.506909	−	0.476019i
$499$	26.2885			1.17684			0.588418	−	0.808557i	$-0.299751\pi$
$499$	26.2885			1.17684			0.588418	+	0.808557i	$0.299751\pi$
$500$	7.55549	−	8.24103i	0.337892	−	0.368550i
$501$	4.43770			0.198262
$502$	−10.5918	−	9.94635i	−0.472735	−	0.443927i
$503$	8.66232	−	13.6496i	0.386234	−	0.608607i	−0.594467	−	0.804120i	$-0.702637\pi$
$503$	8.66232	−	13.6496i	0.386234	−	0.608607i	0.980701	+	0.195513i	$0.0626371\pi$
$504$	0.300710	+	4.77965i	0.0133947	+	0.212902i
$505$	0.896134	+	19.5215i	0.0398775	+	0.868695i
$506$	19.1370	−	4.91356i	0.850745	−	0.218434i
$507$	−0.158762	−	0.488620i	−0.00705088	−	0.0217004i
$508$	4.78348	−	5.78224i	0.212233	−	0.256545i
$509$	−2.25573	−	4.79367i	−0.0999834	−	0.212476i	0.848577	−	0.529072i	$-0.177460\pi$
$509$	−2.25573	−	4.79367i	−0.0999834	−	0.212476i	−0.948560	+	0.316596i	$0.897460\pi$
$510$	0.653774	−	8.17620i	0.0289496	−	0.362048i
$511$	7.70668	+	7.23705i	0.340923	+	0.320148i
$512$	0.876307	+	0.481754i	0.0387276	+	0.0212907i
$513$	−1.08508	−	2.30591i	−0.0479075	−	0.101809i
$514$	7.06903	−	15.0225i	0.311802	−	0.662612i
$515$	−4.25387	+	20.4125i	−0.187448	+	0.899483i
$516$	1.11062	−	0.140304i	0.0488922	−	0.00617652i
$517$	1.91227	−	30.3947i	0.0841016	−	1.33676i
$518$	−9.09631	+	27.9956i	−0.399669	+	1.23005i
$519$	3.55848	+	5.60727i	0.156200	+	0.246132i
$520$	6.85845	+	3.92337i	0.300763	+	0.172051i
$521$	8.73106	+	2.24176i	0.382515	+	0.0982131i	0.435051	−	0.900406i	$-0.356730\pi$
$521$	8.73106	+	2.24176i	0.382515	+	0.0982131i	−0.0525360	+	0.998619i	$0.516730\pi$
$522$	0.555310	+	8.82641i	0.0243053	+	0.386321i
$523$	−3.64336	−	19.0992i	−0.159313	−	0.835149i	−0.968768	−	0.247967i	$-0.920237\pi$
$523$	−3.64336	−	19.0992i	−0.159313	−	0.835149i	0.809455	−	0.587181i	$-0.199763\pi$
$524$	0.498814	+	1.53519i	0.0217908	+	0.0670651i
$525$	16.8896	+	16.9743i	0.737122	+	0.740820i
$526$	−5.91045	+	18.1905i	−0.257708	+	0.793143i
$527$	14.4520	+	1.82572i	0.629540	+	0.0795294i
$528$	3.18788	−	1.26217i	0.138735	−	0.0549290i
$529$	−9.49008	+	3.75739i	−0.412612	+	0.163365i
$530$	2.45016	+	7.99997i	0.106428	+	0.347497i
$531$	0.457496	−	7.27169i	0.0198536	−	0.315565i
$532$	−9.87390	−	7.17381i	−0.428088	−	0.311024i
$533$	34.2239	−	8.78720i	1.48240	−	0.380616i
$534$	3.57570	−	3.35781i	0.154736	−	0.145306i
$535$	−17.1762	+	26.0770i	−0.742590	+	1.12741i
$536$	6.61622	−	3.63730i	0.285777	−	0.157107i
$537$	−5.38760	+	0.680613i	−0.232492	+	0.0293706i
$538$	−0.584996	+	3.06666i	−0.0252210	+	0.132213i
$539$	54.2063	+	6.84785i	2.33483	+	0.294958i
$540$	−0.726948	+	2.11460i	−0.0312828	+	0.0909980i
$541$	−3.75020	+	19.6592i	−0.161234	+	0.845217i	0.806113	+	0.591761i	$0.201567\pi$
$541$	−3.75020	+	19.6592i	−0.161234	+	0.845217i	−0.967347	+	0.253455i	$0.918433\pi$
$542$	−8.69564	−	13.7021i	−0.373510	−	0.588557i
$543$	13.0849	−	9.50675i	0.561528	−	0.407974i
$544$	2.33818	−	2.82638i	0.100249	−	0.121180i
$545$	−18.4231	−	2.64551i	−0.789157	−	0.113321i
$546$	−9.06763	+	14.2883i	−0.388059	+	0.611483i
$547$	7.90130	+	9.55103i	0.337835	+	0.408373i	0.911884	−	0.410449i	$-0.134628\pi$
$547$	7.90130	+	9.55103i	0.337835	+	0.408373i	−0.574048	+	0.818821i	$0.694628\pi$
$548$	−9.15368	+	19.4526i	−0.391026	+	0.830972i
$549$	3.12697	−	2.27188i	0.133456	−	0.0969614i
$550$	7.82108	−	15.2553i	0.333492	−	0.650486i
$551$	−18.2338	−	13.2476i	−0.776785	−	0.564367i
$552$	−5.04975	+	2.77612i	−0.214932	+	0.118160i
$553$	52.8487	+	13.5692i	2.24736	+	0.577023i
$554$	18.0443	+	21.8119i	0.766630	+	0.926697i
$555$	−8.93910	+	10.4399i	−0.379444	+	0.443148i
$556$	−2.56058	−	1.01381i	−0.108593	−	0.0429949i
$557$	8.48692			0.359603			0.179801	−	0.983703i	$-0.442455\pi$
$557$	8.48692			0.359603			0.179801	+	0.983703i	$0.442455\pi$
$558$	−3.69228	−	1.46188i	−0.156307	−	0.0618862i
$559$	3.46636	+	1.90565i	0.146612	+	0.0806004i
$560$	1.82795	+	10.5516i	0.0772448	+	0.445886i
$561$	−2.35668	−	12.3542i	−0.0994991	−	0.521593i
$562$	−6.32503	+	5.93960i	−0.266805	+	0.250547i
$563$	−18.5003	+	17.3729i	−0.779694	+	0.732182i	−0.968278	−	0.249876i	$-0.919610\pi$
$563$	−18.5003	+	17.3729i	−0.779694	+	0.732182i	0.188584	+	0.982057i	$0.439610\pi$
$564$	1.66440	+	8.72509i	0.0700838	+	0.367392i
$565$	−16.4156	−	15.9477i	−0.690611	−	0.670926i
$566$	9.87866	+	5.43084i	0.415231	+	0.228275i
$567$	−4.45279	−	1.76298i	−0.187000	−	0.0740384i
$568$	−11.0059			−0.461797
$569$	−12.6677	−	5.01549i	−0.531057	−	0.210260i	0.0872652	−	0.996185i	$-0.472187\pi$
$569$	−12.6677	−	5.01549i	−0.531057	−	0.210260i	−0.618322	+	0.785925i	$0.712187\pi$
$570$	−2.97139	−	4.86251i	−0.124458	−	0.203668i
$571$	6.10529	+	7.38002i	0.255498	+	0.308844i	0.882630	−	0.470069i	$-0.155771\pi$
$571$	6.10529	+	7.38002i	0.255498	+	0.308844i	−0.627131	+	0.778914i	$0.715771\pi$
$572$	11.7348	+	3.01299i	0.490658	+	0.125980i
