LMFDB - Embedded newform 750.2.m.a.91.3

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			91.3
Character	$\chi$	$=$	750.91
Dual form			750.2.m.a.511.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-0.583892 - 2.15849i) q^{5} +(0.968583 - 0.248690i) q^{6} +(-0.444263 - 1.36730i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})$	\(q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-0.583892 - 2.15849i) q^{5} +(0.968583 - 0.248690i) q^{6} +(-0.444263 - 1.36730i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(1.05195 - 1.97317i) q^{10} +(-0.0647749 - 0.0608276i) q^{11} +(0.876307 + 0.481754i) q^{12} +(-0.661567 - 1.40590i) q^{13} +(0.612127 - 1.30084i) q^{14} +(-2.13534 - 0.663579i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.380021 - 6.04026i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-2.22908 - 3.51246i) q^{19} +(2.11757 - 0.718273i) q^{20} +(-1.39250 - 0.357532i) q^{21} +(-0.00557945 - 0.0886829i) q^{22} +(1.46519 + 7.68081i) q^{23} +(0.309017 + 0.951057i) q^{24} +(-4.31814 + 2.52065i) q^{25} +(0.480144 - 1.47773i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(1.33671 - 0.529239i) q^{28} +(6.11061 - 2.41936i) q^{29} +(-1.10234 - 1.94547i) q^{30} +(0.584223 - 9.28596i) q^{31} +(-0.809017 - 0.587785i) q^{32} +(-0.0860666 + 0.0220981i) q^{33} +(4.41187 - 4.14302i) q^{34} +(-2.69190 + 1.75729i) q^{35} +(0.876307 - 0.481754i) q^{36} +(0.386334 - 0.0488054i) q^{37} +(0.779519 - 4.08638i) q^{38} +(-1.54153 - 0.194740i) q^{39} +(2.03533 + 0.925975i) q^{40} +(-0.426852 + 2.23764i) q^{41} +(-0.770339 - 1.21386i) q^{42} +(-2.33168 + 1.69407i) q^{43} +(0.0566404 - 0.0684664i) q^{44} +(-1.70445 + 1.44736i) q^{45} +(-4.18980 + 6.60207i) q^{46} +(-2.13612 - 2.58212i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(3.99098 - 2.89962i) q^{49} +(-4.87329 - 1.11850i) q^{50} +(-4.89634 - 3.55740i) q^{51} +(1.36159 - 0.748539i) q^{52} +(-3.61249 - 0.927530i) q^{53} +(-0.637424 - 0.770513i) q^{54} +(-0.0934742 + 0.175333i) q^{55} +(1.33671 + 0.529239i) q^{56} -4.16007 q^{57} +(6.11061 + 2.41936i) q^{58} +(11.0328 + 6.06534i) q^{59} +(0.528191 - 2.17279i) q^{60} +(0.957751 + 5.02071i) q^{61} +(6.78256 - 6.36925i) q^{62} +(-1.04801 + 0.984149i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-2.64834 + 2.24888i) q^{65} +(-0.0778671 - 0.0428078i) q^{66} +(5.86244 + 2.32111i) q^{67} +6.05221 q^{68} +(7.27022 + 2.87848i) q^{69} +(-3.16526 - 0.561721i) q^{70} +(6.34099 + 7.66494i) q^{71} +(0.968583 + 0.248690i) q^{72} +(-3.74073 + 2.05648i) q^{73} +(0.315035 + 0.228886i) q^{74} +(-0.185520 + 4.99656i) q^{75} +(3.36557 - 2.44523i) q^{76} +(-0.0543926 + 0.115590i) q^{77} +(-0.990416 - 1.19721i) q^{78} +(2.70862 - 4.26810i) q^{79} +(0.849819 + 2.06829i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-1.84293 + 1.33897i) q^{82} +(2.15073 + 3.38900i) q^{83} +(0.269391 - 1.41220i) q^{84} +(-13.2597 + 2.70659i) q^{85} +(-2.85939 - 0.361225i) q^{86} +(1.23149 - 6.45571i) q^{87} +(0.0881576 - 0.0111369i) q^{88} +(-6.39803 + 3.51735i) q^{89} +(-2.23328 - 0.111695i) q^{90} +(-1.62838 + 1.52915i) q^{91} +(-7.57366 + 1.94458i) q^{92} +(-7.52736 - 5.46894i) q^{93} +(0.210422 - 3.34456i) q^{94} +(-6.28006 + 6.86233i) q^{95} +(-0.929776 + 0.368125i) q^{96} +(13.5007 - 5.34532i) q^{97} +(4.89422 + 0.618284i) q^{98} +(-0.0274587 + 0.0845092i) 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
$5$	−0.583892	−	2.15849i	−0.261125	−	0.965305i
$5$	−0.583892	−	2.15849i	−0.261125	−	0.965305i
$6$	0.968583	−	0.248690i	0.395422	−	0.101527i
$7$	−0.444263	−	1.36730i	−0.167915	−	0.516791i	0.831324	−	0.555788i	$-0.187584\pi$
$7$	−0.444263	−	1.36730i	−0.167915	−	0.516791i	−0.999239	+	0.0389977i	$0.987584\pi$
$8$	−0.637424	+	0.770513i	−0.225363	+	0.272418i
$9$	−0.425779	−	0.904827i	−0.141926	−	0.301609i
$10$	1.05195	−	1.97317i	0.332655	−	0.623972i
$11$	−0.0647749	−	0.0608276i	−0.0195304	−	0.0183402i	0.674721	−	0.738073i	$-0.264264\pi$
$11$	−0.0647749	−	0.0608276i	−0.0195304	−	0.0183402i	−0.694251	+	0.719733i	$0.744264\pi$
$12$	0.876307	+	0.481754i	0.252968	+	0.139070i
$13$	−0.661567	−	1.40590i	−0.183486	−	0.389927i	0.791830	−	0.610741i	$-0.209128\pi$
$13$	−0.661567	−	1.40590i	−0.183486	−	0.389927i	−0.975316	+	0.220815i	$0.929128\pi$
$14$	0.612127	−	1.30084i	0.163598	−	0.347663i
$15$	−2.13534	−	0.663579i	−0.551342	−	0.171335i
$16$	−0.992115	+	0.125333i	−0.248029	+	0.0313333i
$17$	0.380021	−	6.04026i	0.0921687	−	1.46498i	−0.631792	−	0.775138i	$-0.717680\pi$
$17$	0.380021	−	6.04026i	0.0921687	−	1.46498i	0.723961	−	0.689841i	$-0.242320\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	−2.22908	−	3.51246i	−0.511385	−	0.805814i	0.486302	−	0.873791i	$-0.338346\pi$
$19$	−2.22908	−	3.51246i	−0.511385	−	0.805814i	−0.997687	+	0.0679770i	$0.978346\pi$
$20$	2.11757	−	0.718273i	0.473502	−	0.160611i
$21$	−1.39250	−	0.357532i	−0.303868	−	0.0780200i
$22$	−0.00557945	−	0.0886829i	−0.00118954	−	0.0189073i
$23$	1.46519	+	7.68081i	0.305514	+	1.60156i	0.721650	+	0.692258i	$0.243384\pi$
$23$	1.46519	+	7.68081i	0.305514	+	1.60156i	−0.416136	+	0.909302i	$0.636616\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	−4.31814	+	2.52065i	−0.863628	+	0.504130i
$26$	0.480144	−	1.47773i	0.0941640	−	0.289807i
$27$	−0.992115	−	0.125333i	−0.190933	−	0.0241204i
$28$	1.33671	−	0.529239i	0.252614	−	0.100017i
$29$	6.11061	−	2.41936i	1.13471	−	0.449264i	0.275712	−	0.961240i	$-0.411087\pi$
$29$	6.11061	−	2.41936i	1.13471	−	0.449264i	0.858999	+	0.511977i	$0.171087\pi$
$30$	−1.10234	−	1.94547i	−0.201259	−	0.355192i
$31$	0.584223	−	9.28596i	0.104930	−	1.66781i	−0.495861	−	0.868402i	$-0.665147\pi$
$31$	0.584223	−	9.28596i	0.104930	−	1.66781i	0.600791	−	0.799406i	$-0.294853\pi$
$32$	−0.809017	−	0.587785i	−0.143015	−	0.103907i
$33$	−0.0860666	+	0.0220981i	−0.0149823	+	0.00384679i
$34$	4.41187	−	4.14302i	0.756629	−	0.710522i
$35$	−2.69190	+	1.75729i	−0.455014	+	0.297036i
$36$	0.876307	−	0.481754i	0.146051	−	0.0802923i
$37$	0.386334	−	0.0488054i	0.0635130	−	0.00802355i	−0.0935125	−	0.995618i	$-0.529810\pi$
$37$	0.386334	−	0.0488054i	0.0635130	−	0.00802355i	0.157025	+	0.987595i	$0.449810\pi$
$38$	0.779519	−	4.08638i	0.126455	−	0.662899i
$39$	−1.54153	−	0.194740i	−0.246842	−	0.0311834i
$40$	2.03533	+	0.925975i	0.321814	+	0.146410i
$41$	−0.426852	+	2.23764i	−0.0666631	+	0.349460i	−0.999953	−	0.00966277i	$-0.996924\pi$
$41$	−0.426852	+	2.23764i	−0.0666631	+	0.349460i	0.933290	+	0.359123i	$0.116924\pi$
$42$	−0.770339	−	1.21386i	−0.118866	−	0.187303i
$43$	−2.33168	+	1.69407i	−0.355578	+	0.258343i	−0.751205	−	0.660068i	$-0.770527\pi$
$43$	−2.33168	+	1.69407i	−0.355578	+	0.258343i	0.395627	+	0.918411i	$0.370527\pi$
$44$	0.0566404	−	0.0684664i	0.00853886	−	0.0103217i
$45$	−1.70445	+	1.44736i	−0.254084	+	0.215760i
$46$	−4.18980	+	6.60207i	−0.617752	+	0.973422i
$47$	−2.13612	−	2.58212i	−0.311585	−	0.376641i	0.591353	−	0.806413i	$-0.298594\pi$
$47$	−2.13612	−	2.58212i	−0.311585	−	0.376641i	−0.902938	+	0.429772i	$0.858594\pi$
$48$	−0.425779	+	0.904827i	−0.0614559	+	0.130601i
$49$	3.99098	−	2.89962i	0.570140	−	0.414231i
$50$	−4.87329	−	1.11850i	−0.689187	−	0.158179i
$51$	−4.89634	−	3.55740i	−0.685624	−	0.498135i
$52$	1.36159	−	0.748539i	0.188818	−	0.103804i
$53$	−3.61249	−	0.927530i	−0.496214	−	0.127406i	−0.00771429	−	0.999970i	$-0.502456\pi$
$53$	−3.61249	−	0.927530i	−0.496214	−	0.127406i	−0.488499	+	0.872564i	$0.662456\pi$
$54$	−0.637424	−	0.770513i	−0.0867424	−	0.104854i
$55$	−0.0934742	+	0.175333i	−0.0126041	+	0.0236418i
$56$	1.33671	+	0.529239i	0.178625	+	0.0707226i
$57$	−4.16007			−0.551014
$58$	6.11061	+	2.41936i	0.802362	+	0.317678i
$59$	11.0328	+	6.06534i	1.43635	+	0.789641i	0.994225	−	0.107313i	$-0.0342246\pi$
$59$	11.0328	+	6.06534i	1.43635	+	0.789641i	0.442125	+	0.896953i	$0.354225\pi$
$60$	0.528191	−	2.17279i	0.0681891	−	0.280506i
$61$	0.957751	+	5.02071i	0.122627	+	0.642836i	0.989526	+	0.144352i	$0.0461097\pi$
$61$	0.957751	+	5.02071i	0.122627	+	0.642836i	−0.866899	+	0.498484i	$0.833890\pi$
$62$	6.78256	−	6.36925i	0.861386	−	0.808895i
$63$	−1.04801	+	0.984149i	−0.132037	+	0.123991i
$64$	−0.187381	−	0.982287i	−0.0234227	−	0.122786i
$65$	−2.64834	+	2.24888i	−0.328486	+	0.278939i
$66$	−0.0778671	−	0.0428078i	−0.00958477	−	0.00526927i
$67$	5.86244	+	2.32111i	0.716211	+	0.283568i	0.697831	−	0.716263i	$-0.254149\pi$
$67$	5.86244	+	2.32111i	0.716211	+	0.283568i	0.0183809	+	0.999831i	$0.494149\pi$
$68$	6.05221			0.733938
$69$	7.27022	+	2.87848i	0.875231	+	0.346529i
$70$	−3.16526	−	0.561721i	−0.378321	−	0.0671385i
$71$	6.34099	+	7.66494i	0.752537	+	0.909661i	0.998217	−	0.0596902i	$-0.0190113\pi$
$71$	6.34099	+	7.66494i	0.752537	+	0.909661i	−0.245680	+	0.969351i	$0.579011\pi$
$72$	0.968583	+	0.248690i	0.114149	+	0.0293084i
$73$	−3.74073	+	2.05648i	−0.437819	+	0.240693i	−0.685389	−	0.728177i	$-0.740368\pi$
$73$	−3.74073	+	2.05648i	−0.437819	+	0.240693i	0.247570	+	0.968870i	$0.420368\pi$
$74$	0.315035	+	0.228886i	0.0366221	+	0.0266075i
$75$	−0.185520	+	4.99656i	−0.0214220	+	0.576953i
$76$	3.36557	−	2.44523i	0.386057	−	0.280487i
$77$	−0.0543926	+	0.115590i	−0.00619861	+	0.0131727i
$78$	−0.990416	−	1.19721i	−0.112142	−	0.135557i
$79$	2.70862	−	4.26810i	0.304744	−	0.480199i	−0.657098	−	0.753805i	$-0.728216\pi$
$79$	2.70862	−	4.26810i	0.304744	−	0.480199i	0.961842	+	0.273606i	$0.0882164\pi$
