LMFDB - Embedded newform 750.2.m.d.511.6

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:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			511.6
Character	$\chi$	$=$	750.511
Dual form			750.2.m.d.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.728969 + 0.684547i) q^{2} +(0.535827 + 0.844328i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(1.69474 - 1.45871i) q^{5} +(-0.968583 - 0.248690i) q^{6} +(1.39889 - 4.30534i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.425779 + 0.904827i) q^{9} +O(q^{10})$	\(q+(-0.728969 + 0.684547i) q^{2} +(0.535827 + 0.844328i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(1.69474 - 1.45871i) q^{5} +(-0.968583 - 0.248690i) q^{6} +(1.39889 - 4.30534i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.425779 + 0.904827i) q^{9} +(-0.236856 + 2.22349i) q^{10} +(1.08135 - 1.01545i) q^{11} +(0.876307 - 0.481754i) q^{12} +(-2.42797 + 5.15971i) q^{13} +(1.92746 + 4.09606i) q^{14} +(2.13972 + 0.649300i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.330830 - 5.25839i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.691167 + 1.08911i) q^{19} +(-1.34942 - 1.78299i) q^{20} +(4.38468 - 1.12579i) q^{21} +(-0.0931432 + 1.48047i) q^{22} +(1.26555 - 6.63422i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(0.744305 - 4.94429i) q^{25} +(-1.76215 - 5.42333i) q^{26} +(-0.992115 + 0.125333i) q^{27} +(-4.20901 - 1.66646i) q^{28} +(-6.48783 - 2.56872i) q^{29} +(-2.00427 + 0.991421i) q^{30} +(-0.308542 - 4.90413i) q^{31} +(0.809017 - 0.587785i) q^{32} +(1.43679 + 0.368906i) q^{33} +(3.84078 + 3.60674i) q^{34} +(-3.90950 - 9.33702i) q^{35} +(0.876307 + 0.481754i) q^{36} +(7.71900 + 0.975136i) q^{37} +(-0.241705 - 1.26706i) q^{38} +(-5.65746 + 0.714703i) q^{39} +(2.20423 + 0.376002i) q^{40} +(0.264962 + 1.38898i) q^{41} +(-2.42564 + 3.82219i) q^{42} +(9.82026 + 7.13484i) q^{43} +(-0.945553 - 1.14298i) q^{44} +(0.598298 + 2.15454i) q^{45} +(3.61889 + 5.70246i) q^{46} +(-6.00062 + 7.25350i) q^{47} +(-0.425779 - 0.904827i) q^{48} +(-10.9159 - 7.93090i) q^{49} +(2.84202 + 4.11374i) q^{50} +(4.26254 - 3.09692i) q^{51} +(4.99707 + 2.74716i) q^{52} +(9.32563 - 2.39442i) q^{53} +(0.637424 - 0.770513i) q^{54} +(0.351351 - 3.29831i) q^{55} +(4.20901 - 1.66646i) q^{56} -1.28991 q^{57} +(6.48783 - 2.56872i) q^{58} +(4.85940 - 2.67148i) q^{59} +(0.782373 - 2.09473i) q^{60} +(-2.45703 + 12.8802i) q^{61} +(3.58203 + 3.36375i) q^{62} +(3.29997 + 3.09888i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(3.41175 + 12.2861i) q^{65} +(-1.29991 + 0.714632i) q^{66} +(5.02209 - 1.98838i) q^{67} -5.26879 q^{68} +(6.27957 - 2.48626i) q^{69} +(9.24154 + 4.13016i) q^{70} +(-6.10543 + 7.38020i) q^{71} +(-0.968583 + 0.248690i) q^{72} +(-7.69336 - 4.22946i) q^{73} +(-6.29443 + 4.57317i) q^{74} +(4.57342 - 2.02085i) q^{75} +(1.04356 + 