$573$	3.09514	−	1.70157i	0.129301	−	0.0710839i
$574$	38.7425	+	28.1481i	1.61708	+	1.17488i
$575$	−9.82775	+	27.0848i	−0.409846	+	1.12951i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	17.6943	−	37.6024i	0.736624	−	1.56541i	−0.0856564	−	0.996325i	$-0.527299\pi$
$577$	17.6943	−	37.6024i	0.736624	−	1.56541i	0.822281	−	0.569082i	$-0.192701\pi$
$578$	2.25933	+	2.73106i	0.0939757	+	0.113597i
$579$	5.39716	−	8.50456i	0.224298	−	0.353437i
$580$	3.37560	+	19.4852i	0.140164	+	0.809080i
$581$	47.3716	−	57.2624i	1.96530	−	2.37564i
$582$	−13.1494	+	9.55362i	−0.545061	+	0.396010i
$583$	6.87419	+	10.8320i	0.284700	+	0.448615i
$584$	−0.413648	+	2.16842i	−0.0171169	+	0.0897298i
$585$	−6.47016	+	4.53522i	−0.267508	+	0.187508i
$586$	3.48820	+	0.440662i	0.144096	+	0.0182036i
$587$	2.85857	−	14.9852i	0.117986	−	0.618504i	−0.873344	−	0.487105i	$-0.838053\pi$
$587$	2.85857	−	14.9852i	0.117986	−	0.618504i	0.991330	−	0.131399i	$-0.0419470\pi$
$588$	−15.8098	+	1.99724i	−0.651985	+	0.0823648i
$589$	8.86849	−	4.87550i	0.365420	−	0.200891i
$590$	−0.747104	−	16.2750i	−0.0307578	−	0.670032i
$591$	15.9161	−	14.9462i	0.654702	−	0.614807i
$592$	−5.95341	+	1.52858i	−0.244684	+	0.0628241i
$593$	−22.0165	−	15.9959i	−0.904108	−	0.656873i	0.0354099	−	0.999373i	$-0.488726\pi$
$593$	−22.0165	−	15.9959i	−0.904108	−	0.656873i	−0.939518	+	0.342500i	$0.888726\pi$
$594$	−0.215287	+	3.42189i	−0.00883334	+	0.140402i
$595$	39.2759	+	0.666147i	1.61016	+	0.0273094i
$596$	2.67984	−	1.06102i	0.109771	−	0.0434613i
$597$	8.89629	−	3.52229i	0.364101	−	0.144158i
$598$	−20.2019	−	2.55209i	−0.826116	−	0.104363i
$599$	6.83370	−	21.0320i	0.279218	−	0.859343i	−0.708855	−	0.705354i	$-0.750788\pi$
$599$	6.83370	−	21.0320i	0.279218	−	0.859343i	0.988073	−	0.153989i	$-0.0492121\pi$
$600$	−1.10292	+	4.87684i	−0.0450266	+	0.199096i
$601$	−13.8939	−	42.7612i	−0.566746	−	1.74426i	−0.662707	−	0.748879i	$-0.730592\pi$
$601$	−13.8939	−	42.7612i	−0.566746	−	1.74426i	0.0959607	−	0.995385i	$-0.469408\pi$
$602$	1.00457	+	5.26617i	0.0409434	+	0.214633i
$603$	0.474076	+	7.53522i	0.0193059	+	0.306858i
$604$	−11.9245	−	3.06169i	−0.485201	−	0.124578i
$605$	0.344734	−	1.65423i	0.0140154	−	0.0672541i
$606$	−4.68284	−	7.37898i	−0.190228	−	0.299751i
$607$	−4.29426	+	13.2164i	−0.174299	+	0.536436i	−0.999601	−	0.0282556i	$-0.991005\pi$
$607$	−4.29426	+	13.2164i	−0.174299	+	0.536436i	0.825302	+	0.564691i	$0.191005\pi$
$608$	0.160019	−	2.54343i	0.00648963	−	0.103150i
$609$	−42.0201	+	5.30837i	−1.70274	+	0.215106i
$610$	6.39971	−	5.80867i	0.259117	−	0.235186i
$611$	−13.3638	+	28.3996i	−0.540643	+	1.14893i
$612$	1.56183	+	3.31907i	0.0631334	+	0.134165i
$613$	24.9171	+	13.6983i	1.00639	+	0.553269i	0.897607	−	0.440796i	$-0.145304\pi$
$613$	24.9171	+	13.6983i	1.00639	+	0.553269i	0.108786	+	0.994065i	$0.465304\pi$
$614$	−16.5219	−	15.5151i	−0.666768	−	0.626137i
$615$	11.6589	+	19.0792i	0.470133	+	0.769347i
$616$	6.99137	+	14.8574i	0.281690	+	0.598622i
$617$	0.0531303	−	0.0642235i	0.00213895	−	0.00258554i	−0.769443	−	0.638716i	$-0.779466\pi$
$617$	0.0531303	−	0.0642235i	0.00213895	−	0.00258554i	0.771582	+	0.636130i	$0.219466\pi$
$618$	−2.88154	−	8.86848i	−0.115913	−	0.356743i
$619$	−25.7514	+	6.61184i	−1.03504	+	0.265752i	−0.727734	−	0.685859i	$-0.759426\pi$
$619$	−25.7514	+	6.61184i	−1.03504	+	0.265752i	−0.307303	+	0.951612i	$0.599426\pi$
$620$	−8.56210	−	2.35384i	−0.343862	−	0.0945326i
$621$	−0.361833	−	5.75117i	−0.0145198	−	0.230786i
$622$	−5.62955	+	8.87075i	−0.225724	+	0.355685i
$623$	17.1244	+	16.0809i	0.686073	+	0.644266i
$624$	−3.53359			−0.141457
$625$	11.9341	+	21.9677i	0.477362	+	0.878707i
$626$	4.00381			0.160024
$627$	−6.36957	−	5.98143i	−0.254376	−	0.238875i
$628$	−1.77904	+	2.80333i	−0.0709916	+	0.111865i
$629$	1.41571	+	22.5020i	0.0564480	+	0.897215i
$630$	−10.3257	−	2.83867i	−0.411384	−	0.113095i
$631$	36.3497	−	9.33301i	1.44706	−	0.371541i	0.558193	−	0.829711i	$-0.311495\pi$
$631$	36.3497	−	9.33301i	1.44706	−	0.371541i	0.888865	+	0.458169i	$0.151495\pi$
$632$	3.52068	+	10.8355i	0.140045	+	0.431014i
$633$	−9.70288	+	11.7288i	−0.385655	+	0.466177i
$634$	−0.693722	−	1.47423i	−0.0275512	−	0.0585493i
$635$	8.74980	+	14.3186i	0.347225	+	0.568214i
$636$	−2.72761	−	2.56139i	−0.108157	−	0.101566i
$637$	−49.3442	−	27.1272i	−1.95509	−	1.07482i
$638$	12.9107	+	27.4367i	0.511140	+	1.08623i
$639$	4.68609	−	9.95844i	0.185379	−	0.393950i
$640$	−1.65575	+	1.50283i	−0.0654491	+	0.0594046i
$641$	35.9577	−	4.54251i	1.42024	−	0.179418i	0.622596	−	0.782543i	$-0.286078\pi$
$641$	35.9577	−	4.54251i	1.42024	−	0.179418i	0.797647	+	0.603125i	$0.206078\pi$
$642$	0.876837	−	13.9369i	0.0346060	−	0.550046i
$643$	−5.01906	+	15.4471i	−0.197933	+	0.609174i	0.801997	+	0.597328i	$0.203771\pi$