$80$	0.849819	+	2.06829i	0.0950126	+	0.231241i
$81$	−0.637424	+	0.770513i	−0.0708249	+	0.0856126i
$82$	−1.84293	+	1.33897i	−0.203518	+	0.147864i
$83$	2.15073	+	3.38900i	0.236073	+	0.371991i	0.941623	−	0.336668i	$-0.109300\pi$
$83$	2.15073	+	3.38900i	0.236073	+	0.371991i	−0.705550	+	0.708660i	$0.749300\pi$
$84$	0.269391	−	1.41220i	0.0293930	−	0.154084i
$85$	−13.2597	+	2.70659i	−1.43822	+	0.293571i
$86$	−2.85939	−	0.361225i	−0.308336	−	0.0389519i
$87$	1.23149	−	6.45571i	0.132030	−	0.692125i
$88$	0.0881576	−	0.0111369i	0.00939763	−	0.00118720i
$89$	−6.39803	+	3.51735i	−0.678190	+	0.372838i	−0.783318	−	0.621621i	$-0.786475\pi$
$89$	−6.39803	+	3.51735i	−0.678190	+	0.372838i	0.105129	+	0.994459i	$0.466475\pi$
$90$	−2.23328	−	0.111695i	−0.235408	−	0.0117736i
$91$	−1.62838	+	1.52915i	−0.170700	+	0.160298i
$92$	−7.57366	+	1.94458i	−0.789608	+	0.202737i
$93$	−7.52736	−	5.46894i	−0.780550	−	0.567103i
$94$	0.210422	−	3.34456i	0.0217034	−	0.344965i
$95$	−6.28006	+	6.86233i	−0.644321	+	0.704061i
$96$	−0.929776	+	0.368125i	−0.0948949	+	0.0375716i
$97$	13.5007	−	5.34532i	1.37079	−	0.542735i	0.436648	−	0.899633i	$-0.356166\pi$
$97$	13.5007	−	5.34532i	1.37079	−	0.542735i	0.934143	+	0.356898i	$0.116166\pi$
$98$	4.89422	+	0.618284i	0.494391	+	0.0624561i
$99$	−0.0274587	+	0.0845092i	−0.00275970	+	0.00849349i
$100$	−2.78681	−	4.15135i	−0.278681	−	0.415135i
$101$	0.648626	+	1.99626i	0.0645407	+	0.198636i	0.978127	−	0.208010i	$-0.0666985\pi$
$101$	0.648626	+	1.99626i	0.0645407	+	0.198636i	−0.913586	+	0.406645i	$0.866699\pi$
$102$	−1.13407	−	5.94500i	−0.112290	−	0.588643i
$103$	0.327240	+	5.20132i	0.0322439	+	0.512502i	0.980691	+	0.195565i	$0.0626542\pi$
$103$	0.327240	+	5.20132i	0.0322439	+	0.512502i	−0.948447	+	0.316936i	$0.897346\pi$
$104$	1.50496	+	0.386409i	0.147574	+	0.0378905i
$105$	0.0413391	+	3.21445i	0.00403428	+	0.313698i
$106$	−1.99845	−	3.14906i	−0.194107	−	0.305864i
$107$	−2.90369	+	8.93664i	−0.280710	+	0.863938i	0.706941	+	0.707272i	$0.250075\pi$
$107$	−2.90369	+	8.93664i	−0.280710	+	0.863938i	−0.987652	+	0.156666i	$0.949925\pi$
$108$	0.0627905	−	0.998027i	0.00604202	−	0.0960352i
$109$	−6.31392	+	0.797634i	−0.604764	+	0.0763995i	−0.421752	−	0.906711i	$-0.638585\pi$
$109$	−6.31392	+	0.797634i	−0.604764	+	0.0763995i	−0.183012	+	0.983111i	$0.558585\pi$
$110$	−0.188163	+	0.0638245i	−0.0179407	+	0.00608542i
$111$	0.165801	−	0.352344i	0.0157371	−	0.0334430i
$112$	0.612127	+	1.30084i	0.0578406	+	0.122918i
$113$	13.5560	+	7.45248i	1.27524	+	0.701070i	0.968093	−	0.250592i	$-0.0806252\pi$
$113$	13.5560	+	7.45248i	1.27524	+	0.701070i	0.307149	+	0.951662i	$0.400625\pi$
$114$	−3.03256	−	2.84776i	−0.284025	−	0.266717i
$115$	15.7234	−	7.64737i	1.46622	−	0.713121i
$116$	2.79827	+	5.94664i	0.259813	+	0.552131i
$117$	−0.990416	+	1.19721i	−0.0915640	+	0.110682i
$118$	3.89057	+	11.9739i	0.358156	+	1.10229i
$119$	−8.42768	+	2.16386i	−0.772564	+	0.198361i
$120$	1.87241	−	1.22232i	0.170927	−	0.111582i
$121$	−0.690200	−	10.9704i	−0.0627454	−	0.997310i
$122$	−2.73874	+	4.31556i	−0.247954	+	0.390713i
$123$	1.66058	+	1.55939i	0.149730	+	0.140605i
$124$	9.30432			0.835553
$125$	7.96212	+	7.84886i	0.712154	+	0.702024i
$126$	−1.43766			−0.128077
$127$	−6.54502	−	6.14618i	−0.580776	−	0.545385i	0.337500	−	0.941326i	$-0.390419\pi$
$127$	−6.54502	−	6.14618i	−0.580776	−	0.545385i	−0.918276	+	0.395940i	$0.870419\pi$
$128$	0.535827	−	0.844328i	0.0473608	−	0.0746288i
$129$	0.180970	+	2.87643i	0.0159335	+	0.253256i
$130$	−3.47002	−	0.173549i	−0.304341	−	0.0152212i
$131$	2.13275	−	0.547598i	0.186340	−	0.0478439i	−0.154367	−	0.988014i	$-0.549334\pi$
$131$	2.13275	−	0.547598i	0.186340	−	0.0478439i	0.340706	+	0.940170i	$0.389334\pi$
$132$	−0.0274587	−	0.0845092i	−0.00238997	−	0.00735558i
$133$	−3.81229	+	4.60827i	−0.330568	+	0.399588i
$134$	2.68463	+	5.70513i	0.231917	+	0.492848i
$135$	0.308758	+	2.21465i	0.0265737	+	0.190607i
$136$	4.41187	+	4.14302i	0.378315	+	0.355261i
$137$	−13.8546	−	7.61662i	−1.18368	−	0.650731i	−0.236558	−	0.971617i	$-0.576019\pi$
$137$	−13.8546	−	7.61662i	−1.18368	−	0.650731i	−0.947118	+	0.320886i	$0.896019\pi$
$138$	3.32930	+	7.07513i	0.283409	+	0.602275i
$139$	6.24868	−	13.2791i	0.530006	−	1.12632i	−0.443208	−	0.896419i	$-0.646160\pi$
$139$	6.24868	−	13.2791i	0.530006	−	1.12632i	0.973214	−	0.229902i	$-0.0738404\pi$
$140$	−1.92285	−	2.57624i	−0.162510	−	0.217732i
$141$	−3.32475	+	0.420013i	−0.279994	+	0.0353715i
$142$	−0.624630	+	9.92820i	−0.0524178	+	0.833156i
$143$	−0.0426647	+	0.131309i	−0.00356781	+	0.0109806i
$144$	0.535827	+	0.844328i	0.0446522	+	0.0703607i
$145$	−8.79010	−	11.7770i	−0.729978	−	0.978028i
$146$	−4.13463	−	1.06159i	−0.342185	−	0.0878581i
$147$	−0.309753	−	4.92339i	−0.0255480	−	0.406074i
$148$	0.0729672	+	0.382507i	0.00599787	+	0.0314419i
$149$	5.67847	+	17.4765i	0.465199	+	1.43173i	0.858733	+	0.512424i	$0.171252\pi$
$149$	5.67847	+	17.4765i	0.465199	+	1.43173i	−0.393534	+	0.919310i	$0.628748\pi$
$150$	−3.55562	+	3.51534i	−0.290315	+	0.287026i
$151$	−5.74400	+	17.6782i	−0.467440	+	1.43863i	0.388447	+	0.921471i	$0.373012\pi$
$151$	−5.74400	+	17.6782i	−0.467440	+	1.43863i	−0.855888	+	0.517162i	$0.826988\pi$
$152$	4.12726	+	0.521395i	0.334765	+	0.0422907i
$153$	−5.62720	+	2.22797i	−0.454932	+	0.180120i
$154$	−0.118777	+	0.0470273i	−0.00957135	+	0.00378957i
$155$	−20.3848	+	4.16097i	−1.63734	+	0.334217i
$156$	0.0975626	−	1.55071i	0.00781126	−	0.124156i
$157$	−10.0595	−	7.30868i	−0.802838	−	0.583296i	0.108907	−	0.994052i	$-0.465265\pi$
$157$	−10.0595	−	7.30868i	−0.802838	−	0.583296i	−0.911745	+	0.410756i	$0.865265\pi$
$158$	4.89622	−	1.25713i	0.389522	−	0.100012i
$159$	−2.71881	+	2.55313i	−0.215616	+	0.202476i
$160$	−0.796348	+	2.08946i	−0.0629569	+	0.165186i
$161$	9.85104	−	5.41566i	0.776371	−	0.426814i
$162$	−0.992115	+	0.125333i	−0.0779479	+	0.00984711i
$163$	−1.07268	+	5.62317i	−0.0840185	+	0.440440i	0.915274	+	0.402832i	$0.131974\pi$
$163$	−1.07268	+	5.62317i	−0.0840185	+	0.440440i	−0.999293	+	0.0376087i	$0.988026\pi$
$164$	−2.26002	−	0.285508i	−0.176478	−	0.0222944i
$165$	0.0979522	+	0.172871i	0.00762557	+	0.0134580i
$166$	−0.752120	+	3.94275i	−0.0583758	+	0.306017i
$167$	−3.47010	−	5.46801i	−0.268525	−	0.423127i	0.683130	−	0.730297i	$-0.260618\pi$
$167$	−3.47010	−	5.46801i	−0.268525	−	0.423127i	−0.951655	+	0.307169i	$0.900618\pi$
$168$	1.16309	−	0.845038i	0.0897347	−	0.0651961i
$169$	6.74763	−	8.15648i	0.519048	−	0.627421i
$170$	−11.5187	−	7.10389i	−0.883445	−	0.544843i
$171$	−2.22908	+	3.51246i	−0.170462	+	0.268605i
$172$	−1.83713	−	2.22071i	−0.140080	−	0.169328i
$173$	1.14600	−	2.43538i	0.0871289	−	0.185158i	−0.856514	−	0.516124i	$-0.827374\pi$
$173$	1.14600	−	2.43538i	0.0871289	−	0.185158i	0.943643	+	0.330966i	$0.107374\pi$
$174$	5.31696	−	3.86300i	0.403078	−	0.292853i
$175$	5.36487	+	4.78436i	0.405546	+	0.361664i
$176$	0.0718878	+	0.0522296i	0.00541875	+	0.00393695i
$177$	11.0328	−	6.06534i	0.829278	−	0.455899i
$178$	−7.07175	−	1.81572i	−0.530050	−	0.136094i
$179$	10.2093	+	12.3410i	0.763081	+	0.922407i	0.998778	−	0.0494197i	$-0.0157372\pi$
$179$	10.2093	+	12.3410i	0.763081	+	0.922407i	−0.235697	+	0.971827i	$0.575737\pi$
$180$	−1.55153	−	1.61020i	−0.115644	−	0.120018i
$181$	−7.56380	−	2.99472i	−0.562213	−	0.222596i	0.0697902	−	0.997562i	$-0.477767\pi$
$181$	−7.56380	−	2.99472i	−0.562213	−	0.222596i	−0.632003	+	0.774966i	$0.717767\pi$
$182$	−2.23381			−0.165581
$183$	4.75231	+	1.88157i	0.351301	+	0.139090i
$184$	−6.85212	−	3.76698i	−0.505145	−	0.277706i
$185$	−0.330923	−	0.805401i	−0.0243300	−	0.0592142i
$186$	−1.74346	−	9.13952i	−0.127836	−	0.670142i
$187$	−0.392031	+	0.368141i	−0.0286681	+	0.0269212i
$188$	2.44290	−	2.29403i	0.178167	−	0.167310i
$189$	0.269391	+	1.41220i	0.0195953	+	0.102722i
$190$	−9.27556	+	0.703425i	−0.672920	+	0.0510318i
$191$	20.3918	+	11.2105i	1.47550	+	0.811161i	0.997731	−	0.0673267i	$-0.0214470\pi$
$191$	20.3918	+	11.2105i	1.47550	+	0.811161i	0.477765	+	0.878488i	$0.341447\pi$
$192$	−0.929776	−	0.368125i	−0.0671008	−	0.0265671i
$193$	−11.3317			−0.815673			−0.407836	−	0.913055i	$-0.633717\pi$
$193$	−11.3317			−0.815673			−0.407836	+	0.913055i	$0.633717\pi$
$194$	13.5007	+	5.34532i	0.969296	+	0.383771i
$195$	0.479742	+	3.44107i	0.0343550	+	0.246420i
$196$	3.14449	+	3.80104i	0.224606	+	0.271503i
$197$	4.55865	+	1.17046i	0.324790	+	0.0833920i	0.407565	−	0.913176i	$-0.366378\pi$
$197$	4.55865	+	1.17046i	0.324790	+	0.0833920i	−0.0827744	+	0.996568i	$0.526378\pi$
$198$	−0.0778671	+	0.0428078i	−0.00553377	+	0.00304222i
$199$	9.04116	+	6.56879i	0.640911	+	0.465649i	0.860163	−	0.510019i	$-0.170362\pi$
$199$	9.04116	+	6.56879i	0.640911	+	0.465649i	−0.219252	+	0.975668i	$0.570362\pi$
$200$	0.810292	−	4.93391i	0.0572963	−	0.348880i
$201$	5.10103	−	3.70611i	0.359799	−	0.261409i
$202$	−0.893709	+	1.89923i	−0.0628812	+	0.133629i
$203$	−6.02270	−	7.28020i	−0.422711	−	0.510970i
$204$	3.24293	−	5.11005i	0.227051	−	0.357775i
$205$	5.07915	−	0.385185i	0.354743	−	0.0269025i
$206$	−3.32200	+	4.01561i	−0.231455	+	0.279781i
$207$	6.32596	−	4.59608i	0.439685	−	0.319450i
$208$	0.832556	+	1.31190i	0.0577274	+	0.0909638i
$209$	−0.0692667	+	0.363109i	−0.00479128	+	0.0251168i
$210$	−2.17031	+	2.37153i	−0.149765	+	0.163651i
$211$	19.1271	+	2.41631i	1.31676	+	0.166346i	0.752139	−	0.659004i	$-0.229022\pi$
$211$	19.1271	+	2.41631i	1.31676	+	0.166346i	0.564622	+	0.825350i	$0.309022\pi$