0.758189i) q^{76} +(-2.85919 - 6.07609i) q^{77} +(3.63486 - 4.39379i) q^{78} +(5.88631 + 9.27534i) q^{79} +(-1.86420 + 1.23480i) q^{80} +(-0.637424 - 0.770513i) q^{81} +(-1.14397 - 0.831143i) q^{82} +(1.35322 - 2.13233i) q^{83} +(-0.848257 - 4.44672i) q^{84} +(-8.23117 - 8.42904i) q^{85} +(-12.0428 + 1.52136i) q^{86} +(-1.30752 - 6.85425i) q^{87} +(1.47170 + 0.185919i) q^{88} +(-8.38491 - 4.60964i) q^{89} +(-1.91102 - 1.16103i) q^{90} +(18.8178 + 17.6711i) q^{91} +(-6.54167 - 1.67961i) q^{92} +(3.97537 - 2.88828i) q^{93} +(-0.591101 - 9.39528i) q^{94} +(0.417343 + 2.85397i) q^{95} +(0.929776 + 0.368125i) q^{96} +(8.90604 + 3.52615i) q^{97} +(13.3865 - 1.69110i) q^{98} +(0.458395 + 1.41079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{5} + 5 q^{7}+O(q^{10}) $ 140 * q - 20 * q^5 + 5 * q^7	$ 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32} - 15 q^{34} - 25 q^{37} + 35 q^{38} - 10 q^{39} + 5 q^{40} + 55 q^{41} + 35 q^{43} + 25 q^{44} + 20 q^{46} + 10 q^{47} - 60 q^{49} - 5 q^{51} + 40 q^{52} + 40 q^{55} + 20 q^{57} - 25 q^{58} + 75 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 35 q^{65} + 20 q^{66} - 95 q^{67} + 20 q^{68} - 20 q^{69} + 65 q^{70} - 50 q^{71} + 20 q^{73} + 30 q^{74} + 35 q^{75} - 5 q^{76} + 15 q^{77} + 5 q^{78} + 70 q^{79} - 15 q^{82} + 25 q^{83} + 5 q^{84} - 95 q^{85} - 5 q^{86} - 5 q^{88} - 105 q^{89} - 5 q^{90} - 65 q^{91} + 55 q^{92} - 30 q^{93} - 10 q^{94} + 125 q^{95} - 5 q^{97} + 70 q^{98} - 10 q^{99}+O(q^{100}) $ 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{19}{25}\right)$	$1$

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
$5$	1.69474	−	1.45871i	0.757912	−	0.652357i
$5$	1.69474	−	1.45871i	0.757912	−	0.652357i
$6$	−0.968583	−	0.248690i	−0.395422	−	0.101527i
$7$	1.39889	−	4.30534i	0.528731	−	1.62727i	−0.228088	−	0.973641i	$-0.573247\pi$
$7$	1.39889	−	4.30534i	0.528731	−	1.62727i	0.756818	−	0.653625i	$-0.226753\pi$
$8$	0.637424	+	0.770513i	0.225363	+	0.272418i
$9$	−0.425779	+	0.904827i	−0.141926	+	0.301609i
$10$	−0.236856	+	2.22349i	−0.0749003	+	0.703129i
$11$	1.08135	−	1.01545i	0.326039	−	0.306171i	−0.504191	−	0.863592i	$-0.668209\pi$
$11$	1.08135	−	1.01545i	0.326039	−	0.306171i	0.830230	+	0.557421i	$0.188209\pi$
$12$	0.876307	−	0.481754i	0.252968	−	0.139070i
$13$	−2.42797	+	5.15971i	−0.673399	+	1.43105i	0.217141	+	0.976140i	$0.430327\pi$
$13$	−2.42797	+	5.15971i	−0.673399	+	1.43105i	−0.890540	+	0.454905i	$0.849673\pi$
$14$	1.92746	+	4.09606i	0.515136	+	1.09472i
$15$	2.13972	+	0.649300i	0.552474	+	0.167649i
$16$	−0.992115	−	0.125333i	−0.248029	−	0.0313333i
$17$	−0.330830	−	5.25839i	−0.0802381	−	1.27535i	−0.807862	−	0.589372i	$-0.799375\pi$
$17$	−0.330830	−	5.25839i	−0.0802381	−	1.27535i	0.727624	−	0.685976i	$-0.240625\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−0.691167	+	1.08911i	−0.158565	+	0.249858i	−0.914317	−	0.405000i	$-0.867272\pi$