$643$	−5.01906	+	15.4471i	−0.197933	+	0.609174i	−0.999930	+	0.0118461i	$0.996229\pi$
$644$	−14.7874	−	23.3012i	−0.582705	−	0.918196i
$645$	−0.510674	+	2.45051i	−0.0201078	+	0.0964886i
$646$	−9.05451	−	2.32480i	−0.356245	−	0.0914681i
$647$	−1.07276	−	17.0511i	−0.0421747	−	0.670348i	−0.961149	−	0.276030i	$-0.910981\pi$
$647$	−1.07276	−	17.0511i	−0.0421747	−	0.670348i	0.918974	−	0.394318i	$-0.129019\pi$
$648$	−0.187381	−	0.982287i	−0.00736103	−	0.0385879i
$649$	−7.71969	−	23.7588i	−0.303024	−	0.932613i
$650$	−13.2821	+	11.6508i	−0.520967	+	0.456983i
$651$	5.87695	−	18.0874i	0.230336	−	0.708901i
$652$	20.2036	+	2.55230i	0.791233	+	0.0999559i
$653$	−0.169597	+	0.0671483i	−0.00663686	+	0.00262772i	−0.371441	−	0.928457i	$-0.621136\pi$
$653$	−0.169597	+	0.0671483i	−0.00663686	+	0.00262772i	0.364804	+	0.931084i	$0.381136\pi$
$654$	7.73905	−	3.06410i	0.302621	−	0.119816i
$655$	−3.60893	−	0.0612099i	−0.141013	−	0.00239167i
$656$	−0.627871	+	9.97973i	−0.0245143	+	0.389643i
$657$	−1.78592	−	1.29755i	−0.0696754	−	0.0506222i
$658$	−41.2023	+	10.5790i	−1.60623	+	0.412411i
$659$	−25.4482	+	23.8975i	−0.991321	+	0.930913i	−0.997612	−	0.0690676i	$-0.977998\pi$
$659$	−25.4482	+	23.8975i	−0.991321	+	0.930913i	0.00629075	+	0.999980i	$0.497998\pi$
$660$	0.351570	+	7.65865i	0.0136848	+	0.298112i
$661$	−34.5577	+	18.9982i	−1.34414	+	0.738946i	−0.981223	−	0.192877i	$-0.938218\pi$
$661$	−34.5577	+	18.9982i	−1.34414	+	0.738946i	−0.362915	+	0.931822i	$0.618218\pi$
$662$	3.52383	−	0.445164i	0.136958	−	0.0173018i
$663$	−2.42880	+	12.7322i	−0.0943269	+	0.494479i
$664$	15.3956	+	1.94492i	0.597466	+	0.0754776i
$665$	22.3476	−	15.6644i	0.866601	−	0.607439i
$666$	1.15174	−	6.03765i	0.0446291	−	0.233954i
$667$	−27.3074	−	43.0295i	−1.05735	−	1.66611i
$668$	−3.59018	+	2.60842i	−0.138908	+	0.100923i
$669$	−7.44386	+	8.99808i	−0.287796	+	0.347886i
$670$	2.88180	+	16.6348i	0.111333	+	0.642658i
$671$	7.10092	−	11.1893i	0.274128	−	0.431957i
$672$	−3.05269	−	3.69006i	−0.117760	−	0.142347i
$673$	17.1498	−	36.4452i	0.661077	−	1.40486i	−0.239815	−	0.970819i	$-0.577087\pi$
$673$	17.1498	−	36.4452i	0.661077	−	1.40486i	0.900893	−	0.434042i	$-0.142913\pi$
$674$	−17.7115	+	12.8681i	−0.682220	+	0.495662i
$675$	−3.94309	−	3.07441i	−0.151770	−	0.118334i
$676$	0.415645	+	0.301984i	0.0159863	+	0.0116148i
$677$	4.13954	−	2.27573i	0.159095	−	0.0874635i	−0.400217	−	0.916420i	$-0.631065\pi$
$677$	4.13954	−	2.27573i	0.159095	−	0.0874635i	0.559312	+	0.828957i	$0.311065\pi$
$678$	9.91371	+	2.54541i	0.380734	+	0.0977558i
$679$	−49.6171	−	59.9767i	−1.90413	−	2.30170i
$680$	4.27694	+	6.99896i	0.164013	+	0.268398i
$681$	17.9275	+	7.09798i	0.686981	+	0.271995i
$682$	−13.6157			−0.521373
$683$	−24.3011	−	9.62149i	−0.929856	−	0.368156i	−0.146132	−	0.989265i	$-0.546682\pi$
$683$	−24.3011	−	9.62149i	−0.929856	−	0.368156i	−0.783724	+	0.621109i	$0.786682\pi$
$684$	2.23323	+	1.22773i	0.0853897	+	0.0469434i
$685$	−34.4802	−	33.4974i	−1.31742	−	1.27987i
$686$	−8.01855	−	42.0347i	−0.306150	−	1.60489i
$687$	5.75069	−	5.40026i	0.219402	−	0.206033i
$688$	−0.816040	+	0.766312i	−0.0311112	+	0.0292154i
$689$	−2.47751	−	12.9875i	−0.0943855	−	0.494786i
$690$	−2.19950	−	12.6963i	−0.0837334	−	0.483340i
$691$	−23.5126	−	12.9262i	−0.894461	−	0.491734i	−0.0329408	−	0.999457i	$-0.510487\pi$
$691$	−23.5126	−	12.9262i	−0.894461	−	0.491734i	−0.861520	+	0.507723i	$0.830487\pi$
$692$	−6.17474	−	2.44475i	−0.234729	−	0.0929356i
$693$	−16.4202			−0.623751
$694$	24.1434	+	9.55906i	0.916472	+	0.362857i
$695$	4.00521	−	4.67763i	0.151926	−	0.177433i
$696$	−5.63729	−	6.81431i	−0.213681	−	0.258296i
$697$	35.5274	+	9.12190i	1.34570	+	0.345516i
$698$	22.2005	−	12.2048i	0.840300	−	0.461959i
$699$	16.5740	+	12.0417i	0.626887	+	0.455460i
$700$	−23.6412	−	3.80507i	−0.893554	−	0.143818i
$701$	42.3314	−	30.7556i	1.59884	−	1.16162i	0.709143	−	0.705065i	$-0.249082\pi$
$701$	42.3314	−	30.7556i	1.59884	−	1.16162i	0.889694	−	0.456558i	$-0.150918\pi$
$702$	1.50453	−	3.19728i	0.0567848	−	0.120674i
$703$	9.98470	+	12.0694i	0.376580	+	0.455207i
$704$	−1.83717	+	2.89491i	−0.0692408	+	0.109106i
$705$	−19.6600	−	2.82314i	−0.740439	−	0.106325i
$706$	−15.1449	+	18.3071i	−0.569987	+	0.688996i
$707$	33.8607	−	24.6013i	1.27346	−	0.925226i
$708$	3.90407	+	6.15183i	0.146724	+	0.231200i
$709$	1.16741	−	6.11977i	0.0438429	−	0.229833i	−0.953621	−	0.301011i	$-0.902676\pi$
$709$	1.16741	−	6.11977i	0.0438429	−	0.229833i	0.997464	+	0.0711783i	$0.0226759\pi$
$710$	8.00071	−	23.2731i	0.300261	−	0.873425i
$711$	−11.3033	−	1.42794i	−0.423907	−	0.0535520i
$712$	−0.919133	+	4.81827i	−0.0344460	+	0.180572i
$713$	22.7035	−	2.86811i	0.850251	−	0.107412i
$714$	−15.3943	+	8.46309i	−0.576117	+	0.316723i
$715$	−14.9019	+	22.6242i	−0.557299	+	0.846098i