$212$	0.698869	−	3.66360i	0.0479986	−	0.251617i
$213$	9.86939	−	1.24679i	0.676240	−	0.0854289i
$214$	−8.23425	+	4.52682i	−0.562882	+	0.309447i
$215$	5.01807	+	4.04376i	0.342230	+	0.275782i
$216$	0.728969	−	0.684547i	0.0496000	−	0.0465775i
$217$	−12.9562	+	3.32660i	−0.879527	+	0.225824i
$218$	−5.14867	−	3.74073i	−0.348712	−	0.253354i
$219$	−0.268037	+	4.26032i	−0.0181122	+	0.287886i
$220$	−0.180856	−	0.0822805i	−0.0121933	−	0.00554735i
$221$	−8.74342	+	3.46177i	−0.588146	+	0.232864i
$222$	0.362059	−	0.143349i	0.0242998	−	0.00962099i
$223$	−25.0208	−	3.16086i	−1.67552	−	0.211667i	−0.770620	−	0.637295i	$-0.780053\pi$
$223$	−25.0208	−	3.16086i	−1.67552	−	0.211667i	−0.904898	+	0.425628i	$0.860053\pi$
$224$	−0.444263	+	1.36730i	−0.0296835	+	0.0913565i
$225$	4.11933	+	2.83393i	0.274622	+	0.188929i
$226$	4.78033	+	14.7123i	0.317983	+	0.978650i
$227$	−3.72470	−	19.5256i	−0.247217	−	1.29596i	−0.861858	−	0.507150i	$-0.830699\pi$
$227$	−3.72470	−	19.5256i	−0.247217	−	1.29596i	0.614641	−	0.788807i	$-0.289301\pi$
$228$	−0.261213	−	4.15186i	−0.0172992	−	0.274964i
$229$	−23.4463	−	6.02000i	−1.54938	−	0.397813i	−0.625414	−	0.780293i	$-0.715070\pi$
$229$	−23.4463	−	6.02000i	−1.54938	−	0.397813i	−0.923964	+	0.382481i	$0.875070\pi$
$230$	16.6969	+	5.18873i	1.10096	+	0.342135i
$231$	0.0684509	+	0.107861i	0.00450374	+	0.00709676i
$232$	−2.03090	+	6.25046i	−0.133335	+	0.410363i
$233$	−0.696882	+	11.0766i	−0.0456543	+	0.725654i	0.906912	+	0.421321i	$0.138433\pi$
$233$	−0.696882	+	11.0766i	−0.0456543	+	0.725654i	−0.952566	+	0.304333i	$0.901567\pi$
$234$	−1.54153	+	0.194740i	−0.100773	+	0.0127306i
$235$	−4.32622	+	6.11846i	−0.282211	+	0.399125i
$236$	−5.36062	+	11.3919i	−0.348947	+	0.741549i
$237$	−2.15233	−	4.57393i	−0.139809	−	0.297108i
$238$	−7.62478	−	4.19176i	−0.494241	−	0.271711i
$239$	−10.0124	−	9.40229i	−0.647650	−	0.608183i	0.289472	−	0.957186i	$-0.406520\pi$
$239$	−10.0124	−	9.40229i	−0.647650	−	0.608183i	−0.937122	+	0.349003i	$0.886520\pi$
$240$	2.20167	+	0.390718i	0.142117	+	0.0252207i
$241$	−1.94572	−	4.13486i	−0.125335	−	0.266350i	0.832306	−	0.554317i	$-0.187021\pi$
$241$	−1.94572	−	4.13486i	−0.125335	−	0.266350i	−0.957640	+	0.287967i	$0.907021\pi$
$242$	7.00663	−	8.46956i	0.450403	−	0.544444i
$243$	0.309017	+	0.951057i	0.0198234	+	0.0610103i
$244$	−4.95066	+	1.27111i	−0.316934	+	0.0813747i
$245$	−8.58909	−	6.92142i	−0.548737	−	0.442193i
$246$	0.143036	+	2.27349i	0.00911964	+	0.144953i
$247$	−3.46349	+	5.45759i	−0.220377	+	0.347258i
$248$	6.78256	+	6.36925i	0.430693	+	0.404448i
$249$	4.01385			0.254367
$250$	0.431220	+	11.1720i	0.0272728	+	0.706581i
$251$	25.1727			1.58889			0.794444	−	0.607338i	$-0.207763\pi$
$251$	25.1727			1.58889			0.794444	+	0.607338i	$0.207763\pi$
$252$	−1.04801	−	0.984149i	−0.0660185	−	0.0619955i
$253$	0.372298	−	0.586648i	0.0234062	−	0.0368822i
$254$	−0.563762	−	8.96074i	−0.0353736	−	0.562247i
$255$	−4.81966	+	12.6458i	−0.301819	+	0.791912i
$256$	0.968583	−	0.248690i	0.0605364	−	0.0155431i
$257$	−8.73695	−	26.8896i	−0.544996	−	1.67732i	−0.721000	−	0.692935i	$-0.756317\pi$
$257$	−8.73695	−	26.8896i	−0.544996	−	1.67732i	0.176004	−	0.984389i	$-0.443683\pi$
$258$	−1.83713	+	2.22071i	−0.114375	+	0.138255i
$259$	−0.238365	−	0.506552i	−0.0148113	−	0.0314756i
$260$	−2.41073	−	2.50190i	−0.149507	−	0.155161i
$261$	−4.79087	−	4.49893i	−0.296548	−	0.278477i
$262$	1.92957	+	1.06079i	0.119209	+	0.0655357i
$263$	3.04324	+	6.46722i	0.187654	+	0.398786i	0.976411	−	0.215919i	$-0.0692749\pi$
$263$	3.04324	+	6.46722i	0.187654	+	0.398786i	−0.788757	+	0.614706i	$0.789275\pi$
$264$	0.0378340	−	0.0804013i	0.00232852	−	0.00494836i
$265$	0.107244	+	8.33909i	0.00658795	+	0.512266i
$266$	−5.93362	+	0.749590i	−0.363814	+	0.0459603i
$267$	−0.458442	+	7.28672i	−0.0280562	+	0.445940i
$268$	−1.94842	+	5.99662i	−0.119019	+	0.366302i
$269$	−1.65276	−	2.60433i	−0.100771	−	0.158789i	0.790202	−	0.612847i	$-0.209976\pi$
$269$	−1.65276	−	2.60433i	−0.100771	−	0.158789i	−0.890972	+	0.454058i	$0.849976\pi$
$270$	−1.29096	+	1.82577i	−0.0785651	+	0.111113i
$271$	27.2949	+	7.00814i	1.65805	+	0.425714i	0.957626	−	0.288015i	$-0.0929953\pi$
$271$	27.2949	+	7.00814i	1.65805	+	0.425714i	0.700422	+	0.713729i	$0.252995\pi$
$272$	0.380021	+	6.04026i	0.0230422	+	0.366245i
$273$	0.418574	+	2.19424i	0.0253333	+	0.132802i
$274$	−4.88562	−	15.0364i	−0.295151	−	0.908381i
$275$	0.433032	+	0.0993875i	0.0261128	+	0.00599329i
$276$	−2.41630	+	7.43661i	−0.145444	+	0.447631i
$277$	6.27833	+	0.793137i	0.377228	+	0.0476550i	0.311661	−	0.950193i	$-0.399115\pi$
$277$	6.27833	+	0.793137i	0.377228	+	0.0476550i	0.0655666	+	0.997848i	$0.479115\pi$
$278$	13.6453	−	5.40255i	0.818389	−	0.324023i
$279$	−8.65094	+	3.42515i	−0.517918	+	0.205058i
$280$	0.361864	−	3.19428i	0.0216255	−	0.190895i
$281$	1.48381	−	23.5844i	0.0885165	−	1.40693i	−0.663692	−	0.748006i	$-0.731012\pi$
$281$	1.48381	−	23.5844i	0.0885165	−	1.40693i	0.752209	−	0.658925i	$-0.228988\pi$
$282$	−2.71115	−	1.96977i	−0.161447	−	0.117298i
$283$	−12.9298	+	3.31981i	−0.768597	+	0.197342i	−0.612576	−	0.790412i	$-0.709867\pi$
$283$	−12.9298	+	3.31981i	−0.768597	+	0.197342i	−0.156021	+	0.987754i	$0.549867\pi$
$284$	−7.25166	+	6.80976i	−0.430307	+	0.404085i
$285$	2.42903	+	8.97946i	0.143883	+	0.531897i
$286$	−0.120988	+	0.0665138i	−0.00715418	+	0.00393304i
$287$	3.24916	−	0.410464i	0.191792	−	0.0242289i
$288$	−0.187381	+	0.982287i	−0.0110415	+	0.0578818i
$289$	−19.4744	−	2.46019i	−1.14555	−	0.144717i
$290$	1.65422	−	14.6023i	0.0971393	−	0.857477i
$291$	2.72085	−	14.2632i	0.159499	−	0.836124i
$292$	−2.28731	−	3.60422i	−0.133855	−	0.210921i
$293$	−17.0361	+	12.3775i	−0.995261	+	0.723099i	−0.961067	−	0.276316i	$-0.910886\pi$
$293$	−17.0361	+	12.3775i	−0.995261	+	0.723099i	−0.0341938	+	0.999415i	$0.510886\pi$
$294$	3.14449	−	3.80104i	0.183390	−	0.221681i
$295$	6.64999	−	27.3557i	0.387177	−	1.59271i
$296$	−0.208654	+	0.328785i	−0.0121277	+	0.0191103i
$297$	0.0566404	+	0.0684664i	0.00328661	+	0.00397283i
$298$	−7.82409	+	16.6270i	−0.453237	+	0.963178i
$299$	9.82914	−	7.14129i	0.568434	−	0.412991i
$300$	−4.99835	+	0.128583i	−0.288580	+	0.00742373i
$301$	3.35218	+	2.43550i	0.193216	+	0.140380i
$302$	−16.2888	+	8.95483i	−0.937313	+	0.515292i
$303$	2.03305	+	0.521999i	0.116796	+	0.0299881i
$304$	2.65173	+	3.20539i	0.152087	+	0.183842i
$305$	10.2779	−	4.99885i	0.588512	−	0.286233i
$306$	−5.62720	−	2.22797i	−0.321686	−	0.127364i
$307$	5.93227			0.338572			0.169286	−	0.985567i	$-0.445854\pi$
$307$	5.93227			0.338572			0.169286	+	0.985567i	$0.445854\pi$
$308$	−0.118777	−	0.0470273i	−0.00676797	−	0.00267963i
$309$	4.56697	+	2.51071i	0.259806	+	0.142829i
$310$	−17.7082	−	10.9211i	−1.00576	−	0.620278i
$311$	5.89261	+	30.8902i	0.334140	+	1.75162i	0.611867	+	0.790961i	$0.290419\pi$
$311$	5.89261	+	30.8902i	0.334140	+	1.75162i	−0.277727	+	0.960660i	$0.589581\pi$
$312$	1.13266	−	1.06363i	0.0641240	−	0.0602165i
$313$	13.0095	−	12.2168i	0.735342	−	0.690532i	−0.223427	−	0.974721i	$-0.571724\pi$
$313$	13.0095	−	12.2168i	0.735342	−	0.690532i	0.958768	+	0.284189i	$0.0917243\pi$
$314$	−2.32995	−	12.2140i	−0.131487	−	0.689277i
$315$	2.73620	+	1.68748i	0.154167	+	0.0950789i
$316$	4.42976	+	2.43528i	0.249193	+	0.136995i
$317$	9.33805	+	3.69719i	0.524477	+	0.207655i	0.615418	−	0.788201i	$-0.288987\pi$
$317$	9.33805	+	3.69719i	0.524477	+	0.207655i	−0.0909407	+	0.995856i	$0.528987\pi$
$318$	−3.72966			−0.209149
$319$	−0.542978	−	0.214980i	−0.0304009	−	0.0120366i
$320$	−2.01084	+	0.978010i	−0.112410	+	0.0546724i
$321$	5.98958	+	7.24016i	0.334306	+	0.404106i
$322$	10.8884	+	2.79566i	0.606785	+	0.155796i
$323$	−22.0633	+	12.1294i	−1.22763	+	0.674898i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	6.40052	+	4.40330i	0.355037	+	0.244251i
$326$	−4.63127	+	3.36481i	−0.256502	+	0.186360i
$327$	−2.70970	+	5.75842i	−0.149847	+	0.318441i
$328$	−1.45204	−	1.75522i	−0.0801757	−	0.0969158i
$329$	−2.58154	+	4.06785i	−0.142325	+	0.224268i
$330$	−0.0469341	+	0.193070i	−0.00258364	+	0.0106282i
$331$	15.4496	−	18.6754i	0.849187	−	1.02649i	−0.150098	−	0.988671i	$-0.547959\pi$
$331$	15.4496	−	18.6754i	0.849187	−	1.02649i	0.999285	−	0.0378195i	$-0.0120412\pi$
$332$	−3.24727	+	2.35928i	−0.178217	+	0.129482i
$333$	−0.208654	−	0.328785i	−0.0114341	−	0.0180173i
$334$	1.21351	−	6.36146i	0.0664005	−	0.348083i
$335$	1.58704	−	14.0093i	0.0867093	−	0.765409i
$336$	1.42633	+	0.180187i	0.0778125	+	0.00983001i
$337$	1.00203	−	5.25282i	0.0545840	−	0.286139i	−0.944520	−	0.328453i	$-0.893473\pi$
$337$	1.00203	−	5.25282i	0.0545840	−	0.286139i	0.999104	+	0.0423135i	$0.0134728\pi$
$338$	10.5023	−	1.32675i	0.571250	−	0.0721656i
$339$	13.5560	−	7.45248i	0.736261	−	0.404763i
$340$	−3.53384	−	13.0636i	−0.191649	−	0.708474i
$341$	−0.602686	+	0.565960i	−0.0326373	+	0.0306485i
$342$	−4.02937	+	1.03457i	−0.217883	+	0.0559430i
$343$	−13.8793	−	10.0839i	−0.749414	−	0.544481i
$344$	0.180970	−	2.87643i	0.00975723	−	0.155087i
$345$	1.96814	−	17.3734i	0.105961	−	0.935352i
$346$	2.50253	−	0.990822i	0.134537	−	0.0532669i
$347$	11.0787	−	4.38637i	0.594737	−	0.235473i	−0.0514207	−	0.998677i	$-0.516375\pi$
$347$	11.0787	−	4.38637i	0.594737	−	0.235473i	0.646157	+	0.763204i	$0.276375\pi$
$348$	6.52030	+	0.823705i	0.349525	+	0.0441552i
$349$	−0.179091	+	0.551186i	−0.00958652	+	0.0295043i	−0.955735	−	0.294228i	$-0.904938\pi$