$19$	−0.691167	+	1.08911i	−0.158565	+	0.249858i	0.755752	+	0.654858i	$0.227272\pi$
$20$	−1.34942	−	1.78299i	−0.301740	−	0.398689i
$21$	4.38468	−	1.12579i	0.956816	−	0.245669i
$22$	−0.0931432	+	1.48047i	−0.0198582	+	0.315637i
$23$	1.26555	−	6.63422i	0.263884	−	1.38333i	−0.565544	−	0.824718i	$-0.691334\pi$
$23$	1.26555	−	6.63422i	0.263884	−	1.38333i	0.829429	−	0.558613i	$-0.188666\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	0.744305	−	4.94429i	0.148861	−	0.988858i
$26$	−1.76215	−	5.42333i	−0.345585	−	1.06360i
$27$	−0.992115	+	0.125333i	−0.190933	+	0.0241204i
$28$	−4.20901	−	1.66646i	−0.795428	−	0.314932i
$29$	−6.48783	−	2.56872i	−1.20476	−	0.476999i	−0.321963	−	0.946752i	$-0.604343\pi$
$29$	−6.48783	−	2.56872i	−1.20476	−	0.476999i	−0.882798	+	0.469754i	$0.844343\pi$
$30$	−2.00427	+	0.991421i	−0.365927	+	0.181008i
$31$	−0.308542	−	4.90413i	−0.0554158	−	0.880809i	−0.923309	−	0.384058i	$-0.874526\pi$
$31$	−0.308542	−	4.90413i	−0.0554158	−	0.880809i	0.867893	−	0.496751i	$-0.165474\pi$
$32$	0.809017	−	0.587785i	0.143015	−	0.103907i
$33$	1.43679	+	0.368906i	0.250114	+	0.0642182i
$34$	3.84078	+	3.60674i	0.658689	+	0.618550i
$35$	−3.90950	−	9.33702i	−0.660827	−	1.57825i
$36$	0.876307	+	0.481754i	0.146051	+	0.0802923i
$37$	7.71900	+	0.975136i	1.26900	+	0.160311i	0.730848	−	0.682540i	$-0.239125\pi$
$37$	7.71900	+	0.975136i	1.26900	+	0.160311i	0.538147	+	0.842851i	$0.319125\pi$
$38$	−0.241705	−	1.26706i	−0.0392097	−	0.205544i
$39$	−5.65746	+	0.714703i	−0.905918	+	0.114444i
$40$	2.20423	+	0.376002i	0.348519	+	0.0594512i
$41$	0.264962	+	1.38898i	0.0413801	+	0.216922i	0.996971	−	0.0777746i	$-0.0247814\pi$
$41$	0.264962	+	1.38898i	0.0413801	+	0.216922i	−0.955591	+	0.294697i	$0.904781\pi$
$42$	−2.42564	+	3.82219i	−0.374284	+	0.589777i
$43$	9.82026	+	7.13484i	1.49758	+	1.08805i	0.971334	+	0.237718i	$0.0763994\pi$
$43$	9.82026	+	7.13484i	1.49758	+	1.08805i	0.526242	+	0.850335i	$0.323601\pi$
$44$	−0.945553	−	1.14298i	−0.142547	−	0.172310i
$45$	0.598298	+	2.15454i	0.0891890	+	0.321180i
$46$	3.61889	+	5.70246i	0.533577	+	0.840782i
$47$	−6.00062	+	7.25350i	−0.875280	+	1.05803i	0.122568	+	0.992460i	$0.460887\pi$
$47$	−6.00062	+	7.25350i	−0.875280	+	1.05803i	−0.997848	+	0.0655718i	$0.979113\pi$
$48$	−0.425779	−	0.904827i	−0.0614559	−	0.130601i
$49$	−10.9159	−	7.93090i	−1.55942	−	1.13299i
$50$	2.84202	+	4.11374i	0.401923	+	0.581771i
$51$	4.26254	−	3.09692i	0.596875	−	0.433655i
$52$	4.99707	+	2.74716i	0.692969	+	0.380963i
$53$	9.32563	−	2.39442i	1.28097	−	0.328898i	0.453931	−	0.891037i	$-0.350021\pi$
$53$	9.32563	−	2.39442i	1.28097	−	0.328898i	0.827043	+	0.562138i	$0.190021\pi$
$54$	0.637424	−	0.770513i	0.0867424	−	0.104854i
$55$	0.351351	−	3.29831i	0.0473761	−	0.444745i
$56$	4.20901	−	1.66646i	0.562452	−	0.222691i
$57$	−1.28991			−0.170853
$58$	6.48783	−	2.56872i	0.851894	−	0.337289i