$716$	3.95861	−	3.71738i	0.147940	−	0.138925i
$717$	−26.4309	+	6.78629i	−0.987078	+	0.253439i
$718$	8.11623	+	5.89678i	0.302895	+	0.220066i
$719$	3.28344	−	52.1888i	0.122452	−	1.94631i	−0.160187	−	0.987087i	$-0.551210\pi$
$719$	3.28344	−	52.1888i	0.122452	−	1.94631i	0.282638	−	0.959227i	$-0.408790\pi$
$720$	−0.654820	−	2.13804i	−0.0244037	−	0.0796800i
$721$	41.5217	−	16.4396i	1.54635	−	0.612243i
$722$	11.6272	−	4.60353i	0.432719	−	0.171326i
$723$	24.6768	+	3.11741i	0.917740	+	0.115938i
$724$	−4.99799	+	15.3822i	−0.185749	+	0.571677i
$725$	−43.6574	−	7.02668i	−1.62140	−	0.260964i
$726$	0.233521	+	0.718703i	0.00866677	+	0.0266736i
$727$	−8.17688	−	42.8647i	−0.303264	−	1.58976i	−0.728737	−	0.684793i	$-0.759892\pi$
$727$	−8.17688	−	42.8647i	−0.303264	−	1.58976i	0.425474	−	0.904971i	$-0.360108\pi$
$728$	−1.06258	−	16.8893i	−0.0393820	−	0.625959i
$729$	0.968583	+	0.248690i	0.0358735	+	0.00921074i
$730$	−4.28465	−	2.45103i	−0.158582	−	0.0907166i
$731$	2.20028	+	3.46708i	0.0813802	+	0.128235i
$732$	−1.19440	+	3.67597i	−0.0441462	+	0.135868i
$733$	−1.93363	+	30.7341i	−0.0714201	+	1.13519i	0.785200	+	0.619243i	$0.212560\pi$
$733$	−1.93363	+	30.7341i	−0.0714201	+	1.13519i	−0.856620	+	0.515948i	$0.827440\pi$
$734$	−33.9006	+	4.28264i	−1.25129	+	0.158075i
$735$	7.26952	−	34.8833i	0.268140	−	1.28669i
$736$	2.45357	−	5.21410i	0.0904398	−	0.192194i
$737$	11.0220	+	23.4230i	0.406002	+	0.862799i
$738$	−8.76259	−	4.81728i	−0.322556	−	0.177326i
$739$	−11.1592	−	10.4792i	−0.410498	−	0.385483i	0.451604	−	0.892219i	$-0.350852\pi$
$739$	−11.1592	−	10.4792i	−0.410498	−	0.385483i	−0.862102	+	0.506736i	$0.830852\pi$
$740$	1.09549	−	13.7003i	0.0402709	−	0.503633i
$741$	3.83423	+	8.14814i	0.140854	+	0.299330i
$742$	11.4223	−	13.8072i	0.419327	−	0.506879i
$743$	−9.59397	−	29.5272i	−0.351969	−	1.08325i	−0.957746	−	0.287614i	$-0.907138\pi$
$743$	−9.59397	−	29.5272i	−0.351969	−	1.08325i	0.605778	−	0.795634i	$-0.292862\pi$
$744$	3.84639	−	0.987585i	0.141015	−	0.0362066i
$745$	0.295542	+	6.43811i	0.0108278	+	0.235874i
$746$	−1.74971	−	27.8109i	−0.0640615	−	1.01823i
$747$	−8.31496	+	13.1023i	−0.304228	+	0.479387i
$748$	9.16818	+	8.60950i	0.335222	+	0.314794i
$749$	66.8772			2.44364
$750$	−9.51081	−	5.87745i	−0.347286	−	0.214614i
$751$	7.89014			0.287915			0.143958	−	0.989584i	$-0.454017\pi$
$751$	7.89014			0.287915			0.143958	+	0.989584i	$0.454017\pi$
$752$	−6.47500	−	6.08043i	−0.236119	−	0.221731i
$753$	−7.78547	+	12.2679i	−0.283718	+	0.447069i
$754$	−1.96224	−	31.1889i	−0.0714605	−	1.13583i
$755$	15.1427	−	22.9899i	0.551101	−	0.836688i
$756$	4.63864	−	1.19100i	0.168706	−	0.0433162i
$757$	1.55571	+	4.78798i	0.0565432	+	0.174022i	0.975339	−	0.220710i	$-0.0708374\pi$
$757$	1.55571	+	4.78798i	0.0565432	+	0.174022i	−0.918796	+	0.394732i	$0.870837\pi$
$758$	−3.19198	+	3.85845i	−0.115938	+	0.140145i
$759$	−8.41245	−	17.8774i	−0.305352	−	0.648907i
$760$	5.26202	+	2.18732i	0.190873	+	0.0793423i
$761$	−0.378854	−	0.355767i	−0.0137334	−	0.0128966i	0.677650	−	0.735385i	$-0.262998\pi$
$761$	−0.378854	−	0.355767i	−0.0137334	−	0.0128966i	−0.691383	+	0.722488i	$0.742998\pi$
$762$	−6.57615	−	3.61527i	−0.238229	−	0.130967i
$763$	16.9725	+	36.0685i	0.614447	+	1.30577i
$764$	−1.50386	+	3.19587i	−0.0544079	+	0.115623i
$765$	−8.15388	+	0.889873i	−0.294804	+	0.0321734i
$766$	18.4569	−	2.33165i	0.666875	−	0.0842459i
$767$	−1.61660	+	25.6952i	−0.0583721	+	0.927798i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	4.84425	+	7.63331i	0.174688	+	0.275264i	0.920379	−	0.391028i	$-0.127880\pi$
$769$	4.84425	+	7.63331i	0.174688	+	0.275264i	−0.745691	+	0.666292i	$0.767880\pi$
$770$	−36.4999	+	3.98341i	−1.31536	+	0.143552i
$771$	−16.0810	−	4.12889i	−0.579142	−	0.148698i
$772$	0.632462	+	10.0527i	0.0227628	+	0.361805i
$773$	−0.869841	−	4.55986i	−0.0312860	−	0.164007i	0.963215	−	0.268731i	$-0.0866042\pi$
$773$	−0.869841	−	4.55986i	−0.0312860	−	0.164007i	−0.994501	+	0.104724i	$0.966604\pi$
$774$	−0.345927	−	1.06465i	−0.0124341	−	0.0382682i
$775$	11.2016	−	16.3943i	0.402375	−	0.588902i
$776$	5.02263	−	15.4581i	0.180302	−	0.554913i
$777$	29.2042	+	3.68934i	1.04769	+	0.132354i
$778$	−1.67529	+	0.663293i	−0.0600619	+	0.0237802i
$779$	23.6937	−	9.38099i	0.848914	−	0.336109i
$780$	2.56873	−	7.47213i	0.0919754	−	0.267545i
$781$	2.36943	−	37.6610i	0.0847849	−	1.34762i
$782$	−17.1010	−	12.4246i	−0.611531	−	0.444303i
$783$	8.56601	−	2.19938i	0.306124	−	0.0785993i
$784$	11.6164	−	10.9086i	0.414873	−	0.389592i
$785$	−4.63465	−	5.79984i	−0.165418	−	0.207005i
$786$	1.41453	−	0.777645i	0.0504546	−	0.0277377i
$787$	−26.6550	+	3.36731i	−0.950149	+	0.120032i	−0.585104	−	0.810958i	$-0.698946\pi$
$787$	−26.6550	+	3.36731i	−0.950149	+	0.120032i	−0.365045	+	0.930990i	$0.618946\pi$
$788$	−4.09124	+	21.4470i	−0.145744	+	0.764019i