$349$	−0.179091	+	0.551186i	−0.00958652	+	0.0295043i	0.946149	+	0.323732i	$0.104938\pi$
$350$	0.635703	+	7.16015i	0.0339798	+	0.382726i
$351$	0.480144	+	1.47773i	0.0256282	+	0.0788755i
$352$	0.0166504	+	0.0872843i	0.000887468	+	0.00465227i
$353$	−1.64766	−	26.1888i	−0.0876960	−	1.39389i	−0.758219	−	0.652000i	$-0.773930\pi$
$353$	−1.64766	−	26.1888i	−0.0876960	−	1.39389i	0.670523	−	0.741888i	$-0.266070\pi$
$354$	12.1946	+	3.13104i	0.648135	+	0.166413i
$355$	12.8422	−	18.1624i	0.681594	−	0.963962i
$356$	−3.91214	−	6.16455i	−0.207343	−	0.326720i
$357$	−2.68877	+	8.27518i	−0.142305	+	0.437969i
$358$	−1.00569	+	15.9849i	−0.0531522	+	0.844831i
$359$	10.6070	−	1.33998i	0.559818	−	0.0707215i	0.159668	−	0.987171i	$-0.448958\pi$
$359$	10.6070	−	1.33998i	0.559818	−	0.0707215i	0.400151	+	0.916449i	$0.368958\pi$
$360$	−0.0287544	−	2.23588i	−0.00151549	−	0.117841i
$361$	0.721200	−	1.53263i	0.0379579	−	0.0806646i
$362$	−3.46375	−	7.36084i	−0.182050	−	0.386877i
$363$	−9.63245	−	5.29549i	−0.505573	−	0.277941i
$364$	−1.62838	−	1.52915i	−0.0853502	−	0.0801492i
$365$	6.62308	+	6.87355i	0.346668	+	0.359778i
$366$	2.17626	+	4.62479i	0.113755	+	0.241742i
$367$	−1.87644	+	2.26823i	−0.0979496	+	0.118401i	−0.817210	−	0.576339i	$-0.804481\pi$
$367$	−1.87644	+	2.26823i	−0.0979496	+	0.118401i	0.719261	+	0.694740i	$0.244481\pi$
$368$	−2.41630	−	7.43661i	−0.125958	−	0.387660i
$369$	2.20642	−	0.566512i	0.114862	−	0.0294915i
$370$	0.310102	−	0.813645i	0.0161214	−	0.0422994i
$371$	0.336683	+	5.35142i	0.0174797	+	0.277832i
$372$	4.98551	−	7.85590i	0.258486	−	0.407309i
$373$	2.32103	+	2.17959i	0.120178	+	0.112855i	0.742307	−	0.670060i	$-0.233732\pi$
$373$	2.32103	+	2.17959i	0.120178	+	0.112855i	−0.622128	+	0.782915i	$0.713732\pi$
$374$	−0.537788			−0.0278084
$375$	10.8933	−	2.51701i	0.562529	−	0.129978i
$376$	3.35117			0.172823
$377$	−7.44395	−	6.99034i	−0.383383	−	0.360021i
$378$	−0.770339	+	1.21386i	−0.0396220	+	0.0624342i
$379$	1.68539	+	26.7885i	0.0865726	+	1.37603i	0.766260	+	0.642530i	$0.222115\pi$
$379$	1.68539	+	26.7885i	0.0865726	+	1.37603i	−0.679688	+	0.733502i	$0.737885\pi$
$380$	−7.24312	−	5.83678i	−0.371564	−	0.299421i
$381$	−8.69639	+	2.23285i	−0.445529	+	0.114393i
$382$	7.19086	+	22.1312i	0.367917	+	1.13233i
$383$	8.94581	−	10.8136i	0.457110	−	0.552551i	−0.490724	−	0.871315i	$-0.663268\pi$
$383$	8.94581	−	10.8136i	0.457110	−	0.552551i	0.947834	+	0.318764i	$0.103268\pi$
$384$	−0.425779	−	0.904827i	−0.0217280	−	0.0461743i
$385$	0.281259	+	0.0499135i	0.0143343	+	0.00254383i
$386$	−8.26045	−	7.75708i	−0.420446	−	0.394825i
$387$	2.52562	+	1.38847i	0.128384	+	0.0705800i
$388$	6.18249	+	13.1385i	0.313868	+	0.667004i
$389$	11.0732	−	23.5318i	0.561436	−	1.19311i	−0.399601	−	0.916689i	$-0.630851\pi$
$389$	11.0732	−	23.5318i	0.561436	−	1.19311i	0.961036	−	0.276422i	$-0.0891488\pi$
$390$	−2.00586	+	2.83684i	−0.101571	+	0.143649i
$391$	46.9509	−	5.93128i	2.37441	−	0.299958i
$392$	−0.309753	+	4.92339i	−0.0156449	+	0.248669i
$393$	0.680434	−	2.09416i	0.0343234	−	0.105636i
$394$	2.52188	+	3.97384i	0.127050	+	0.200199i
$395$	−10.7942	−	3.35441i	−0.543115	−	0.168779i
$396$	−0.0860666	−	0.0220981i	−0.00432501	−	0.00111047i
$397$	1.32939	+	21.1300i	0.0667199	+	1.06048i	0.878878	+	0.477046i	$0.158292\pi$
$397$	1.32939	+	21.1300i	0.0667199	+	1.06048i	−0.812158	+	0.583437i	$0.801708\pi$
$398$	2.09408	+	10.9775i	0.104967	+	0.550254i
$399$	1.84816	+	5.68806i	0.0925238	+	0.284759i
$400$	3.96817	−	3.04198i	0.198408	−	0.152099i
$401$	7.60631	−	23.4098i	0.379841	−	1.16903i	−0.560313	−	0.828281i	$-0.689319\pi$
$401$	7.60631	−	23.4098i	0.379841	−	1.16903i	0.940154	−	0.340749i	$-0.110681\pi$
$402$	6.25550	+	0.790253i	0.311996	+	0.0394143i
$403$	−13.4416	+	5.32192i	−0.669576	+	0.265104i
$404$	−1.95160	+	0.772692i	−0.0970956	+	0.0384429i
$405$	2.03533	+	0.925975i	0.101136	+	0.0460121i
$406$	0.593276	−	9.42986i	0.0294438	−	0.467996i
$407$	−0.0279935	−	0.0203384i	−0.00138758	−	0.00100814i
$408$	5.86206	−	1.50512i	0.290215	−	0.0745147i
$409$	26.1277	−	24.5355i	1.29193	−	1.21320i	0.328728	−	0.944425i	$-0.393380\pi$
$409$	26.1277	−	24.5355i	1.29193	−	1.21320i	0.963202	−	0.268778i	$-0.0866199\pi$
$410$	3.96622	+	3.19613i	0.195878	+	0.157846i
$411$	−13.8546	+	7.61662i	−0.683396	+	0.375700i
$412$	−5.17051	+	0.653188i	−0.254733	+	0.0321802i
$413$	3.39167	−	17.7798i	0.166893	−	0.874886i
$414$	7.75766	+	0.980020i	0.381268	+	0.0481654i
$415$	6.05933	−	6.62113i	0.297441	−	0.325018i
$416$	−0.291149	+	1.52626i	−0.0142748	+	0.0748309i
$417$	−7.86372	−	12.3912i	−0.385088	−	0.606802i
$418$	−0.299058	+	0.217279i	−0.0146274	+	0.0106274i
$419$	−10.6714	+	12.8995i	−0.521333	+	0.630184i	−0.963808	−	0.266597i	$-0.914101\pi$
$419$	−10.6714	+	12.8995i	−0.521333	+	0.630184i	0.442475	+	0.896781i	$0.354101\pi$
$420$	−3.20551	+	0.243094i	−0.156413	+	0.0118618i
$421$	−1.93495	+	3.04900i	−0.0943039	+	0.148599i	−0.888204	−	0.459449i	$-0.848047\pi$
$421$	−1.93495	+	3.04900i	−0.0943039	+	0.148599i	0.793901	+	0.608048i	$0.208047\pi$
$422$	12.2889	+	14.8548i	0.598216	+	0.723120i
$423$	−1.42686	+	3.03223i	−0.0693763	+	0.147432i
$424$	3.01736	−	2.19224i	0.146536	−	0.106465i
$425$	13.5844	+	27.0406i	0.658940	+	1.31166i
$426$	8.04797	+	5.84719i	0.389925	+	0.283297i
$427$	6.43932	−	3.54004i	0.311620	−	0.171315i
$428$	−9.10133	−	2.33683i	−0.439930	−	0.112955i
$429$	0.0880066	+	0.106382i	0.00424900	+	0.00513616i
$430$	0.889877	+	6.38288i	0.0429137	+	0.307810i
$431$	−8.85215	−	3.50481i	−0.426393	−	0.168821i	0.145120	−	0.989414i	$-0.453643\pi$
$431$	−8.85215	−	3.50481i	−0.426393	−	0.168821i	−0.571513	+	0.820593i	$0.693643\pi$
$432$	1.00000			0.0481125
$433$	−2.41322	−	0.955463i	−0.115972	−	0.0459166i	0.309422	−	0.950925i	$-0.399864\pi$
$433$	−2.41322	−	0.955463i	−0.115972	−	0.0459166i	−0.425394	+	0.905008i	$0.639864\pi$
$434$	−11.7219	−	6.44417i	−0.562670	−	0.309330i
$435$	−14.6536	+	1.11128i	−0.702588	+	0.0532818i
$436$	−1.19251	−	6.25138i	−0.0571111	−	0.299387i
$437$	23.7125	−	22.2676i	1.13432	−	1.06520i
$438$	−3.11178	+	2.92216i	−0.148687	+	0.139626i
$439$	−3.38125	−	17.7251i	−0.161378	−	0.845974i	−0.967239	−	0.253869i	$-0.918297\pi$
$439$	−3.38125	−	17.7251i	−0.161378	−	0.845974i	0.805860	−	0.592106i	$-0.201703\pi$
$440$	−0.0755134	−	0.183784i	−0.00359996	−	0.00876157i
$441$	−4.32293	−	2.37655i	−0.205854	−	0.113169i
$442$	−8.74342	−	3.46177i	−0.415882	−	0.164659i
$443$	25.4329			1.20835			0.604176	−	0.796851i	$-0.293502\pi$
$443$	25.4329			1.20835			0.604176	+	0.796851i	$0.293502\pi$
$444$	0.362059	+	0.143349i	0.0171826	+	0.00680307i
$445$	11.3279	+	11.7563i	0.536994	+	0.557303i
$446$	−16.0756	−	19.4321i	−0.761203	−	0.920136i
$447$	17.7986	+	4.56991i	0.841845	+	0.216149i
$448$	−1.25983	+	0.692600i	−0.0595216	+	0.0327223i
$449$	−6.44422	−	4.68200i	−0.304122	−	0.220957i	0.425248	−	0.905077i	$-0.360187\pi$
$449$	−6.44422	−	4.68200i	−0.304122	−	0.220957i	−0.729370	+	0.684119i	$0.760187\pi$
$450$	1.06290	+	4.88572i	0.0501057	+	0.230315i
$451$	0.163760	−	0.118978i	0.00771114	−	0.00560247i
$452$	−6.58658	+	13.9972i	−0.309807	+	0.658373i
$453$	11.8484	+	14.3223i	0.556687	+	0.672920i
$454$	10.6510	−	16.7833i	0.499875	−	0.787677i
$455$	4.25145	+	2.62198i	0.199311	+	0.122920i
$456$	2.65173	−	3.20539i	0.124178	−	0.150106i
$457$	−0.882577	+	0.641230i	−0.0412852	+	0.0299955i	−0.608236	−	0.793756i	$-0.708123\pi$
$457$	−0.882577	+	0.641230i	−0.0412852	+	0.0299955i	0.566951	+	0.823751i	$0.308123\pi$
$458$	−12.9707	−	20.4385i	−0.606080	−	0.955029i
$459$	−1.13407	+	5.94500i	−0.0529339	+	0.277489i
$460$	8.61956	+	15.2122i	0.401889	+	0.709273i
$461$	−12.3571	−	1.56107i	−0.575529	−	0.0727062i	−0.167819	−	0.985818i	$-0.553672\pi$
$461$	−12.3571	−	1.56107i	−0.575529	−	0.0727062i	−0.407710	+	0.913112i	$0.633672\pi$
$462$	−0.0239376	+	0.125485i	−0.00111368	+	0.00583811i
$463$	6.81524	−	0.860965i	0.316731	−	0.0400125i	0.0346394	−	0.999400i	$-0.488972\pi$
$463$	6.81524	−	0.860965i	0.316731	−	0.0400125i	0.282092	+	0.959387i	$0.408972\pi$
$464$	−5.75920	+	3.16614i	−0.267364	+	0.146985i
$465$	−7.40948	+	19.4410i	−0.343607	+	0.901554i
$466$	−8.09048	+	7.59746i	−0.374784	+	0.351946i
$467$	−15.5752	+	3.99904i	−0.720735	+	0.185053i	−0.591204	−	0.806522i	$-0.701347\pi$
$467$	−15.5752	+	3.99904i	−0.720735	+	0.185053i	−0.129531	+	0.991575i	$0.541347\pi$
$468$	−1.25703	−	0.913288i	−0.0581064	−	0.0422168i
$469$	0.569182	−	9.04690i	0.0262824	−	0.417747i
$470$	−7.34205	+	1.49867i	−0.338664	+	0.0691285i
$471$	−11.5611	+	4.57736i	−0.532707	+	0.210914i
$472$	−11.7060	+	4.63474i	−0.538813	+	0.213331i
$473$	0.254081	+	0.0320978i	0.0116826	+	0.00147586i
$474$	1.56209	−	4.80762i	0.0717492	−	0.220821i
$475$	18.4791	+	9.54858i	0.847881	+	0.438119i
$476$	−2.68877	−	8.27518i	−0.123239	−	0.379292i
$477$	0.698869	+	3.66360i	0.0319990	+	0.167745i
$478$	−0.862431	−	13.7079i	−0.0394467	−	0.626987i
$479$	−29.0323	−	7.45423i	−1.32652	−	0.340592i	−0.482025	−	0.876157i	$-0.660099\pi$
$479$	−29.0323	−	7.45423i	−1.32652	−	0.340592i	−0.844494	+	0.535565i	$0.820099\pi$
$480$	1.33748	+	1.79197i	0.0610474	+	0.0817917i
$481$	−0.324201	−	0.510860i	−0.0147823	−	0.0232932i
$482$	1.41214	−	4.34612i	0.0643212	−	0.197960i
$483$	0.705863	−	11.2194i	0.0321179	−	0.510499i
$484$	10.9054	−	1.37768i	0.495701	−	0.0626216i
$485$	−19.4208	−	26.0201i	−0.881852	−	1.18151i
$486$	−0.425779	+	0.904827i	−0.0193137	+	0.0410438i