$59$	4.85940	−	2.67148i	0.632641	−	0.347797i	−0.132952	−	0.991122i	$-0.542446\pi$
$59$	4.85940	−	2.67148i	0.632641	−	0.347797i	0.765593	+	0.643325i	$0.222446\pi$
$60$	0.782373	−	2.09473i	0.101004	−	0.270428i
$61$	−2.45703	+	12.8802i	−0.314590	+	1.64914i	0.376533	+	0.926403i	$0.377116\pi$
$61$	−2.45703	+	12.8802i	−0.314590	+	1.64914i	−0.691123	+	0.722737i	$0.742884\pi$
$62$	3.58203	+	3.36375i	0.454918	+	0.427197i
$63$	3.29997	+	3.09888i	0.415757	+	0.390422i
$64$	−0.187381	+	0.982287i	−0.0234227	+	0.122786i
$65$	3.41175	+	12.2861i	0.423175	+	1.52390i
$66$	−1.29991	+	0.714632i	−0.160008	+	0.0879651i
$67$	5.02209	−	1.98838i	0.613546	−	0.242920i	−0.0407372	−	0.999170i	$-0.512971\pi$
$67$	5.02209	−	1.98838i	0.613546	−	0.242920i	0.654283	+	0.756250i	$0.272971\pi$
$68$	−5.26879			−0.638935
$69$	6.27957	−	2.48626i	0.755971	−	0.299310i
$70$	9.24154	+	4.13016i	1.10458	+	0.493648i
$71$	−6.10543	+	7.38020i	−0.724581	+	0.875868i	−0.996250	−	0.0865227i	$-0.972424\pi$
$71$	−6.10543	+	7.38020i	−0.724581	+	0.875868i	0.271669	+	0.962391i	$0.412424\pi$
$72$	−0.968583	+	0.248690i	−0.114149	+	0.0293084i
$73$	−7.69336	−	4.22946i	−0.900440	−	0.495021i	−0.0369100	−	0.999319i	$-0.511751\pi$
$73$	−7.69336	−	4.22946i	−0.900440	−	0.495021i	−0.863530	+	0.504298i	$0.831751\pi$
$74$	−6.29443	+	4.57317i	−0.731713	+	0.531621i
$75$	4.57342	−	2.02085i	0.528093	−	0.233347i
$76$	1.04356	+	0.758189i	0.119704	+	0.0869703i
$77$	−2.85919	−	6.07609i	−0.325835	−	0.692434i
$78$	3.63486	−	4.39379i	0.411567	−	0.497499i
$79$	5.88631	+	9.27534i	0.662262	+	1.04356i	0.994935	+	0.100516i	$0.0320493\pi$
$79$	5.88631	+	9.27534i	0.662262	+	1.04356i	−0.332674	+	0.943042i	$0.607951\pi$
$80$	−1.86420	+	1.23480i	−0.208424	+	0.138055i
$81$	−0.637424	−	0.770513i	−0.0708249	−	0.0856126i
$82$	−1.14397	−	0.831143i	−0.126330	−	0.0917844i
$83$	1.35322	−	2.13233i	0.148535	−	0.234053i	−0.761911	−	0.647682i	$-0.775739\pi$
$83$	1.35322	−	2.13233i	0.148535	−	0.234053i	0.910446	+	0.413628i	$0.135739\pi$
$84$	−0.848257	−	4.44672i	−0.0925524	−	0.485177i
$85$	−8.23117	−	8.42904i	−0.892795	−	0.914257i
$86$	−12.0428	+	1.52136i	−1.29861	+	0.164052i
$87$	−1.30752	−	6.85425i	−0.140181	−	0.734852i
$88$	1.47170	+	0.185919i	0.156884	+	0.0198190i
$89$	−8.38491	−	4.60964i	−0.888798	−	0.488621i	−0.0291897	−	0.999574i	$-0.509293\pi$
$89$	−8.38491	−	4.60964i	−0.888798	−	0.488621i	−0.859609	+	0.510953i	$0.829293\pi$
$90$	−1.91102	−	1.16103i	−0.201440	−	0.122383i
$91$	18.8178	+	17.6711i	1.97264	+	1.85244i
$92$	−6.54167	−	1.67961i	−0.682016	−	0.175112i
$93$	3.97537	−	2.88828i	0.412227	−	0.299500i
$94$	−0.591101	−	9.39528i	−0.0609674	−	0.969049i
$95$	0.417343	+	2.85397i	0.0428185	+	0.292811i
$96$	0.929776	+	0.368125i	0.0948949	+	0.0375716i
$97$	8.90604	+	3.52615i	0.904272	+	0.358026i	0.773803	−	0.633426i	$-0.218352\pi$