$789$	18.9758	+	2.39720i	0.675556	+	0.0853426i
$790$	−25.4722	−	0.432026i	−0.906260	−	0.0153708i
$791$	−9.18500	+	48.1495i	−0.326581	+	1.71200i
$792$	−1.83717	−	2.89491i	−0.0652809	−	0.102866i
$793$	−11.0494	+	8.02788i	−0.392377	+	0.285078i
$794$	−10.5406	+	12.7414i	−0.374073	+	0.452177i
$795$	7.39916	−	3.90581i	0.262421	−	0.138525i
$796$	−5.12690	+	8.07870i	−0.181718	+	0.286342i
$797$	26.1276	+	31.5829i	0.925487	+	1.11872i	0.992655	+	0.120980i	$0.0386038\pi$
$797$	26.1276	+	31.5829i	0.925487	+	1.11872i	−0.0671674	+	0.997742i	$0.521396\pi$
$798$	−5.19655	+	11.0432i	−0.183956	+	0.390927i
$799$	−26.3596	+	19.1514i	−0.932537	+	0.677527i
$800$	−1.97425	−	4.59373i	−0.0698003	−	0.162413i
$801$	−3.96835	−	2.88317i	−0.140215	−	0.101872i
$802$	−22.5309	+	12.3864i	−0.795592	+	0.437380i
$803$	−7.33104	−	1.88229i	−0.258707	−	0.0664246i
$804$	−4.81262	−	5.81746i	−0.169728	−	0.205166i
$805$	60.0225	−	14.3307i	2.11551	−	0.505092i
$806$	13.0470	+	5.16567i	0.459561	+	0.181953i
$807$	3.12195			0.109898
$808$	8.12576	+	3.21721i	0.285863	+	0.113181i
$809$	−0.699096	−	0.384331i	−0.0245789	−	0.0135124i	0.469417	−	0.882977i	$-0.344464\pi$
$809$	−0.699096	−	0.384331i	−0.0245789	−	0.0135124i	−0.493996	+	0.869464i	$0.664464\pi$
$810$	2.21336	+	0.317834i	0.0777697	+	0.0111676i
$811$	9.62904	+	50.4772i	0.338121	+	1.77249i	0.592681	+	0.805437i	$0.298069\pi$
$811$	9.62904	+	50.4772i	0.338121	+	1.77249i	−0.254560	+	0.967057i	$0.581931\pi$
$812$	30.8748	−	28.9934i	1.08349	−	1.01747i
$813$	−11.8300	+	11.1091i	−0.414897	+	0.389614i
$814$	−3.94893	−	20.7010i	−0.138410	−	0.725570i
$815$	−20.0840	+	40.8671i	−0.703513	+	1.43151i
$816$	−3.21445	−	1.76716i	−0.112528	−	0.0618629i
$817$	2.65252	+	1.05021i	0.0927999	+	0.0367421i
$818$	−8.48692			−0.296738
$819$	15.7343	+	6.22966i	0.549802	+	0.217682i
$820$	−20.6467	−	8.58244i	−0.721015	−	0.299712i
$821$	−27.9092	−	33.7364i	−0.974037	−	1.17741i	−0.984128	−	0.177460i	$-0.943212\pi$
$821$	−27.9092	−	33.7364i	−0.974037	−	1.17741i	0.0100910	−	0.999949i	$-0.496788\pi$
$822$	20.8232	+	5.34650i	0.726294	+	0.186481i
$823$	−31.4382	+	17.2833i	−1.09587	+	0.602459i	−0.923896	−	0.382643i	$-0.875014\pi$
$823$	−31.4382	+	17.2833i	−1.09587	+	0.602459i	−0.171972	+	0.985102i	$0.555014\pi$
$824$	7.54398	+	5.48102i	0.262807	+	0.190940i
$825$	−16.4506	−	4.82400i	−0.572735	−	0.167950i
$826$	−28.2296	+	20.5100i	−0.982233	+	0.713634i
$827$	1.35014	−	2.86919i	0.0469489	−	0.0997714i	−0.879976	−	0.475017i	$-0.842442\pi$
$827$	1.35014	−	2.86919i	0.0469489	−	0.0997714i	0.926925	+	0.375246i	$0.122442\pi$
$828$	3.67318	+	4.44011i	0.127652	+	0.154305i
$829$	7.55919	−	11.9114i	0.262542	−	0.413699i	−0.687327	−	0.726348i	$-0.741216\pi$
$829$	7.55919	−	11.9114i	0.262542	−	0.413699i	0.949869	+	0.312649i	$0.101216\pi$
$830$	−15.3046	+	31.1418i	−0.531229	+	1.08095i
$831$	18.0443	−	21.8119i	0.625951	−	0.756645i
$832$	2.85873	−	2.07699i	0.0991087	−	0.0720067i
$833$	−31.3213	−	49.3544i	−1.08522	−	1.71003i
$834$	−0.516043	+	2.70519i	−0.0178691	+	0.0936732i
$835$	−2.90590	−	9.48798i	−0.100563	−	0.328345i
$836$	8.66889	+	1.09514i	0.299820	+	0.0378760i
$837$	−0.744119	+	3.90081i	−0.0257205	+	0.134832i
$838$	22.3816	−	2.82745i	0.773158	−	0.0976726i
$839$	−31.5569	+	17.3485i	−1.08946	+	0.598938i	−0.922098	−	0.386957i	$-0.873526\pi$
$839$	−31.5569	+	17.3485i	−1.08946	+	0.598938i	−0.167366	+	0.985895i	$0.553526\pi$
$840$	10.0222	−	3.77274i	0.345797	−	0.130172i
$841$	35.8753	−	33.6892i	1.23708	−	1.16170i
$842$	−10.9679	+	2.81607i	−0.377978	+	0.0970483i
$843$	7.01959	+	5.10003i	0.241767	+	0.175654i
$844$	0.955799	−	15.1920i	0.0329000	−	0.522930i
$845$	−0.940728	+	0.659398i	−0.0323620	+	0.0226840i
$846$	8.25866	−	3.26984i	0.283939	−	0.112419i
$847$	−3.36492	+	1.33227i	−0.115620	+	0.0457773i
$848$	3.71223	+	0.468964i	0.127478	+	0.0161043i
$849$	3.48357	−	10.7213i	0.119556	−	0.367955i
$850$	−17.9091	+	3.95614i	−0.614278	+	0.135695i
$851$	10.9452	+	33.6860i	0.375198	+	1.15474i
$852$	2.06230	+	10.8110i	0.0706532	+	0.370377i
$853$	0.477337	+	7.58706i	0.0163437	+	0.259776i	0.997710	+	0.0676315i	$0.0215442\pi$
$853$	0.477337	+	7.58706i	0.0163437	+	0.259776i	−0.981367	+	0.192144i	$0.938456\pi$
$854$	−17.9290	−	4.60339i	−0.613519	−	0.157525i
$855$	−4.21960	+	3.82990i	−0.144307	+	0.130980i
$856$	7.48254	+	11.7906i	0.255748	+	0.402994i
$857$	−10.5636	+	32.5113i	−0.360844	+	1.11056i	0.591698	+	0.806159i	$0.298458\pi$
$857$	−10.5636	+	32.5113i	−0.360844	+	1.11056i	−0.952543	+	0.304405i	$0.901542\pi$
$858$	0.760736	−	12.0915i	0.0259711	−	0.412799i
$859$	17.9557	−	2.26834i	0.612642	−	0.0773947i	0.187111	−	0.982339i	$-0.440087\pi$
$859$	17.9557	−	2.26834i	0.612642	−	0.0773947i	0.425531	+	0.904944i	$0.360087\pi$
$860$	−1.02723	−	2.28267i	−0.0350282	−	0.0778384i