$487$	−3.83494	−	8.14966i	−0.173778	−	0.369296i	0.798897	−	0.601467i	$-0.205417\pi$
$487$	−3.83494	−	8.14966i	−0.173778	−	0.369296i	−0.972675	+	0.232171i	$0.925417\pi$
$488$	−4.47902	−	2.46236i	−0.202755	−	0.111466i
$489$	4.17303	+	3.91873i	0.188711	+	0.177211i
$490$	−1.52314	−	10.9251i	−0.0688085	−	0.493547i
$491$	5.63526	+	11.9755i	0.254316	+	0.540449i	0.990692	−	0.136124i	$-0.0434645\pi$
$491$	5.63526	+	11.9755i	0.254316	+	0.540449i	−0.736376	+	0.676572i	$0.763465\pi$
$492$	−1.45204	+	1.75522i	−0.0654632	+	0.0791314i
$493$	−12.2914	−	37.8291i	−0.553577	−	1.70374i
$494$	−6.26075	+	1.60749i	−0.281685	+	0.0723243i
$495$	0.198445	+	0.00992499i	0.00891944	+	0.000446095i
$496$	0.584223	+	9.28596i	0.0262324	+	0.416952i
$497$	7.66320	−	12.0753i	0.343742	−	0.541650i
$498$	2.92597	+	2.74767i	0.131116	+	0.123126i
$499$	5.25468			0.235232			0.117616	−	0.993059i	$-0.462475\pi$
$499$	5.25468			0.235232			0.117616	+	0.993059i	$0.462475\pi$
$500$	−7.33343	+	8.43924i	−0.327961	+	0.377414i
$501$	−6.47617			−0.289334
$502$	18.3501	+	17.2319i	0.819006	+	0.769097i
$503$	−12.8544	+	20.2553i	−0.573149	+	0.903138i	−0.999999	−	0.00118403i	$-0.999623\pi$
$503$	−12.8544	+	20.2553i	−0.573149	+	0.903138i	0.426850	+	0.904322i	$0.359623\pi$
$504$	−0.0902717	−	1.43483i	−0.00402102	−	0.0639123i
$505$	3.93018	−	2.56565i	0.174891	−	0.114170i
$506$	0.672982	−	0.172792i	0.0299177	−	0.00768156i
$507$	−3.27118	−	10.0677i	−0.145278	−	0.447121i
$508$	5.72309	−	6.91802i	0.253921	−	0.306938i
$509$	17.3301	+	36.8283i	0.768143	+	1.63239i	0.774636	+	0.632407i	$0.217933\pi$
$509$	17.3301	+	36.8283i	0.768143	+	1.63239i	−0.00649349	+	0.999979i	$0.502067\pi$
$510$	−12.1700	+	5.91912i	−0.538899	+	0.262103i
$511$	4.47369	+	4.20108i	0.197905	+	0.185845i
$512$	0.876307	+	0.481754i	0.0387276	+	0.0212907i
$513$	1.77127	+	3.76414i	0.0782035	+	0.166191i
$514$	12.0382	−	25.5825i	0.530983	−	1.12840i
$515$	11.0359	−	3.74336i	0.486301	−	0.164952i
$516$	−2.85939	+	0.361225i	−0.125878	+	0.0159021i
$517$	−0.0186977	+	0.297192i	−0.000822324	+	0.0130705i
$518$	0.172998	−	0.532433i	0.00760109	−	0.0233938i
$519$	−1.44220	−	2.27254i	−0.0633055	−	0.0997535i
$520$	−0.0446779	−	3.47407i	−0.00195926	−	0.152348i
$521$	−34.7858	−	8.93148i	−1.52399	−	0.391295i	−0.608477	−	0.793572i	$-0.708219\pi$
$521$	−34.7858	−	8.93148i	−1.52399	−	0.391295i	−0.915518	+	0.402276i	$0.868219\pi$
$522$	−0.412667	−	6.55915i	−0.0180619	−	0.287086i
$523$	6.02075	+	31.5619i	0.263269	+	1.38010i	0.830717	+	0.556695i	$0.187931\pi$
$523$	6.02075	+	31.5619i	0.263269	+	1.38010i	−0.567448	+	0.823409i	$0.692069\pi$
$524$	0.680434	+	2.09416i	0.0297249	+	0.0914839i
$525$	6.91421	−	1.96612i	0.301761	−	0.0858086i
$526$	−2.20869	+	6.79765i	−0.0963034	+	0.296392i
$527$	−55.8676	−	7.05773i	−2.43363	−	0.307439i
$528$	0.0826183	−	0.0327109i	0.00359550	−	0.00142356i
$529$	−35.4633	+	14.0409i	−1.54188	+	0.610474i
$530$	−5.63033	+	6.15235i	−0.244566	+	0.267241i
$531$	0.790541	−	12.5653i	0.0343066	−	0.545287i
$532$	−4.83855	−	3.51541i	−0.209778	−	0.152413i
$533$	3.42829	−	0.880235i	0.148496	−	0.0381272i
$534$	−5.32229	+	4.99797i	−0.230318	+	0.216283i
$535$	20.9851	+	1.04954i	0.907264	+	0.0453757i
$536$	−5.52530	+	3.03756i	−0.238657	+	0.131203i
$537$	15.8903	−	2.00741i	0.685715	−	0.0866260i
$538$	0.577978	−	3.02987i	0.0249184	−	0.130627i
$539$	−0.434892	−	0.0549396i	−0.0187321	−	0.00236642i
$540$	−2.19089	+	0.447208i	−0.0942810	+	0.0192448i
$541$	−0.956410	+	5.01368i	−0.0411193	+	0.215555i	−0.996916	−	0.0784726i	$-0.974996\pi$
$541$	−0.956410	+	5.01368i	−0.0411193	+	0.215555i	0.955797	+	0.294027i	$0.0949957\pi$
$542$	15.0997	+	23.7934i	0.648589	+	1.02201i
$543$	−6.58141	+	4.78168i	−0.282436	+	0.205201i
$544$	−3.85782	+	4.66330i	−0.165403	+	0.199938i
$545$	5.40834	+	13.1628i	0.231668	+	0.563832i
$546$	−1.19694	+	1.88607i	−0.0512241	+	0.0807163i
$547$	26.4300	+	31.9484i	1.13006	+	1.36601i	0.921673	+	0.387968i	$0.126823\pi$
$547$	26.4300	+	31.9484i	1.13006	+	1.36601i	0.208392	+	0.978045i	$0.433177\pi$
$548$	6.73165	−	14.3055i	0.287562	−	0.611100i
$549$	4.13508	−	3.00431i	0.176481	−	0.128221i
$550$	0.247631	+	0.368881i	0.0105590	+	0.0157291i
$551$	−22.1189	−	16.0703i	−0.942297	−	0.684619i
$552$	−6.85212	+	3.76698i	−0.291646	+	0.160333i
$553$	−7.03911	−	1.80734i	−0.299333	−	0.0768558i
$554$	4.03376	+	4.87598i	0.171378	+	0.207161i
$555$	−0.857340	−	0.152147i	−0.0363921	−	0.00645830i
$556$	13.6453	+	5.40255i	0.578689	+	0.229119i
$557$	−34.6847			−1.46964			−0.734819	−	0.678263i	$-0.762733\pi$
$557$	−34.6847			−1.46964			−0.734819	+	0.678263i	$0.762733\pi$
$558$	−8.65094	−	3.42515i	−0.366224	−	0.144998i
$559$	3.92425	+	2.15738i	0.165978	+	0.0912473i
$560$	2.45042	−	2.08082i	0.103549	−	0.0879306i
$561$	0.100771	+	0.528263i	0.00425458	+	0.0223033i
$562$	17.2263	−	16.1766i	0.726648	−	0.682368i
$563$	17.4374	−	16.3749i	0.734901	−	0.690118i	−0.223768	−	0.974642i	$-0.571836\pi$
$563$	17.4374	−	16.3749i	0.734901	−	0.690118i	0.958669	+	0.284525i	$0.0918358\pi$
$564$	−0.627947	−	3.29181i	−0.0264413	−	0.138610i
$565$	8.17083	−	33.6119i	0.343749	−	1.41406i
$566$	−11.6980	−	6.43102i	−0.491703	−	0.270316i
$567$	1.33671	+	0.529239i	0.0561364	+	0.0222260i
$568$	−9.94783			−0.417402
$569$	−12.2300	−	4.84218i	−0.512706	−	0.202995i	0.0975027	−	0.995235i	$-0.468915\pi$
$569$	−12.2300	−	4.84218i	−0.512706	−	0.202995i	−0.610209	+	0.792240i	$0.708915\pi$
$570$	−4.37617	+	8.20853i	−0.183298	+	0.343817i
$571$	−6.24935	−	7.55416i	−0.261527	−	0.316132i	0.623362	−	0.781933i	$-0.285766\pi$
$571$	−6.24935	−	7.55416i	−0.261527	−	0.316132i	−0.884889	+	0.465801i	$0.845766\pi$
$572$	−0.133728	−	0.0343356i	−0.00559147	−	0.00143564i
$573$	20.3918	−	11.2105i	0.851878	−	0.468324i
$574$	2.64951	+	1.92499i	0.110589	+	0.0803473i
$575$	−25.6876	−	29.4736i	−1.07124	−	1.22913i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	0.0312675	−	0.0664469i	0.00130168	−	0.00276622i	−0.904175	−	0.427162i	$-0.859513\pi$
$577$	0.0312675	−	0.0664469i	0.00130168	−	0.00276622i	0.905477	+	0.424396i	$0.139513\pi$
$578$	−12.5121	−	15.1246i	−0.520436	−	0.629098i
$579$	−6.07182	+	9.56766i	−0.252336	+	0.397618i
$580$	11.2018	−	9.51224i	0.465131	−	0.394974i
$581$	3.67829	−	4.44629i	0.152601	−	0.184463i
$582$	11.7473	−	8.53488i	0.486939	−	0.353782i
$583$	0.177579	+	0.279820i	0.00735458	+	0.0115890i
$584$	0.799883	−	4.19313i	0.0330994	−	0.173513i
$585$	3.16245	+	1.43876i	0.130751	+	0.0594854i
$586$	−20.8918	−	2.63924i	−0.863030	−	0.109026i
$587$	−0.170349	+	0.892999i	−0.00703104	+	0.0368580i	−0.985630	−	0.168919i	$-0.945972\pi$
$587$	−0.170349	+	0.892999i	−0.00703104	+	0.0368580i	0.978599	+	0.205777i	$0.0659723\pi$
$588$	4.89422	−	0.618284i	0.201834	−	0.0254976i
$589$	−33.9189	+	18.6471i	−1.39760	+	0.768339i
$590$	23.5739	−	15.3892i	0.970523	−	0.633564i
$591$	3.43090	−	3.22183i	0.141128	−	0.132528i
$592$	−0.377171	+	0.0968410i	−0.0155016	+	0.00398014i
$593$	11.9221	+	8.66192i	0.489583	+	0.355703i	0.805024	−	0.593243i	$-0.202153\pi$
$593$	11.9221	+	8.66192i	0.489583	+	0.355703i	−0.315441	+	0.948945i	$0.602153\pi$
$594$	−0.00557945	+	0.0886829i	−0.000228928	+	0.00363870i
$595$	9.59152	+	16.9276i	0.393214	+	0.693963i
$596$	−17.0855	+	6.76463i	−0.699849	+	0.277090i
$597$	10.3907	−	4.11397i	0.425263	−	0.168374i
$598$	12.0537	+	1.52273i	0.492912	+	0.0622692i
$599$	5.43199	−	16.7179i	0.221945	−	0.683077i	−0.776642	−	0.629942i	$-0.783079\pi$
$599$	5.43199	−	16.7179i	0.221945	−	0.683077i	0.998587	−	0.0531348i	$-0.0169213\pi$
$600$	−3.73166	−	3.32787i	−0.152344	−	0.135860i
$601$	2.00907	+	6.18327i	0.0819516	+	0.252221i	0.983634	−	0.180178i	$-0.0576673\pi$
$601$	2.00907	+	6.18327i	0.0819516	+	0.252221i	−0.901682	+	0.432399i	$0.857667\pi$
$602$	0.776418	+	4.07012i	0.0316444	+	0.165886i
$603$	−0.395908	−	6.29278i	−0.0161226	−	0.256262i
$604$	−18.0040	−	4.62264i	−0.732572	−	0.188093i
$605$	−23.2765	+	7.89533i	−0.946324	+	0.320991i
$606$	1.12470	+	1.77224i	0.0456878	+	0.0719924i
$607$	−13.1035	+	40.3283i	−0.531853	+	1.63688i	0.218498	+	0.975837i	$0.429884\pi$
$607$	−13.1035	+	40.3283i	−0.531853	+	1.63688i	−0.750351	+	0.661039i	$0.770116\pi$
$608$	−0.261213	+	4.15186i	−0.0105936	+	0.168380i
$609$	−9.37400	+	1.18421i	−0.379854	+	0.0479867i
$610$	10.9142	+	3.39171i	0.441904	+	0.137326i
$611$	−2.21702	+	4.71141i	−0.0896912	+	0.190603i
$612$	−2.57690	−	5.47620i	−0.104165	−	0.221362i
$613$	−22.0966	−	12.1477i	−0.892472	−	0.490641i	−0.0316222	−	0.999500i	$-0.510067\pi$
$613$	−22.0966	−	12.1477i	−0.892472	−	0.490641i	−0.860850	+	0.508859i	$0.830067\pi$
$614$	4.32444	+	4.06092i	0.174520	+	0.163885i
$615$	2.39632	−	4.49486i	0.0966291	−	0.181250i
$616$	−0.0543926	−	0.115590i	−0.00219154	−	0.00465726i
$617$	−1.00997	+	1.22084i	−0.0406598	+	0.0491493i	−0.790451	−	0.612525i	$-0.790154\pi$
$617$	−1.00997	+	1.22084i	−0.0406598	+	0.0491493i	0.749791	+	0.661674i	$0.230154\pi$
$618$	1.61048	+	4.95653i	0.0647828	+	0.199381i
$619$	−21.1918	+	5.44113i	−0.851771	+	0.218698i	−0.649245	−	0.760579i	$-0.724915\pi$
$619$	−21.1918	+	5.44113i	−0.851771	+	0.218698i	−0.202526	+	0.979277i	$0.564915\pi$
$620$	−5.43272	−	20.0833i	−0.218183	−	0.806564i
$621$	−0.490979	−	7.80389i	−0.0197023	−	0.313159i
$622$	−16.8502	+	26.5517i	−0.675633	+	1.06463i
$623$	7.65167	+	7.18540i	0.306558	+	0.287877i
$624$	1.55378			0.0622009
$625$	12.2927	−	21.7690i	0.491706	−	0.870761i
$626$	17.8465			0.713289