$97$	8.90604	+	3.52615i	0.904272	+	0.358026i	0.130468	+	0.991452i	$0.458352\pi$
$98$	13.3865	−	1.69110i	1.35224	−	0.170827i
$99$	0.458395	+	1.41079i	0.0460704	+	0.141790i
$100$	−4.88780	−	1.05329i	−0.488780	−	0.105329i
$101$	3.50060	−	10.7738i	0.348323	−	1.07203i	−0.611457	−	0.791277i	$-0.709416\pi$
$101$	3.50060	−	10.7738i	0.348323	−	1.07203i	0.959781	−	0.280751i	$-0.0905836\pi$
$102$	−0.987273	+	5.17547i	−0.0977546	+	0.512447i
$103$	0.630807	−	10.0264i	0.0621552	−	0.987929i	−0.836134	−	0.548525i	$-0.815190\pi$
$103$	0.630807	−	10.0264i	0.0621552	−	0.987929i	0.898289	−	0.439404i	$-0.144810\pi$
$104$	−5.52327	+	1.41814i	−0.541601	+	0.139060i
$105$	5.78869	−	8.30393i	0.564919	−	0.810381i
$106$	−5.15900	+	8.12929i	−0.501087	+	0.789586i
$107$	3.89329	+	11.9823i	0.376379	+	1.15838i	0.942544	+	0.334083i	$0.108427\pi$
$107$	3.89329	+	11.9823i	0.376379	+	1.15838i	−0.566165	+	0.824292i	$0.691573\pi$
$108$	0.0627905	+	0.998027i	0.00604202	+	0.0960352i
$109$	−6.55126	−	0.827617i	−0.627497	−	0.0792713i	−0.194848	−	0.980834i	$-0.562421\pi$
$109$	−6.55126	−	0.827617i	−0.627497	−	0.0792713i	−0.432649	+	0.901562i	$0.642421\pi$
$110$	2.00173	+	2.64488i	0.190857	+	0.252180i
$111$	3.31271	+	7.03987i	0.314429	+	0.668195i
$112$	−1.92746	+	4.09606i	−0.182128	+	0.387042i
$113$	7.39810	−	4.06714i	0.695955	−	0.382604i	−0.0941652	−	0.995557i	$-0.530018\pi$
$113$	7.39810	−	4.06714i	0.695955	−	0.382604i	0.790120	+	0.612952i	$0.210018\pi$
$114$	0.940303	−	0.883003i	0.0880674	−	0.0827008i
$115$	−7.53266	−	13.0894i	−0.702424	−	1.22059i
$116$	−2.97102	+	6.31374i	−0.275852	+	0.586216i
$117$	−3.63486	−	4.39379i	−0.336043	−	0.406206i
$118$	−1.71360	+	5.27392i	−0.157750	+	0.485503i
$119$	−23.1020	−	5.93158i	−2.11775	−	0.543747i
$120$	0.863615	+	2.06256i	0.0788369	+	0.188285i
$121$	−0.552527	+	8.78217i	−0.0502298	+	0.798379i
$122$	−7.02601	−	11.0712i	−0.636105	−	1.00234i
$123$	−1.03078	+	0.967966i	−0.0929423	+	0.0872786i
$124$	−4.91383			−0.441275
$125$	−5.95090	−	9.46503i	−0.532265	−	0.846578i
$126$	−4.52690			−0.403289
$127$	2.09359	−	1.96601i	0.185776	−	0.174455i	−0.586079	−	0.810254i	$-0.699329\pi$
$127$	2.09359	−	1.96601i	0.185776	−	0.174455i	0.771855	+	0.635799i	$0.219329\pi$
$128$	−0.535827	−	0.844328i	−0.0473608	−	0.0746288i
$129$	−0.762184	+	12.1146i	−0.0671065	+	1.06663i
$130$	−10.8975	−	6.62068i	−0.955771	−	0.580672i
$131$	9.75058	+	2.50352i	0.851912	+	0.218734i	0.649307	−	0.760527i	$-0.275059\pi$
$131$	9.75058	+	2.50352i	0.851912	+	0.218734i	0.202606	+	0.979260i	$0.435059\pi$
$132$	0.458395	−	1.41079i	0.0398981	−	0.122794i
$133$	3.72210	+	4.49925i	0.322747	+	0.390134i
$134$	−2.29980	+	4.88733i	−0.198673	+	0.422201i
$135$	−1.49855	+	1.65962i	−0.128975	+	0.142837i
$136$	3.84078	−	3.60674i	0.329344	−	0.309275i
$137$	3.51567	−	1.93275i	0.300364	−	0.165126i	−0.324444	−	0.945905i	$-0.605177\pi$