$861$	20.3899	−	43.3307i	0.694885	−	1.47671i
$862$	5.43764	+	11.5556i	0.185207	+	0.393584i
$863$	16.4940	+	9.06764i	0.561462	+	0.308666i	0.737095	−	0.675790i	$-0.236197\pi$
$863$	16.4940	+	9.06764i	0.561462	+	0.308666i	−0.175633	+	0.984456i	$0.556197\pi$
$864$	0.728969	+	0.684547i	0.0248000	+	0.0232888i
$865$	9.65840	−	11.2799i	0.328395	−	0.383529i
$866$	−8.16420	−	17.3498i	−0.277431	−	0.589571i
$867$	2.25933	−	2.73106i	0.0767308	−	0.0927516i
$868$	5.87695	+	18.0874i	0.199477	+	0.613927i
$869$	−37.8360	+	9.71463i	−1.28350	+	0.329546i
$870$	18.5076	−	6.96698i	0.627465	−	0.236203i
$871$	−1.67519	−	26.6263i	−0.0567616	−	0.902199i
$872$	−4.45998	+	7.02781i	−0.151034	+	0.237992i
$873$	11.8484	+	11.1263i	0.401006	+	0.376570i
$874$	−14.6856			−0.496747
$875$	25.2321	−	47.2257i	0.853002	−	1.59652i
$876$	2.20752			0.0745852
$877$	16.5062	+	15.5003i	0.557374	+	0.523409i	0.911234	−	0.411890i	$-0.135131\pi$
$877$	16.5062	+	15.5003i	0.557374	+	0.523409i	−0.353860	+	0.935298i	$0.615131\pi$
$878$	15.0501	−	23.7151i	0.507915	−	0.800346i
$879$	−0.220766	−	3.50898i	−0.00744627	−	0.118355i
$880$	−4.78606	−	5.98933i	−0.161338	−	0.201900i
$881$	−18.1550	+	4.66140i	−0.611656	+	0.157047i	−0.541796	−	0.840510i	$-0.682255\pi$
$881$	−18.1550	+	4.66140i	−0.611656	+	0.157047i	−0.0698602	+	0.997557i	$0.522255\pi$
$882$	4.92432	+	15.1555i	0.165811	+	0.510313i
$883$	20.2718	−	24.5044i	0.682202	−	0.824640i	−0.309808	−	0.950799i	$-0.600265\pi$
$883$	20.2718	−	24.5044i	0.682202	−	0.824640i	0.992010	+	0.126159i	$0.0402649\pi$
$884$	−5.51888	−	11.7282i	−0.185620	−	0.394462i
$885$	−15.8467	+	3.78350i	−0.532682	+	0.127181i
$886$	11.5096	+	10.8083i	0.386674	+	0.363111i
$887$	0.497983	+	0.273768i	0.0167206	+	0.00919224i	0.490092	−	0.871671i	$-0.336963\pi$
$887$	0.497983	+	0.273768i	0.0167206	+	0.00919224i	−0.473371	+	0.880863i	$0.656963\pi$
$888$	2.61706	+	5.56154i	0.0878228	+	0.186633i
$889$	15.3022	−	32.5188i	0.513219	−	1.09065i
$890$	−9.52056	−	5.44623i	−0.319130	−	0.182558i
$891$	3.40162	−	0.429725i	0.113959	−	0.0143963i
$892$	0.733270	−	11.6550i	0.0245517	−	0.390238i
$893$	−6.99505	+	21.5286i	−0.234080	+	0.720426i
$894$	−1.54438	−	2.43356i	−0.0516519	−	0.0813904i
$895$	4.98309	+	11.0732i	0.166566	+	0.370137i
$896$	4.63864	+	1.19100i	0.154966	+	0.0397885i
$897$	1.27857	+	20.3222i	0.0426901	+	0.678540i
$898$	3.91892	+	20.5437i	0.130776	+	0.685552i
$899$	10.8528	+	33.4014i	0.361960	+	1.11400i
$900$	4.99712	+	0.169558i	0.166571	+	0.00565194i
$901$	4.24137	−	13.0536i	0.141300	−	0.434878i
$902$	−34.0144	−	4.29701i	−1.13255	−	0.143075i
$903$	4.98465	−	1.97356i	0.165879	−	0.0656760i
$904$	−9.51651	+	3.76785i	−0.316515	+	0.125317i
$905$	−28.8941	−	21.7509i	−0.960471	−	0.723023i
$906$	−0.773031	+	12.2870i	−0.0256822	+	0.408208i
$907$	−0.595827	−	0.432894i	−0.0197841	−	0.0143740i	0.577849	−	0.816144i	$-0.303892\pi$
$907$	−0.595827	−	0.432894i	−0.0197841	−	0.0143740i	−0.597633	+	0.801770i	$0.703892\pi$
$908$	−18.6757	+	4.79511i	−0.619775	+	0.159131i
$909$	−6.37080	+	5.98258i	−0.211306	+	0.198430i
$910$	36.4866	+	10.0307i	1.20952	+	0.332514i
$911$	−26.2601	+	14.4366i	−0.870037	+	0.478307i	−0.853220	−	0.521552i	$-0.825353\pi$
$911$	−26.2601	+	14.4366i	−0.870037	+	0.478307i	−0.0168171	+	0.999859i	$0.505353\pi$
$912$	−2.52836	+	0.319406i	−0.0837224	+	0.0105766i
$913$	−9.96979	+	52.2635i	−0.329952	+	1.72967i
$914$	−24.4182	−	3.08473i	−0.807681	−	0.102034i
$915$	−6.90497	−	5.19792i	−0.228271	−	0.171838i
$916$	−1.47821	+	7.74907i	−0.0488416	+	0.256036i
$917$	4.14223	+	6.52711i	0.136788	+	0.215544i
$918$	2.96762	−	2.15610i	0.0979460	−	0.0711619i
$919$	15.3086	−	18.5049i	0.504983	−	0.610420i	−0.454995	−	0.890494i	$-0.650359\pi$
$919$	15.3086	−	18.5049i	0.504983	−	0.610420i	0.959978	+	0.280074i	$0.0903590\pi$
$920$	9.24214	+	8.97870i	0.304704	+	0.296019i
$921$	−12.1444	+	19.1365i	−0.400170	+	0.630568i
$922$	−11.1451	−	13.4721i	−0.367044	−	0.443680i
$923$	−16.5587	+	35.1890i	−0.545036	+	1.15826i
$924$	13.2842	−	9.65153i	0.437018	−	0.317512i
$925$	28.1744	+	12.2759i	0.926367	+	0.403630i
$926$	21.9907	+	15.9772i	0.722660	+	0.525043i
$927$	−8.17145	+	4.49229i	−0.268386	+	0.147546i
$928$	8.56601	+	2.19938i	0.281193	+	0.0721981i
$929$	−30.0077	−	36.2731i	−0.984522	−	1.19008i	−0.981767	−	0.190086i	$-0.939123\pi$
$929$	−30.0077	−	36.2731i	−0.984522	−	1.19008i	−0.00275411	−	0.999996i	$-0.500877\pi$
$930$	−0.707773	+	8.85151i	−0.0232088	+	0.290252i
$931$	−37.7590	−	14.9498i	−1.23750	−	0.489961i
$932$	−20.4866			−0.671061
$933$	9.76850	+	3.86762i	0.319806	+	0.126620i
$934$	−9.74270	−	5.35609i	−0.318791	−	0.175257i
$935$	−24.8705	+	13.1284i	−0.813351	+	0.429345i
$936$	0.662128	+	3.47100i	0.0216423	+	0.113453i
$937$	37.7278	−	35.4288i	1.23251	−	1.15741i	0.250597	−	0.968091i	$-0.419373\pi$