$627$	0.269468	+	0.253047i	0.0107615	+	0.0101057i
$628$	6.66261	−	10.4986i	0.265867	−	0.418940i
$629$	−0.147982	−	2.35211i	−0.00590043	−	0.0937847i
$630$	0.839441	+	3.10318i	0.0334441	+	0.123634i
$631$	−8.29254	+	2.12916i	−0.330121	+	0.0847606i	−0.410113	−	0.912035i	$-0.634511\pi$
$631$	−8.29254	+	2.12916i	−0.330121	+	0.0847606i	0.0799918	+	0.996796i	$0.474511\pi$
$632$	1.56209	+	4.80762i	0.0621366	+	0.191237i
$633$	12.2889	−	14.8548i	0.488442	−	0.590425i
$634$	4.27624	+	9.08747i	0.169831	+	0.360910i
$635$	−9.44487	+	17.7160i	−0.374808	+	0.703040i
$636$	−2.71881	−	2.55313i	−0.107808	−	0.101238i
$637$	−6.71687	−	3.69263i	−0.266132	−	0.146307i
$638$	−0.248650	−	0.528408i	−0.00984414	−	0.0209199i
$639$	4.23558	−	9.00107i	0.167557	−	0.356077i
$640$	−2.13534	−	0.663579i	−0.0844066	−	0.0262303i
$641$	38.6441	−	4.88188i	1.52635	−	0.192823i	0.683092	−	0.730332i	$-0.260635\pi$
$641$	38.6441	−	4.88188i	1.52635	−	0.192823i	0.843258	+	0.537509i	$0.180635\pi$
$642$	−0.590014	+	9.37800i	−0.0232860	+	0.370120i
$643$	−7.71306	+	23.7383i	−0.304173	+	0.936149i	0.675811	+	0.737075i	$0.263793\pi$
$643$	−7.71306	+	23.7383i	−0.304173	+	0.936149i	−0.979984	+	0.199074i	$0.936207\pi$
$644$	6.02352	+	9.49155i	0.237360	+	0.374020i
$645$	6.10307	−	2.07015i	0.240308	−	0.0815120i
$646$	−24.3866	−	6.26141i	−0.959477	−	0.246352i
$647$	0.784198	+	12.4645i	0.0308300	+	0.490029i	0.982899	+	0.184145i	$0.0589518\pi$
$647$	0.784198	+	12.4645i	0.0308300	+	0.490029i	−0.952069	+	0.305883i	$0.901048\pi$
$648$	−0.187381	−	0.982287i	−0.00736103	−	0.0385879i
$649$	−0.345709	−	1.06398i	−0.0135703	−	0.0417650i
$650$	1.65151	+	7.59132i	0.0647777	+	0.297756i
$651$	−4.13356	+	12.7218i	−0.162007	+	0.498607i
$652$	−5.67943	−	0.717478i	−0.222423	−	0.0280986i
$653$	−17.8878	+	7.08229i	−0.700005	+	0.277151i	−0.691048	−	0.722808i	$-0.742851\pi$
$653$	−17.8878	+	7.08229i	−0.700005	+	0.277151i	−0.00895625	+	0.999960i	$0.502851\pi$
$654$	−5.91720	+	2.34278i	−0.231381	+	0.0916101i
$655$	−2.42728	−	4.28379i	−0.0948418	−	0.167381i
$656$	0.143036	−	2.27349i	0.00558462	−	0.0887650i
$657$	3.45349	+	2.50910i	0.134733	+	0.0978895i
$658$	−4.66650	+	1.19815i	−0.181919	+	0.0467088i
$659$	6.47410	−	6.07959i	0.252195	−	0.236827i	−0.548130	−	0.836393i	$-0.684660\pi$
$659$	6.47410	−	6.07959i	0.252195	−	0.236827i	0.800325	+	0.599566i	$0.204660\pi$
$660$	−0.166379	+	0.108614i	−0.00647630	+	0.00422778i
$661$	−3.31459	+	1.82221i	−0.128923	+	0.0708757i	−0.544910	−	0.838495i	$-0.683436\pi$
$661$	−3.31459	+	1.82221i	−0.128923	+	0.0708757i	0.415987	+	0.909370i	$0.363436\pi$
$662$	24.0464	−	3.03777i	0.934591	−	0.118066i
$663$	−1.76209	+	9.23722i	−0.0684341	+	0.358744i
$664$	−3.98220	−	0.503068i	−0.154539	−	0.0195228i
$665$	12.1729	+	5.53805i	0.472043	+	0.214756i
$666$	0.0729672	−	0.382507i	0.00282742	−	0.0148219i
$667$	27.5359	+	43.3896i	1.06619	+	1.68005i
$668$	5.23933	−	3.80660i	0.202716	−	0.147282i
$669$	−16.0756	+	19.4321i	−0.621520	+	0.751288i
$670$	10.7469	−	9.12593i	0.415190	−	0.352565i
$671$	0.243360	−	0.383473i	0.00939479	−	0.0148038i
$672$	0.916401	+	1.10774i	0.0353510	+	0.0427320i
$673$	−11.7454	+	24.9602i	−0.452751	+	0.962144i	0.539968	+	0.841686i	$0.318436\pi$
$673$	−11.7454	+	24.9602i	−0.452751	+	0.962144i	−0.992718	+	0.120458i	$0.961564\pi$
$674$	4.32625	−	3.14320i	0.166641	−	0.121072i
$675$	4.60001	−	1.95957i	0.177054	−	0.0754238i
$676$	8.56407	+	6.22216i	0.329387	+	0.239314i
$677$	−14.0950	+	7.74878i	−0.541714	+	0.297810i	−0.729021	−	0.684492i	$-0.760024\pi$
$677$	−14.0950	+	7.74878i	−0.541714	+	0.297810i	0.187307	+	0.982301i	$0.440024\pi$
$678$	14.9835	+	3.84710i	0.575437	+	0.147747i
$679$	−13.3065	−	16.0848i	−0.510657	−	0.617279i
$680$	6.36660	−	11.9420i	0.244148	−	0.457956i
$681$	−18.4818	−	7.31745i	−0.708223	−	0.280405i
$682$	−0.826766			−0.0316585
$683$	−31.2359	−	12.3672i	−1.19521	−	0.473216i	−0.315589	−	0.948896i	$-0.602202\pi$
$683$	−31.2359	−	12.3672i	−1.19521	−	0.473216i	−0.879619	+	0.475680i	$0.842202\pi$
$684$	−3.64550	−	2.00413i	−0.139389	−	0.0766297i
$685$	−8.35079	+	34.3522i	−0.319067	+	1.31253i
$686$	−3.21468	−	16.8519i	−0.122737	−	0.643410i
$687$	−17.6460	+	16.5707i	−0.673238	+	0.632212i
$688$	2.10097	−	1.97295i	0.0800989	−	0.0752179i
$689$	1.08589	+	5.69243i	0.0413691	+	0.216864i
$690$	13.3276	−	11.3174i	0.507374	−	0.430845i
$691$	−9.43745	−	5.18828i	−0.359017	−	0.197371i	0.292029	−	0.956409i	$-0.405670\pi$
$691$	−9.43745	−	5.18828i	−0.359017	−	0.197371i	−0.651046	+	0.759038i	$0.725670\pi$
$692$	2.50253	+	0.990822i	0.0951319	+	0.0376654i
$693$	0.127748			0.00485276
$694$	11.0787	+	4.38637i	0.420542	+	0.166504i
$695$	−32.3114	−	5.73412i	−1.22564	−	0.217508i
$696$	4.18923	+	5.06391i	0.158792	+	0.191947i
$697$	13.3537	+	3.42865i	0.505808	+	0.129869i
$698$	−0.507864	+	0.279201i	−0.0192229	+	0.0105679i
$699$	8.97889	+	6.52355i	0.339613	+	0.246743i
$700$	−4.43806	+	5.65470i	−0.167743	+	0.213727i
$701$	−26.7883	+	19.4628i	−1.01178	+	0.735101i	−0.964582	−	0.263784i	$-0.915029\pi$
$701$	−26.7883	+	19.4628i	−1.01178	+	0.735101i	−0.0471982	+	0.998886i	$0.515029\pi$
$702$	−0.661567	+	1.40590i	−0.0249692	+	0.0530623i
$703$	−1.03260	−	1.24819i	−0.0389451	−	0.0470765i
$704$	−0.0476126	+	0.0750255i	−0.00179447	+	0.00282763i
$705$	2.84789	+	6.93118i	0.107258	+	0.261043i
$706$	16.7264	−	20.2187i	0.629505	−	0.760941i
$707$	2.44133	−	1.77373i	0.0918157	−	0.0667080i
$708$	6.74613	+	10.6302i	0.253535	+	0.399507i
$709$	−2.89856	+	15.1948i	−0.108858	+	0.570652i	0.885506	+	0.464628i	$0.153812\pi$
$709$	−2.89856	+	15.1948i	−0.108858	+	0.570652i	−0.994364	+	0.106024i	$0.966188\pi$
$710$	21.7946	−	4.44875i	0.817938	−	0.166959i
$711$	−5.01517	−	0.633563i	−0.188084	−	0.0237605i
$712$	1.36810	−	7.17181i	0.0512715	−	0.268775i
$713$	72.1798	−	9.11842i	2.70315	−	0.341488i
$714$	−7.62478	+	4.19176i	−0.285350	+	0.156873i
$715$	0.308340	+	0.0154212i	0.0115312	+	0.000576722i
$716$	−11.6756	+	10.9641i	−0.436336	+	0.409747i
$717$	−13.3035	+	3.41577i	−0.496830	+	0.127564i
$718$	8.64948	+	6.28422i	0.322796	+	0.234525i
$719$	−1.36302	+	21.6645i	−0.0508319	+	0.807950i	0.887197	+	0.461392i	$0.152650\pi$
$719$	−1.36302	+	21.6645i	−0.0508319	+	0.807950i	−0.938028	+	0.346558i	$0.887350\pi$
$720$	1.50961	−	1.64957i	0.0562597	−	0.0614759i
$721$	6.96639	−	2.75819i	0.259442	−	0.102720i
$722$	1.57489	−	0.623542i	0.0586113	−	0.0232058i
$723$	−4.53375	−	0.572745i	−0.168612	−	0.0213006i
$724$	2.51388	−	7.73692i	0.0934275	−	0.287540i
$725$	−20.2881	+	25.8498i	−0.753481	+	0.960039i
$726$	−3.39675	−	10.4541i	−0.126065	−	0.387988i
$727$	−1.67119	−	8.76067i	−0.0619809	−	0.324915i	0.937769	−	0.347259i	$-0.112887\pi$
$727$	−1.67119	−	8.76067i	−0.0619809	−	0.324915i	−0.999750	+	0.0223431i	$0.992887\pi$
$728$	−0.140262	−	2.22940i	−0.00519846	−	0.0826272i
$729$	0.968583	+	0.248690i	0.0358735	+	0.00921074i
$730$	0.122745	+	9.54441i	0.00454300	+	0.353255i
$731$	9.34652	+	14.7278i	0.345693	+	0.544726i
$732$	−1.57946	+	4.86108i	−0.0583785	+	0.179671i
$733$	−1.18306	+	18.8042i	−0.0436973	+	0.694549i	0.913810	+	0.406141i	$0.133126\pi$
$733$	−1.18306	+	18.8042i	−0.0436973	+	0.694549i	−0.957508	+	0.288408i	$0.906874\pi$
$734$	−2.92058	+	0.368955i	−0.107801	+	0.0136184i
$735$	−10.4462	+	3.54333i	−0.385314	+	0.130698i
$736$	3.32930	−	7.07513i	0.122720	−	0.260793i
$737$	−0.238552	−	0.506948i	−0.00878716	−	0.0186737i
$738$	1.99622	+	1.09743i	0.0734817	+	0.0403969i
$739$	−27.7590	−	26.0674i	−1.02113	−	0.958906i	−0.0219659	−	0.999759i	$-0.506993\pi$
$739$	−27.7590	−	26.0674i	−1.02113	−	0.958906i	−0.999165	+	0.0408528i	$0.986993\pi$
$740$	0.783033	−	0.380842i	0.0287848	−	0.0140000i
$741$	2.75216	+	5.84864i	0.101103	+	0.214855i
$742$	−3.41787	+	4.13149i	−0.125474	+	0.151672i
$743$	−10.1739	−	31.3119i	−0.373243	−	1.14872i	−0.944657	−	0.328061i	$-0.893605\pi$
$743$	−10.1739	−	31.3119i	−0.373243	−	1.14872i	0.571414	−	0.820662i	$-0.306395\pi$
$744$	9.01201	−	2.31389i	0.330396	−	0.0848314i
$745$	34.4073	−	22.4613i	1.26059	−	0.822920i
$746$	0.199925	+	3.17771i	0.00731976	+	0.116344i
$747$	2.15073	−	3.38900i	0.0786910	−	0.123997i
$748$	−0.392031	−	0.368141i	−0.0143341	−	0.0134606i
$749$	13.5091			0.493611
$750$	9.66391	+	5.62218i	0.352876	+	0.205293i
$751$	−9.32373			−0.340228			−0.170114	−	0.985424i	$-0.554414\pi$
$751$	−9.32373			−0.340228			−0.170114	+	0.985424i	$0.554414\pi$
$752$	2.44290	+	2.29403i	0.0890834	+	0.0836548i
$753$	13.4882	−	21.2540i	0.491538	−	0.774539i
$754$	−0.641193	−	10.1915i	−0.0233509	−	0.371152i
$755$	41.5121	+	2.07618i	1.51078	+	0.0755598i
$756$	−1.39250	+	0.357532i	−0.0506446	+	0.0130033i
$757$	11.3628	+	34.9711i	0.412988	+	1.27105i	0.914038	+	0.405629i	$0.132947\pi$
$757$	11.3628	+	34.9711i	0.412988	+	1.27105i	−0.501050	+	0.865418i	$0.667053\pi$
$758$	−17.1094	+	20.6817i	−0.621441	+	0.751193i
$759$	−0.295836	−	0.628683i	−0.0107382	−	0.0228198i
$760$	−1.28445	−	9.21309i	−0.0465921	−	0.334194i
$761$	34.3051	+	32.2147i	1.24356	+	1.16778i	0.979099	+	0.203384i	$0.0651940\pi$
$761$	34.3051	+	32.2147i	1.24356	+	1.16778i	0.264461	+	0.964396i	$0.414806\pi$
$762$	−7.86789	−	4.32541i	−0.285023	−	0.156693i
$763$	3.89564	+	8.27867i	0.141032	+	0.299708i
$764$	−9.90794	+	21.0554i	−0.358457	+	0.761759i
$765$	8.09472	+	10.8453i	0.292665	+	0.392114i
$766$	13.9237	−	1.75897i	0.503082	−	0.0635541i
$767$	1.22833	−	19.5237i	0.0443523	−	0.704959i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	26.0084	+	40.9826i	0.937886	+	1.47787i	0.877432	+	0.479701i	$0.159255\pi$