$137$	3.51567	−	1.93275i	0.300364	−	0.165126i	0.624808	+	0.780778i	$0.285177\pi$
$138$	−2.87565	+	6.11107i	−0.244792	+	0.520208i
$139$	9.76158	+	20.7444i	0.827966	+	1.75952i	0.625492	+	0.780231i	$0.284898\pi$
$139$	9.76158	+	20.7444i	0.827966	+	1.75952i	0.202474	+	0.979288i	$0.435102\pi$
$140$	−9.56408	+	3.31551i	−0.808312	+	0.280212i
$141$	−9.33963	−	1.17987i	−0.786538	−	0.0993629i
$142$	−0.601426	−	9.55939i	−0.0504705	−	0.802206i
$143$	2.61396	+	8.04494i	0.218590	+	0.672752i
$144$	0.535827	−	0.844328i	0.0446522	−	0.0703607i
$145$	−14.7422	+	5.11059i	−1.22428	+	0.424411i
$146$	8.50349	−	2.18332i	0.703753	−	0.180693i
$147$	0.847223	−	13.4662i	0.0698778	−	1.11068i
$148$	1.45789	−	7.64254i	0.119838	−	0.628213i
$149$	2.47878	−	7.62889i	0.203069	−	0.624983i	−0.796718	−	0.604351i	$-0.793432\pi$
$149$	2.47878	−	7.62889i	0.203069	−	0.624983i	0.999787	−	0.0206314i	$-0.00656766\pi$
$150$	−1.95052	+	4.60386i	−0.159259	+	0.375903i
$151$	2.79240	+	8.59412i	0.227242	+	0.699379i	0.998056	+	0.0623192i	$0.0198497\pi$
$151$	2.79240	+	8.59412i	0.227242	+	0.699379i	−0.770814	+	0.637060i	$0.780150\pi$
$152$	−1.27974	+	0.161668i	−0.103800	+	0.0131130i
$153$	4.89880	+	1.93957i	0.396044	+	0.156805i
$154$	6.24363	+	2.47203i	0.503126	+	0.199202i
$155$	−7.67663	−	7.86117i	−0.616602	−	0.631424i
$156$	0.358058	+	5.69117i	0.0286676	+	0.455658i
$157$	−1.50243	+	1.09158i	−0.119907	+	0.0871178i	−0.646123	−	0.763234i	$-0.723611\pi$
$157$	−1.50243	+	1.09158i	−0.119907	+	0.0871178i	0.526215	+	0.850351i	$0.323611\pi$
$158$	−10.6403	−	2.73198i	−0.846501	−	0.217344i
$159$	7.01860	+	6.59090i	0.556611	+	0.522692i
$160$	0.513665	−	2.17627i	0.0406088	−	0.172049i
$161$	−26.7922	−	14.7291i	−2.11152	−	1.16082i
$162$	0.992115	+	0.125333i	0.0779479	+	0.00984711i
$163$	2.04128	+	10.7008i	0.159886	+	0.838150i	0.968348	+	0.249603i	$0.0803000\pi$
$163$	2.04128	+	10.7008i	0.159886	+	0.838150i	−0.808463	+	0.588547i	$0.799700\pi$
$164$	1.40287	−	0.177224i	0.109546	−	0.0138389i
$165$	2.97312	−	1.47067i	0.231457	−	0.114492i
$166$	0.473227	+	2.48074i	0.0367295	+	0.192543i
$167$	−1.99155	+	3.13818i	−0.154111	+	0.242840i	−0.912607	−	0.408837i	$-0.865934\pi$
$167$	−1.99155	+	3.13818i	−0.154111	+	0.242840i	0.758496	+	0.651677i	$0.225934\pi$
$168$	3.66234	+	2.66085i	0.282556	+	0.205289i
$169$	−12.4410	−	15.0386i	−0.957001	−	1.15682i
$170$	11.7703	+	0.509883i	0.902743	+	0.0391062i
$171$	−0.691167	−	1.08911i	−0.0528549	−	0.0832860i
$172$	7.73738	−	9.35289i	0.589970	−	0.713151i
$173$	−4.79644	−	10.1930i	−0.364667	−	0.774956i	−0.999996	−	0.00271500i	$-0.999136\pi$
$173$	−4.79644	−	10.1930i	−0.364667	−	0.774956i	0.635330	−	0.772241i	$-0.280864\pi$
$174$	5.64519	+	4.10147i	0.427961	+	0.310932i
$175$	−20.2457	−	10.1210i	−1.53043	−	0.765076i
$176$	−1.20009	+	0.871919i	−0.0904604	+	0.0657233i
$177$	4.85940	+	2.67148i	0.365255	+	0.200801i
$178$	9.26785	−	2.37958i	0.694655	−	0.178357i