$937$	37.7278	−	35.4288i	1.23251	−	1.15741i	0.981916	−	0.189316i	$-0.0606269\pi$
$938$	26.3582	−	24.7520i	0.860626	−	0.808182i
$939$	−0.750239	−	3.93289i	−0.0244831	−	0.128345i
$940$	17.5647	−	9.27191i	0.572897	−	0.302416i
$941$	−1.57029	−	0.863272i	−0.0511899	−	0.0281419i	0.455953	−	0.890004i	$-0.349298\pi$
$941$	−1.57029	−	0.863272i	−0.0511899	−	0.0281419i	−0.507143	+	0.861862i	$0.669298\pi$
$942$	3.08703	+	1.22224i	0.100581	+	0.0398228i
$943$	57.6223			1.87644
$944$	−6.77442	−	2.68218i	−0.220489	−	0.0872976i
$945$	−0.853554	+	10.6747i	−0.0277661	+	0.347247i
$946$	−2.44655	−	2.95738i	−0.0795443	−	0.0961526i
$947$	−46.6557	−	11.9792i	−1.51611	−	0.389270i	−0.603252	−	0.797551i	$-0.706129\pi$
$947$	−46.6557	−	11.9792i	−1.51611	−	0.389270i	−0.912857	+	0.408281i	$0.866129\pi$
$948$	9.98390	−	5.48869i	0.324262	−	0.178264i
$949$	6.31071	+	4.58500i	0.204854	+	0.148835i
$950$	−8.45052	+	9.53702i	−0.274171	+	0.309422i
$951$	−1.31813	+	0.957678i	−0.0427433	+	0.0310548i
$952$	7.47978	−	15.8953i	0.242421	−	0.515171i
$953$	−22.2263	−	26.8670i	−0.719981	−	0.870307i	0.275881	−	0.961192i	$-0.411031\pi$
$953$	−22.2263	−	26.8670i	−0.719981	−	0.870307i	−0.995861	+	0.0908847i	$0.971031\pi$
$954$	−2.00492	+	3.15925i	−0.0649117	+	0.102285i
$955$	−5.66477	−	5.50331i	−0.183308	−	0.178083i
$956$	17.3941	−	21.0259i	0.562566	−	0.680026i
$957$	24.5315	−	17.8231i	0.792989	−	0.576141i
$958$	−13.6327	−	21.4817i	−0.440453	−	0.694043i
$959$	−19.2926	+	101.135i	−0.622991	+	3.26583i
$960$	1.78647	+	1.34482i	0.0576580	+	0.0434038i
$961$	15.1099	+	1.90882i	0.487415	+	0.0615749i
$962$	−4.06978	+	21.3345i	−0.131215	+	0.687853i
$963$	−13.8544	+	1.75021i	−0.446451	+	0.0563998i
$964$	−21.7963	+	11.9826i	−0.702012	+	0.385935i
$965$	−21.7172	−	5.97038i	−0.699103	−	0.192193i
$966$	−20.1176	+	18.8917i	−0.647273	+	0.607830i
$967$	8.87383	−	2.27841i	0.285363	−	0.0732688i	−0.103295	−	0.994651i	$-0.532939\pi$
$967$	8.87383	−	2.27841i	0.285363	−	0.0732688i	0.388658	+	0.921382i	$0.372939\pi$
$968$	−0.611365	−	0.444183i	−0.0196500	−	0.0142766i
$969$	−0.586978	+	9.32975i	−0.0188565	+	0.299715i
$970$	29.0365	+	21.8581i	0.932306	+	0.701821i
$971$	−15.1305	+	5.99058i	−0.485560	+	0.192247i	−0.598133	−	0.801397i	$-0.704091\pi$
$971$	−15.1305	+	5.99058i	−0.485560	+	0.192247i	0.112573	+	0.993643i	$0.464091\pi$
$972$	−0.929776	+	0.368125i	−0.0298226	+	0.0118076i
$973$	−13.0851	−	1.65303i	−0.419488	−	0.0529936i
$974$	12.2015	−	37.5524i	0.390962	−	1.20326i
$975$	13.9333	+	10.8637i	0.446222	+	0.347917i
$976$	−1.19440	−	3.67597i	−0.0382317	−	0.117665i
$977$	0.145336	+	0.761877i	0.00464971	+	0.0243746i	0.984536	−	0.175180i	$-0.0560506\pi$
$977$	0.145336	+	0.761877i	0.00464971	+	0.0243746i	−0.979887	+	0.199554i	$0.936051\pi$
$978$	−1.27868	−	20.3240i	−0.0408875	−	0.649889i
$979$	−16.2897	−	4.18248i	−0.520621	−	0.133673i
$980$	14.6227	+	32.4941i	0.467106	+	1.03799i
$981$	−4.45998	−	7.02781i	−0.142396	−	0.224381i
$982$	−8.28373	+	25.4947i	−0.264345	+	0.813569i
$983$	−0.747822	+	11.8863i	−0.0238518	+	0.379114i	0.967934	+	0.251205i	$0.0808267\pi$
$983$	−0.747822	+	11.8863i	−0.0238518	+	0.379114i	−0.991786	+	0.127909i	$0.959173\pi$
$984$	9.92061	−	1.25326i	0.316258	−	0.0399526i
$985$	−42.3779	−	24.2422i	−1.35027	−	0.772422i
$986$	13.8126	−	29.3534i	0.439884	−	0.934801i
$987$	18.1121	+	38.4902i	0.576515	+	1.22516i
$988$	−7.89131	−	4.33829i	−0.251056	−	0.138019i
$989$	4.70246	+	4.41590i	0.149529	+	0.140418i
$990$	7.45711	−	1.78043i	0.237003	−	0.0565858i
$991$	−9.69731	−	20.6078i	−0.308045	−	0.654629i	0.689528	−	0.724259i	$-0.257818\pi$
$991$	−9.69731	−	20.6078i	−0.308045	−	0.654629i	−0.997573	+	0.0696299i	$0.977818\pi$
$992$	−2.53131	+	3.05982i	−0.0803691	+	0.0971495i
$993$	−1.09758	−	3.37800i	−0.0348306	−	0.107198i
$994$	−51.0524	+	13.1080i	−1.61928	+	0.415761i
$995$	−13.3563	−	16.7141i	−0.423422	−	0.529874i
$996$	−0.974383	−	15.4874i	−0.0308745	−	0.490736i
$997$	14.6661	−	23.1101i	0.464481	−	0.731905i	−0.528659	−	0.848834i	$-0.677305\pi$
$997$	14.6661	−	23.1101i	0.464481	−	0.731905i	0.993140	+	0.116929i	$0.0373050\pi$
$998$	19.1635	+	17.9957i	0.606611	+	0.569645i
$999$	−6.14652			−0.194467

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.a.91.1	✓	100
125.11	even	25	inner	750.2.m.a.511.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.a.91.1	✓	100	1.1	even	1	trivial