$769$	26.0084	+	40.9826i	0.937886	+	1.47787i	0.0604541	+	0.998171i	$0.480745\pi$
$770$	0.170861	+	0.228921i	0.00615740	+	0.00824972i
$771$	−27.3851	−	7.03130i	−0.986250	−	0.253226i
$772$	−0.711523	−	11.3093i	−0.0256083	−	0.407032i
$773$	3.41537	+	17.9040i	0.122842	+	0.643963i	0.989439	+	0.144953i	$0.0463030\pi$
$773$	3.41537	+	17.9040i	0.122842	+	0.643963i	−0.866596	+	0.499010i	$0.833697\pi$
$774$	0.890624	+	2.74106i	0.0320128	+	0.0985253i
$775$	20.8839	+	41.5707i	0.750172	+	1.49326i
$776$	−4.48705	+	13.8097i	−0.161076	+	0.495740i
$777$	−0.555419	−	0.0701657i	−0.0199255	−	0.00251718i
$778$	24.1807	−	9.57382i	0.866920	−	0.343238i
$779$	8.81110	−	3.48856i	0.315691	−	0.124991i
$780$	−3.40416	+	0.694862i	−0.121888	+	0.0248800i
$781$	0.0555035	−	0.882203i	0.00198607	−	0.0315677i
$782$	38.2860	+	27.8164i	1.36910	+	0.994713i
$783$	−6.36565	+	1.63442i	−0.227490	+	0.0584094i
$784$	−3.59609	+	3.37695i	−0.128432	+	0.120606i
$785$	−9.90201	+	25.9809i	−0.353418	+	0.927297i
$786$	1.92957	−	1.06079i	0.0688254	−	0.0378371i
$787$	−1.09277	+	0.138049i	−0.0389531	+	0.00492092i	−0.144786	−	0.989463i	$-0.546249\pi$
$787$	−1.09277	+	0.138049i	−0.0389531	+	0.00492092i	0.105833	+	0.994384i	$0.466249\pi$
$788$	−0.881912	+	4.62315i	−0.0314168	+	0.164693i
$789$	7.09111	+	0.895815i	0.252450	+	0.0318919i
$790$	−5.57237	−	9.83439i	−0.198256	−	0.349892i
$791$	4.16734	−	21.8460i	0.148174	−	0.776753i
$792$	−0.0476126	−	0.0750255i	−0.00169184	−	0.00266591i
$793$	6.42500	−	4.66804i	0.228158	−	0.165767i
$794$	−13.4954	+	16.3131i	−0.478933	+	0.578931i
$795$	7.09839	+	4.37776i	0.251754	+	0.155263i
$796$	−5.98813	+	9.43578i	−0.212244	+	0.334442i
$797$	25.3434	+	30.6348i	0.897708	+	1.08514i	0.995944	+	0.0899789i	$0.0286800\pi$
$797$	25.3434	+	30.6348i	0.897708	+	1.08514i	−0.0982361	+	0.995163i	$0.531320\pi$
$798$	−2.54649	+	5.41157i	−0.0901448	+	0.191568i
$799$	−16.4085	+	11.9214i	−0.580490	+	0.421751i
$800$	4.97505	+	0.498890i	0.175895	+	0.0176384i
$801$	5.90674	+	4.29150i	0.208704	+	0.151633i
$802$	21.5699	−	11.8581i	0.761659	−	0.418726i
$803$	0.367396	+	0.0943313i	0.0129651	+	0.00332888i
$804$	4.01910	+	4.85825i	0.141743	+	0.171337i
$805$	−17.4416	−	18.1012i	−0.614735	−	0.637983i
$806$	−13.4416	−	5.32192i	−0.473462	−	0.187457i
$807$	−3.08450			−0.108580
$808$	−1.95160	−	0.772692i	−0.0686570	−	0.0271832i
$809$	24.8523	+	13.6627i	0.873762	+	0.480355i	0.854495	−	0.519460i	$-0.173867\pi$
$809$	24.8523	+	13.6627i	0.873762	+	0.480355i	0.0192670	+	0.999814i	$0.493867\pi$
$810$	0.849819	+	2.06829i	0.0298596	+	0.0726722i
$811$	4.20663	+	22.0519i	0.147715	+	0.774348i	0.976622	+	0.214962i	$0.0689629\pi$
$811$	4.20663	+	22.0519i	0.147715	+	0.774348i	−0.828908	+	0.559386i	$0.811037\pi$
$812$	6.88766	−	6.46795i	0.241710	−	0.226980i
$813$	20.5425	−	19.2907i	0.720457	−	0.676554i
$814$	−0.00648374	−	0.0339889i	−0.000227255	−	0.00119131i
$815$	12.7639	−	0.967966i	0.447099	−	0.0339064i
$816$	5.30359	+	2.91567i	0.185663	+	0.102069i
$817$	11.1478	+	4.41374i	0.390014	+	0.154417i
$818$	35.8420			1.25318
$819$	2.07695	+	0.822321i	0.0725743	+	0.0287342i
$820$	0.703347	+	5.04494i	0.0245619	+	0.176177i
$821$	−29.7981	−	36.0197i	−1.03996	−	1.25710i	−0.965646	−	0.259860i	$-0.916323\pi$
$821$	−29.7981	−	36.0197i	−1.03996	−	1.25710i	−0.0743136	−	0.997235i	$-0.523677\pi$
$822$	−15.3135	−	3.93183i	−0.534119	−	0.137138i
$823$	30.5064	−	16.7710i	1.06339	−	0.584602i	0.148748	−	0.988875i	$-0.452476\pi$
$823$	30.5064	−	16.7710i	1.06339	−	0.584602i	0.914638	+	0.404274i	$0.132476\pi$
$824$	−4.21628	−	3.06331i	−0.146881	−	0.106715i
$825$	0.315946	−	0.312367i	0.0109998	−	0.0108752i
$826$	14.6435	−	10.6391i	0.509513	−	0.370183i
$827$	−1.48215	+	3.14974i	−0.0515395	+	0.109527i	−0.928938	−	0.370235i	$-0.879277\pi$
$827$	−1.48215	+	3.14974i	−0.0515395	+	0.109527i	0.877399	+	0.479762i	$0.159277\pi$
$828$	4.98422	+	6.02489i	0.173214	+	0.209379i
$829$	−21.1074	+	33.2600i	−0.733092	+	1.15517i	0.249316	+	0.968422i	$0.419794\pi$
$829$	−21.1074	+	33.2600i	−0.733092	+	1.15517i	−0.982408	+	0.186746i	$0.940206\pi$
$830$	8.94953	−	0.678701i	0.310643	−	0.0235580i
$831$	4.03376	−	4.87598i	0.139930	−	0.169146i
$832$	−1.25703	+	0.913288i	−0.0435798	+	0.0316626i
$833$	−15.9978	−	25.2085i	−0.554291	−	0.873422i
$834$	2.74998	−	14.4159i	0.0952241	−	0.499182i
$835$	−9.77646	+	10.6829i	−0.338328	+	0.369697i
$836$	−0.366741	−	0.0463302i	−0.0126840	−	0.00160236i
$837$	−1.74346	+	9.13952i	−0.0602627	+	0.315908i
$838$	−16.6095	+	2.09827i	−0.573765	+	0.0724834i
$839$	−9.11254	+	5.00966i	−0.314600	+	0.172953i	−0.631229	−	0.775597i	$-0.717449\pi$
$839$	−9.11254	+	5.00966i	−0.314600	+	0.172953i	0.316629	+	0.948550i	$0.397449\pi$
$840$	−2.50313	−	2.01711i	−0.0863660	−	0.0695970i
$841$	10.3461	−	9.71564i	0.356762	−	0.335022i
$842$	−3.49770	+	0.898058i	−0.120539	+	0.0309491i
$843$	−19.1179	−	13.8900i	−0.658457	−	0.478397i
$844$	−1.21054	+	19.2410i	−0.0416686	+	0.662304i
$845$	−21.5455	−	9.80216i	−0.741189	−	0.337205i
$846$	−3.11584	+	1.23365i	−0.107125	+	0.0424137i
$847$	−14.6932	+	5.81745i	−0.504865	+	0.199890i
$848$	3.70026	+	0.467451i	0.127067	+	0.0160523i
$849$	−4.12513	+	12.6958i	−0.141574	+	0.435720i
$850$	−8.60796	+	29.0109i	−0.295251	+	0.995066i
$851$	0.940919	+	2.89585i	0.0322543	+	0.0992685i
$852$	1.86404	+	9.77163i	0.0638609	+	0.334771i
$853$	−1.71731	−	27.2958i	−0.0587994	−	0.934590i	−0.911268	−	0.411813i	$-0.864896\pi$
$853$	−1.71731	−	27.2958i	−0.0587994	−	0.934590i	0.852469	−	0.522778i	$-0.175104\pi$
$854$	7.11739	+	1.82743i	0.243552	+	0.0625335i
$855$	8.88315	+	2.76053i	0.303797	+	0.0944082i
$856$	−5.03492	−	7.93376i	−0.172090	−	0.271170i
$857$	2.58239	−	7.94777i	0.0882126	−	0.271490i	−0.897213	−	0.441598i	$-0.854412\pi$
$857$	2.58239	−	7.94777i	0.0882126	−	0.271490i	0.985425	+	0.170108i	$0.0544116\pi$
$858$	−0.00866924	+	0.137794i	−0.000295963	+	0.00470420i
$859$	−50.0623	+	6.32434i	−1.70810	+	0.215784i	−0.917830	−	0.396973i	$-0.870061\pi$
$859$	−50.0623	+	6.32434i	−1.70810	+	0.215784i	−0.790272	+	0.612756i	$0.790061\pi$
$860$	−3.72069	+	5.26208i	−0.126874	+	0.179435i
$861$	1.39442	−	2.96329i	0.0475217	−	0.100989i
$862$	−4.05373	−	8.61461i	−0.138071	−	0.293415i
$863$	−4.52102	−	2.48545i	−0.153897	−	0.0846058i	0.402944	−	0.915225i	$-0.367987\pi$
$863$	−4.52102	−	2.48545i	−0.153897	−	0.0846058i	−0.556841	+	0.830619i	$0.687987\pi$
$864$	0.728969	+	0.684547i	0.0248000	+	0.0232888i
$865$	−5.92587	−	1.05163i	−0.201486	−	0.0357566i
$866$	−1.10511	−	2.34847i	−0.0375530	−	0.0798042i
$867$	−12.5121	+	15.1246i	−0.424934	+	0.513657i
$868$	−4.13356	−	12.7218i	−0.140302	−	0.431806i
$869$	−0.435069	+	0.111707i	−0.0147587	+	0.00378939i
$870$	−11.4428	−	9.22102i	−0.387946	−	0.312622i
$871$	−0.615153	−	9.77758i	−0.0208437	−	0.331301i
$872$	3.41006	−	5.37339i	0.115479	−	0.181966i
$873$	−10.5849	−	9.93990i	−0.358245	−	0.336415i
$874$	32.5289			1.10031
$875$	7.19447	−	14.3736i	0.243218	−	0.485915i
$876$	−4.26874			−0.144228
$877$	−38.7913	−	36.4275i	−1.30989	−	1.23007i	−0.955507	−	0.294968i	$-0.904691\pi$
$877$	−38.7913	−	36.4275i	−1.30989	−	1.23007i	−0.354383	−	0.935100i	$-0.615309\pi$
$878$	9.66886	−	15.2357i	0.326308	−	0.514180i
$879$	1.32223	+	21.0162i	0.0445977	+	0.708860i
$880$	0.0707621	−	0.185665i	0.00238539	−	0.00625878i
$881$	−24.4960	+	6.28952i	−0.825293	+	0.211899i	−0.637638	−	0.770336i	$-0.720089\pi$
$881$	−24.4960	+	6.28952i	−0.825293	+	0.211899i	−0.187654	+	0.982235i	$0.560089\pi$
$882$	−1.52442	−	4.69168i	−0.0513299	−	0.157977i
$883$	−30.1903	+	36.4938i	−1.01599	+	1.22812i	−0.0425638	+	0.999094i	$0.513553\pi$
$883$	−30.1903	+	36.4938i	−1.01599	+	1.22812i	−0.973421	+	0.229021i	$0.926447\pi$
$884$	−4.00394	−	8.50880i	−0.134667	−	0.286182i
$885$	−19.5340	−	20.2727i	−0.656627	−	0.681459i
$886$	18.5398	+	17.4100i	0.622856	+	0.584900i
$887$	−10.8809	−	5.98181i	−0.365344	−	0.200849i	0.288498	−	0.957480i	$-0.406844\pi$
$887$	−10.8809	−	5.98181i	−0.365344	−	0.200849i	−0.653842	+	0.756631i	$0.726844\pi$
$888$	0.165801	+	0.352344i	0.00556390	+	0.0118239i
$889$	−5.49596	+	11.6795i	−0.184329	+	0.391718i
$890$	0.209939	+	16.3245i	0.00703718	+	0.547198i
$891$	0.0881576	−	0.0111369i	0.00295339	−	0.000373100i
$892$	1.58356	−	25.1699i	0.0530214	−	0.842751i
$893$	−4.30804	+	13.2588i	−0.144163	+	0.443688i
$894$	9.84631	+	15.5153i	0.329310	+	0.518909i
$895$	20.6767	−	29.2425i	0.691145	−	0.977470i
$896$	−1.39250	−	0.357532i	−0.0465201	−	0.0119443i
$897$	−0.762872	−	12.1255i	−0.0254716	−	0.404859i
$898$	−1.49259	−	7.82441i	−0.0498082	−	0.261104i
$899$	−18.8961	−	58.1563i	−0.630221	−	1.93962i
$900$	−2.56968	+	4.28914i	−0.0856561	+	0.142971i
$901$	−6.97535	+	21.4679i	−0.232383	+	0.715200i
$902$	0.200822	+	0.0253697i	0.00668664	+	0.000844719i
$903$	3.85254	−	1.52533i	0.128205	−	0.0507598i
$904$	−14.3832	+	5.69469i	−0.478377	+	0.189403i
$905$	−2.04762	+	18.0750i	−0.0680652	+	0.600832i
$906$	−1.16715	+	18.5513i	−0.0387759	+	0.616326i
$907$	15.4085	+	11.1949i	0.511630	+	0.371721i	0.813442	−	0.581646i	$-0.197591\pi$
$907$	15.4085	+	11.1949i	0.511630	+	0.371721i	−0.301811	+	0.953368i	$0.597591\pi$
$908$	19.2532	−	4.94337i	0.638938	−	0.164051i
$909$	1.53010	−	1.43686i	0.0507503	−	0.0476577i
$910$	1.30431	+	4.82165i	0.0432373	+	0.159836i
$911$	−43.8601	+	24.1123i	−1.45315	+	0.798877i	−0.995900	−	0.0904606i	$-0.971166\pi$