$179$	−5.40792	+	6.53706i	−0.404207	+	0.488603i	−0.932862	−	0.360234i	$-0.882697\pi$
$179$	−5.40792	+	6.53706i	−0.404207	+	0.488603i	0.528655	+	0.848837i	$0.322697\pi$
$180$	2.18786	−	0.461833i	0.163073	−	0.0344230i
$181$	−10.6240	+	4.20632i	−0.789672	+	0.312653i	−0.728119	−	0.685451i	$-0.759605\pi$
$181$	−10.6240	+	4.20632i	−0.789672	+	0.312653i	−0.0615529	+	0.998104i	$0.519605\pi$
$182$	−25.8143			−1.91348
$183$	−12.1917	+	4.82702i	−0.901233	+	0.356823i
$184$	5.91844	−	3.25369i	0.436313	−	0.239865i
$185$	14.5042	−	9.60721i	1.06637	−	0.706336i
$186$	−0.920760	+	4.82679i	−0.0675134	+	0.353918i
$187$	−5.69740	−	5.35022i	−0.416635	−	0.391247i
$188$	6.86241	+	6.44423i	0.500492	+	0.469994i
$189$	−0.848257	+	4.44672i	−0.0617016	+	0.323451i
$190$	−2.25791	−	1.79476i	−0.163806	−	0.130206i
$191$	−3.19928	+	1.75882i	−0.231492	+	0.127264i	−0.593279	−	0.804997i	$-0.702167\pi$
$191$	−3.19928	+	1.75882i	−0.231492	+	0.127264i	0.361787	+	0.932261i	$0.382167\pi$
$192$	−0.929776	+	0.368125i	−0.0671008	+	0.0265671i
$193$	20.1637			1.45142			0.725708	−	0.688003i	$-0.241512\pi$
$193$	20.1637			1.45142			0.725708	+	0.688003i	$0.241512\pi$
$194$	−8.90604	+	3.52615i	−0.639417	+	0.253163i
$195$	−8.54539	+	9.46385i	−0.611948	+	0.677721i
$196$	−8.60067	+	10.3964i	−0.614333	+	0.742601i
$197$	−5.90195	+	1.51536i	−0.420496	+	0.107965i	−0.453008	−	0.891506i	$-0.649649\pi$
$197$	−5.90195	+	1.51536i	−0.420496	+	0.107965i	0.0325121	+	0.999471i	$0.489649\pi$
$198$	−1.29991	−	0.714632i	−0.0923806	−	0.0507867i
$199$	−9.74624	+	7.08106i	−0.690893	+	0.501963i	−0.876953	−	0.480575i	$-0.840428\pi$
$199$	−9.74624	+	7.08106i	−0.690893	+	0.501963i	0.186061	+	0.982538i	$0.440428\pi$
$200$	4.28408	−	2.57811i	0.302930	−	0.182300i
$201$	4.36982	+	3.17486i	0.308223	+	0.223937i
$202$	4.82331	+	10.2501i	0.339367	+	0.721191i
$203$	−20.1350	+	24.3390i	−1.41320	+	1.70826i
$204$	−2.82316	−	4.44859i	−0.197661	−	0.311463i
$205$	2.47516	+	1.96746i	0.172873	+	0.137413i
$206$	6.40370	+	7.74074i	0.446167	+	0.539323i
$207$	5.46398	+	3.96981i	0.379773	+	0.275921i
$208$	3.05551	−	4.81472i	0.211862	−	0.333840i
$209$	0.358544	+	1.87955i	0.0248010	+	0.130011i
$210$	1.46466	+	10.0159i	0.101071	+	0.691165i
$211$	−6.76008	+	0.853997i	−0.465383	+	0.0587916i	−0.354529	−	0.935045i	$-0.615359\pi$
$211$	−6.76008	+	0.853997i	−0.465383	+	0.0587916i	−0.110854	+	0.993837i	$0.535359\pi$
$212$	−1.80413	−	9.45758i	−0.123908	−	0.649549i
$213$	−9.50276	−	1.20048i	−0.651118	−	0.0822554i
$214$	−11.0406	−	6.06960i	−0.754717	−	0.414909i
$215$	27.0505	−	2.23324i	1.84483	−	0.152306i
$216$	−0.728969	−	0.684547i	−0.0496000	−	0.0465775i
$217$	−21.5456	−	5.53197i	−1.46261	−	0.375534i
$218$	5.34221	−	3.88134i	0.361820	−	0.262877i
$219$	−0.551257	−	8.76198i	−0.0372505	−	0.592080i
$220$	−3.26974	−	0.557760i	−0.220446	−	0.0376042i
$221$	27.9350	+	11.0603i	1.87911	+	0.743993i