750.2.m.a.511.1	yes	100	125.11	even	25	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.15608 - 0.592736i) q^{5} +(0.968583 - 0.248690i) q^{6} +(1.47991 + 4.55470i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})\)	\(q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.15608 - 0.592736i) q^{5} +(0.968583 - 0.248690i) q^{6} +(1.47991 + 4.55470i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(-1.16596 - 1.90802i) q^{10} +(-2.49938 - 2.34708i) q^{11} +(0.876307 + 0.481754i) q^{12} +(1.50453 + 3.19728i) q^{13} +(-2.03910 + 4.33330i) q^{14} +(-1.65575 + 1.50283i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(-0.230327 + 3.66094i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.36553 + 2.15173i) q^{19} +(0.456185 - 2.18904i) q^{20} +(4.63864 + 1.19100i) q^{21} +(-0.215287 - 3.42189i) q^{22} +(1.07979 + 5.66047i) q^{23} +(0.309017 + 0.951057i) q^{24} +(4.29733 + 2.55597i) q^{25} +(-1.09194 + 3.36064i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(-4.45279 + 1.76298i) q^{28} +(-8.22281 + 3.25564i) q^{29} +(-2.23575 - 0.0379198i) q^{30} +(0.249351 - 3.96331i) q^{31} +(-0.809017 - 0.587785i) q^{32} +(-3.32094 + 0.852672i) q^{33} +(-2.67399 + 2.51104i) q^{34} +(-0.491068 - 10.6975i) q^{35} +(0.876307 - 0.481754i) q^{36} +(6.09805 - 0.770363i) q^{37} +(-0.477533 + 2.50332i) q^{38} +(3.50572 + 0.442876i) q^{39} +(1.83105 - 1.28346i) q^{40} +(1.87371 - 9.82234i) q^{41} +(2.56613 + 4.04357i) q^{42} +(0.905649 - 0.657993i) q^{43} +(2.18551 - 2.64183i) q^{44} +(0.381689 + 2.20325i) q^{45} +(-3.08772 + 4.86547i) q^{46} +(5.66187 + 6.84402i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(-12.8920 + 9.36662i) q^{49} +(1.38294 + 4.80494i) q^{50} +(2.96762 + 2.15610i) q^{51} +(-3.09651 + 1.70232i) q^{52} +(-3.62418 - 0.930532i) q^{53} +(-0.637424 - 0.770513i) q^{54} +(3.99766 + 6.54195i) q^{55} +(-4.45279 - 1.76298i) q^{56} +2.54846 q^{57} +(-8.22281 - 3.25564i) q^{58} +(6.38483 + 3.51009i) q^{59} +(-1.60383 - 1.55812i) q^{60} +(0.724257 + 3.79669i) q^{61} +(2.89484 - 2.71844i) q^{62} +(3.49110 - 3.27836i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-1.34873 - 7.78538i) q^{65} +(-3.00456 - 1.65177i) q^{66} +(-7.01992 - 2.77938i) q^{67} -3.66818 q^{68} +(5.35787 + 2.12133i) q^{69} +(6.96496 - 8.13429i) q^{70} +(7.01543 + 8.48019i) q^{71} +(0.968583 + 0.248690i) q^{72} +(1.93446 - 1.06348i) q^{73} +(4.97264 + 3.61283i) q^{74} +(4.46070 - 2.25880i) q^{75} +(-2.06175 + 1.49795i) q^{76} +(6.99137 - 14.8574i) q^{77} +(2.25239 + 2.72268i) q^{78} +(6.10476 - 9.61956i) q^{79} +(2.21336 + 0.317834i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(8.08973 - 5.87753i) q^{82} +(-8.31496 - 13.1023i) q^{83} +(-0.897387 + 4.70427i) q^{84} +(2.66657 - 7.75674i) q^{85} +(1.11062 + 0.140304i) q^{86} +(-1.65717 + 8.68721i) q^{87} +(3.40162 - 0.429725i) q^{88} +(4.29841 - 2.36307i) q^{89} +(-1.22999 + 1.86738i) q^{90} +(-12.3361 + 11.5844i) q^{91} +(-5.58150 + 1.43308i) q^{92} +(-3.21273 - 2.33418i) q^{93} +(-0.557732 + 8.86489i) q^{94} +(-1.66878 - 5.44870i) q^{95} +(-0.929776 + 0.368125i) q^{96} +(-15.1122 + 5.98334i) q^{97} +(-15.8098 - 1.99724i) q^{98} +(-1.05951 + 3.26085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 20 q^{5} + 5 q^{7}+O(q^{10}) \) 100 * q - 20 * q^5 + 5 * q^7	\( 100 q - 20 q^{5} + 5 q^{7} - 20 q^{10} + 10 q^{11} + 10 q^{13} - 20 q^{14} - 20 q^{15} + 15 q^{17} - 25 q^{18} + 15 q^{19} + 5 q^{20} + 5 q^{21} + 10 q^{22} - 5 q^{23} - 25 q^{24} + 10 q^{26} + 5 q^{28} + 25 q^{29} + 5 q^{30} - 25 q^{31} - 25 q^{32} + 10 q^{33} - 10 q^{34} + 40 q^{35} + 30 q^{37} - 35 q^{38} + 10 q^{39} + 5 q^{40} - 15 q^{41} + 5 q^{42} + 35 q^{43} - 15 q^{44} + 5 q^{45} + 20 q^{46} - 110 q^{47} + 20 q^{49} + 15 q^{51} - 40 q^{52} + 45 q^{53} + 60 q^{55} + 5 q^{56} - 60 q^{57} + 25 q^{58} - 20 q^{60} + 25 q^{62} + 5 q^{63} + 70 q^{65} - 15 q^{66} - 45 q^{67} - 60 q^{68} + 20 q^{69} - 10 q^{70} + 10 q^{71} + 60 q^{73} + 30 q^{74} - 25 q^{75} + 15 q^{76} + 5 q^{77} + 10 q^{78} - 10 q^{79} + 5 q^{80} - 15 q^{82} - 5 q^{83} + 5 q^{84} - 10 q^{85} + 35 q^{86} + 25 q^{87} + 10 q^{88} + 5 q^{90} + 15 q^{91} - 55 q^{92} + 40 q^{94} - 125 q^{95} + 80 q^{97} - 5 q^{98} + 10 q^{99}+O(q^{100}) \) 100 * q - 20 * q^5 + 5 * q^7 - 20 * q^10 + 10 * q^11 + 10 * q^13 - 20 * q^14 - 20 * q^15 + 15 * q^17 - 25 * q^18 + 15 * q^19 + 5 * q^20 + 5 * q^21 + 10 * q^22 - 5 * q^23 - 25 * q^24 + 10 * q^26 + 5 * q^28 + 25 * q^29 + 5 * q^30 - 25 * q^31 - 25 * q^32 + 10 * q^33 - 10 * q^34 + 40 * q^35 + 30 * q^37 - 35 * q^38 + 10 * q^39 + 5 * q^40 - 15 * q^41 + 5 * q^42 + 35 * q^43 - 15 * q^44 + 5 * q^45 + 20 * q^46 - 110 * q^47 + 20 * q^49 + 15 * q^51 - 40 * q^52 + 45 * q^53 + 60 * q^55 + 5 * q^56 - 60 * q^57 + 25 * q^58 - 20 * q^60 + 25 * q^62 + 5 * q^63 + 70 * q^65 - 15 * q^66 - 45 * q^67 - 60 * q^68 + 20 * q^69 - 10 * q^70 + 10 * q^71 + 60 * q^73 + 30 * q^74 - 25 * q^75 + 15 * q^76 + 5 * q^77 + 10 * q^78 - 10 * q^79 + 5 * q^80 - 15 * q^82 - 5 * q^83 + 5 * q^84 - 10 * q^85 + 35 * q^86 + 25 * q^87 + 10 * q^88 + 5 * q^90 + 15 * q^91 - 55 * q^92 + 40 * q^94 - 125 * q^95 + 80 * q^97 - 5 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more