$911$	−43.8601	+	24.1123i	−1.45315	+	0.798877i	−0.457252	+	0.889337i	$0.651166\pi$
$912$	4.12726	−	0.521395i	0.136667	−	0.0172651i
$913$	0.0668320	−	0.350346i	0.00221182	−	0.0115948i
$914$	−1.08232	−	0.136729i	−0.0358001	−	0.00452260i
$915$	1.28651	−	11.3564i	0.0425308	−	0.375432i
$916$	4.53591	−	23.7781i	0.149871	−	0.785649i
$917$	−1.69623	−	2.67284i	−0.0560146	−	0.0882648i
$918$	−4.89634	+	3.55740i	−0.161603	+	0.117412i
$919$	30.0484	−	36.3223i	0.991206	−	1.19816i	0.0110490	−	0.999939i	$-0.496483\pi$
$919$	30.0484	−	36.3223i	0.991206	−	1.19816i	0.980157	−	0.198223i	$-0.0635171\pi$
$920$	−4.13009	+	16.9897i	−0.136165	+	0.560135i
$921$	3.17867	−	5.00878i	0.104741	−	0.165045i
$922$	−7.93934	−	9.59701i	−0.261468	−	0.316061i
$923$	6.58116	−	13.9857i	0.216621	−	0.460344i
$924$	−0.103351	+	0.0750885i	−0.00339998	+	0.00247023i
$925$	−1.54522	+	1.18456i	−0.0508066	+	0.0389481i
$926$	5.55747	+	4.03774i	0.182630	+	0.132688i
$927$	4.56697	−	2.51071i	0.149999	−	0.0824626i
$928$	−6.36565	−	1.63442i	−0.208963	−	0.0536525i
$929$	33.2271	+	40.1647i	1.09015	+	1.31776i	0.944532	+	0.328419i	$0.106516\pi$
$929$	33.2271	+	40.1647i	1.09015	+	1.31776i	0.145615	+	0.989341i	$0.453484\pi$
$930$	−18.7095	+	9.09973i	−0.613510	+	0.298392i
$931$	−19.0810	−	7.55470i	−0.625354	−	0.247595i
$932$	−11.0985			−0.363544
$933$	29.2389	+	11.5765i	0.957237	+	0.378997i
$934$	−14.0914	−	7.74680i	−0.461084	−	0.253483i
$935$	1.02353	+	0.631239i	0.0334731	+	0.0206437i
$936$	−0.291149	−	1.52626i	−0.00951651	−	0.0498873i
$937$	−33.9050	+	31.8389i	−1.10763	+	1.04013i	−0.108690	+	0.994076i	$0.534666\pi$
$937$	−33.9050	+	31.8389i	−1.10763	+	1.04013i	−0.998939	+	0.0460569i	$0.985334\pi$
$938$	6.60794	−	6.20527i	0.215757	−	0.202609i
$939$	−3.34410	−	17.5304i	−0.109130	−	0.572082i
$940$	−6.37804	−	3.93350i	−0.208029	−	0.128297i
$941$	−39.7583	−	21.8573i	−1.29608	−	0.712528i	−0.323754	−	0.946141i	$-0.604945\pi$
$941$	−39.7583	−	21.8573i	−1.29608	−	0.712528i	−0.972330	+	0.233613i	$0.924945\pi$
$942$	−11.5611	−	4.57736i	−0.376681	−	0.149138i
$943$	−17.8123			−0.580048
$944$	−11.7060	−	4.63474i	−0.380998	−	0.150848i
$945$	2.89092	−	1.40605i	0.0940416	−	0.0457388i
$946$	0.163244	+	0.197328i	0.00530753	+	0.00641570i
$947$	19.0528	+	4.89193i	0.619134	+	0.158966i	0.545213	−	0.838298i	$-0.316449\pi$
$947$	19.0528	+	4.89193i	0.619134	+	0.158966i	0.0739207	+	0.997264i	$0.476449\pi$
$948$	4.42976	−	2.43528i	0.143872	−	0.0790942i
$949$	5.36595	+	3.89859i	0.174186	+	0.126554i
$950$	6.93427	+	19.6105i	0.224977	+	0.636247i
$951$	8.12522	−	5.90332i	0.263478	−	0.191428i
$952$	3.70472	−	7.87293i	0.120071	−	0.255163i
$953$	2.45365	+	2.96595i	0.0794815	+	0.0960767i	0.808755	−	0.588146i	$-0.200142\pi$
$953$	2.45365	+	2.96595i	0.0794815	+	0.0960767i	−0.729274	+	0.684222i	$0.760142\pi$
$954$	−1.99845	+	3.14906i	−0.0647023	+	0.101955i
$955$	12.2911	−	50.5611i	0.397729	−	1.63612i
$956$	8.75505	−	10.5830i	0.283159	−	0.342280i
$957$	−0.472456	+	0.343259i	−0.0152723	+	0.0110960i
$958$	−16.0609	−	25.3079i	−0.518903	−	0.817660i
$959$	−4.25913	+	22.3271i	−0.137534	+	0.720981i
$960$	−0.251703	+	2.22186i	−0.00812367	+	0.0717101i
$961$	−55.1323	−	6.96482i	−1.77846	−	0.224672i
$962$	0.113375	−	0.594332i	0.00365535	−	0.0191620i
$963$	9.32245	−	1.17770i	0.300412	−	0.0379508i
$964$	4.00453	−	2.20151i	0.128977	−	0.0709058i
$965$	6.61649	+	24.4593i	0.212992	+	0.787373i
$966$	8.19474	−	7.69537i	0.263661	−	0.247594i
$967$	24.0733	−	6.18098i	0.774146	−	0.198767i	0.159105	−	0.987262i	$-0.449139\pi$
$967$	24.0733	−	6.18098i	0.774146	−	0.198767i	0.615042	+	0.788495i	$0.289139\pi$
$968$	8.89280	+	6.46100i	0.285825	+	0.207664i
$969$	−1.58091	+	25.1279i	−0.0507863	+	0.807225i
$970$	3.65483	−	32.2622i	0.117349	−	1.03588i
$971$	−15.4360	+	6.11154i	−0.495365	+	0.196129i	−0.602505	−	0.798115i	$-0.705831\pi$
$971$	−15.4360	+	6.11154i	−0.495365	+	0.196129i	0.107140	+	0.994244i	$0.465831\pi$
$972$	−0.929776	+	0.368125i	−0.0298226	+	0.0118076i
$973$	−20.9326	−	2.64440i	−0.671068	−	0.0847756i
$974$	2.78328	−	8.56604i	0.0891819	−	0.274474i
$975$	7.14740	−	3.04473i	0.228900	−	0.0975095i
$976$	−1.57946	−	4.86108i	−0.0505573	−	0.155599i
$977$	−6.65974	−	34.9116i	−0.213064	−	1.11692i	−0.914623	−	0.404308i	$-0.867512\pi$
$977$	−6.65974	−	34.9116i	−0.213064	−	1.11692i	0.701559	−	0.712612i	$-0.252488\pi$
$978$	0.359448	+	5.71327i	0.0114939	+	0.182690i
$979$	0.628383	+	0.161341i	0.0200832	+	0.00515649i
$980$	6.36845	−	9.00674i	0.203433	−	0.287710i
$981$	3.41006	+	5.37339i	0.108875	+	0.171559i
$982$	−4.08989	+	12.5874i	−0.130514	+	0.401680i
$983$	−2.19411	+	34.8744i	−0.0699814	+	1.11232i	0.793709	+	0.608298i	$0.208148\pi$
$983$	−2.19411	+	34.8744i	−0.0699814	+	1.11232i	−0.863690	+	0.504024i	$0.831852\pi$
$984$	−2.26002	+	0.285508i	−0.0720470	+	0.00910165i
$985$	−0.135333	−	10.5232i	−0.00431206	−	0.335297i
$986$	16.9357	−	35.9903i	0.539344	−	1.14616i
$987$	2.05134	+	4.35933i	0.0652950	+	0.138759i
$988$	−5.66429	−	3.11397i	−0.180205	−	0.0990686i
$989$	−16.4282	−	15.4271i	−0.522386	−	0.490553i
$990$	0.137866	+	0.143080i	0.00438167	+	0.00454738i
$991$	−4.48108	−	9.52278i	−0.142346	−	0.302501i	0.820923	−	0.571039i	$-0.193460\pi$
$991$	−4.48108	−	9.52278i	−0.142346	−	0.302501i	−0.963269	+	0.268538i	$0.913460\pi$
$992$	−5.93080	+	7.16910i	−0.188303	+	0.227619i
$993$	−7.48982	−	23.0513i	−0.237682	−	0.731511i
$994$	13.8523	−	3.55667i	0.439369	−	0.112811i
$995$	8.89958	−	23.3507i	0.282136	−	0.740267i
$996$	0.252031	+	4.00593i	0.00798592	+	0.126933i
$997$	7.58881	−	11.9581i	0.240340	−	0.378715i	−0.702650	−	0.711535i	$-0.748000\pi$
$997$	7.58881	−	11.9581i	0.240340	−	0.378715i	0.942990	+	0.332820i	$0.108000\pi$
$998$	3.83050	+	3.59708i	0.121252	+	0.113863i
$999$	−0.389405			−0.0123202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.a.91.3	✓	100
125.11	even	25	inner	750.2.m.a.511.3	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.a.91.3	✓	100	1.1	even	1	trivial
750.2.m.a.511.3	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)

\(f(q)\)	\(=\)	\(q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-0.583892 - 2.15849i) q^{5} +(0.968583 - 0.248690i) q^{6} +(-0.444263 - 1.36730i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})\)	\(q+(0.728969 + 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-0.583892 - 2.15849i) q^{5} +(0.968583 - 0.248690i) q^{6} +(-0.444263 - 1.36730i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(1.05195 - 1.97317i) q^{10} +(-0.0647749 - 0.0608276i) q^{11} +(0.876307 + 0.481754i) q^{12} +(-0.661567 - 1.40590i) q^{13} +(0.612127 - 1.30084i) q^{14} +(-2.13534 - 0.663579i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.380021 - 6.04026i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-2.22908 - 3.51246i) q^{19} +(2.11757 - 0.718273i) q^{20} +(-1.39250 - 0.357532i) q^{21} +(-0.00557945 - 0.0886829i) q^{22} +(1.46519 + 7.68081i) q^{23} +(0.309017 + 0.951057i) q^{24} +(-4.31814 + 2.52065i) q^{25} +(0.480144 - 1.47773i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(1.33671 - 0.529239i) q^{28} +(6.11061 - 2.41936i) q^{29} +(-1.10234 - 1.94547i) q^{30} +(0.584223 - 9.28596i) q^{31} +(-0.809017 - 0.587785i) q^{32} +(-0.0860666 + 0.0220981i) q^{33} +(4.41187 - 4.14302i) q^{34} +(-2.69190 + 1.75729i) q^{35} +(0.876307 - 0.481754i) q^{36} +(0.386334 - 0.0488054i) q^{37} +(0.779519 - 4.08638i) q^{38} +(-1.54153 - 0.194740i) q^{39} +(2.03533 + 0.925975i) q^{40} +(-0.426852 + 2.23764i) q^{41} +(-0.770339 - 1.21386i) q^{42} +(-2.33168 + 1.69407i) q^{43} +(0.0566404 - 0.0684664i) q^{44} +(-1.70445 + 1.44736i) q^{45} +(-4.18980 + 6.60207i) q^{46} +(-2.13612 - 2.58212i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(3.99098 - 2.89962i) q^{49} +(-4.87329 - 1.11850i) q^{50} +(-4.89634 - 3.55740i) q^{51} +(1.36159 - 0.748539i) q^{52} +(-3.61249 - 0.927530i) q^{53} +(-0.637424 - 0.770513i) q^{54} +(-0.0934742 + 0.175333i) q^{55} +(1.33671 + 0.529239i) q^{56} -4.16007 q^{57} +(6.11061 + 2.41936i) q^{58} +(11.0328 + 6.06534i) q^{59} +(0.528191 - 2.17279i) q^{60} +(0.957751 + 5.02071i) q^{61} +(6.78256 - 6.36925i) q^{62} +(-1.04801 + 0.984149i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(-2.64834 + 2.24888i) q^{65} +(-0.0778671 - 0.0428078i) q^{66} +(5.86244 + 2.32111i) q^{67} +6.05221 q^{68} +(7.27022 + 2.87848i) q^{69} +(-3.16526 - 0.561721i) q^{70} +(6.34099 + 7.66494i) q^{71} +(0.968583 + 0.248690i) q^{72} +(-3.74073 + 2.05648i) q^{73} +(0.315035 + 0.228886i) q^{74} +(-0.185520 + 4.99656i) q^{75} +(3.36557 - 2.44523i) q^{76} +(-0.0543926 + 0.115590i) q^{77} +(-0.990416 - 1.19721i) q^{78} +(2.70862 - 4.26810i) q^{79} +(0.849819 + 2.06829i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-1.84293 + 1.33897i) q^{82} +(2.15073 + 3.38900i) q^{83} +(0.269391 - 1.41220i) q^{84} +(-13.2597 + 2.70659i) q^{85} +(-2.85939 - 0.361225i) q^{86} +(1.23149 - 6.45571i) q^{87} +(0.0881576 - 0.0111369i) q^{88} +(-6.39803 + 3.51735i) q^{89} +(-2.23328 - 0.111695i) q^{90} +(-1.62838 + 1.52915i) q^{91} +(-7.57366 + 1.94458i) q^{92} +(-7.52736 - 5.46894i) q^{93} +(0.210422 - 3.34456i) q^{94} +(-6.28006 + 6.86233i) q^{95} +(-0.929776 + 0.368125i) q^{96} +(13.5007 - 5.34532i) q^{97} +(4.89422 + 0.618284i) q^{98} +(-0.0274587 + 0.0845092i) 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

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