$222$	−7.23398	−	2.86414i	−0.485513	−	0.192228i
$223$	2.39276	−	0.302275i	0.160231	−	0.0202419i	−0.0448085	−	0.998996i	$-0.514268\pi$
$223$	2.39276	−	0.302275i	0.160231	−	0.0202419i	0.205039	+	0.978754i	$0.434268\pi$
$224$	−1.39889	−	4.30534i	−0.0934673	−	0.287663i
$225$	4.15682	+	2.77864i	0.277121	+	0.185243i
$226$	−2.60883	+	8.02917i	−0.173537	+	0.534092i
$227$	−0.774604	+	4.06061i	−0.0514122	+	0.269512i	−0.998706	−	0.0508535i	$-0.983806\pi$
$227$	−0.774604	+	4.06061i	−0.0514122	+	0.269512i	0.947294	+	0.320366i	$0.103806\pi$
$228$	−0.0809940	+	1.28736i	−0.00536396	+	0.0852577i
$229$	−26.8790	+	6.90136i	−1.77622	+	0.456055i	−0.987356	−	0.158517i	$-0.949329\pi$
$229$	−26.8790	+	6.90136i	−1.77622	+	0.456055i	−0.788861	+	0.614572i	$0.789329\pi$
$230$	14.4514	+	4.38528i	0.952894	+	0.289157i
$231$	3.59818	−	5.66982i	0.236743	−	0.373047i
$232$	−2.15627	−	6.63632i	−0.141566	−	0.435696i
$233$	0.109908	+	1.74693i	0.00720029	+	0.114445i	0.999985	−	0.00546457i	$-0.00173943\pi$
$233$	0.109908	+	1.74693i	0.00720029	+	0.114445i	−0.992785	+	0.119910i	$0.961739\pi$
$234$	5.65746	+	0.714703i	0.369840	+	0.0467216i
$235$	0.411283	+	21.0460i	0.0268291	+	1.37289i
$236$	−2.36108	−	5.01756i	−0.153693	−	0.326615i
$237$	−4.67739	+	9.93996i	−0.303829	+	0.645670i
$238$	20.9011	−	11.4905i	1.35481	−	0.744815i
$239$	13.1262	−	12.3263i	0.849063	−	0.797323i	−0.131952	−	0.991256i	$-0.542124\pi$
$239$	13.1262	−	12.3263i	0.849063	−	0.797323i	0.981015	+	0.193933i	$0.0621244\pi$
$240$	−2.04147	−	0.912359i	−0.131776	−	0.0588925i
$241$	1.92760	−	4.09635i	0.124167	−	0.263869i	−0.833073	−	0.553163i	$-0.813421\pi$
$241$	1.92760	−	4.09635i	0.124167	−	0.263869i	0.957240	+	0.289294i	$0.0934206\pi$
$242$	−5.60903	−	6.78016i	−0.360562	−	0.435845i
$243$	0.309017	−	0.951057i	0.0198234	−	0.0610103i
$244$	12.7005	+	3.26094i	0.813067	+	0.208760i
$245$	−30.0686	+	2.48241i	−1.92101	+	0.158596i
$246$	0.0887873	−	1.41123i	0.00566087	−	0.0899770i
$247$	−3.94133	−	6.21054i	−0.250781	−	0.395167i
$248$	3.58203	−	3.36375i	0.227459	−	0.213598i
$249$	2.52547			0.160045
$250$	10.8173	+	2.82604i	0.684145	+	0.178734i
$251$	3.06463			0.193437			0.0967187	−	0.995312i	$-0.469165\pi$
$251$	3.06463			0.193437			0.0967187	+	0.995312i	$0.469165\pi$
$252$	3.29997	−	3.09888i	0.207879	−	0.195211i
$253$	−5.36825	−	8.45902i	−0.337499	−	0.531814i
$254$	−0.180334	+	2.86632i	−0.0113152	+	0.179849i
$255$	2.70639	−	11.4663i	0.169481	−	0.718048i
$256$	0.968583	+	0.248690i	0.0605364	+	0.0155431i
$257$	−0.588614	+	1.81157i	−0.0367168	+	0.113003i	−0.967735	−	0.251970i	$-0.918922\pi$
$257$	−0.588614	+	1.81157i	−0.0367168	+	0.113003i	0.931018	+	0.364972i	$0.118922\pi$
$258$	−7.73738	−	9.35289i	−0.481708	−	0.582285i
$259$	14.9963	−	31.8688i	0.931826	−	1.98023i
$260$	12.4761	−	2.63357i	0.773734	−	0.163327i
$261$	5.08663	−	4.77666i	0.314854	−	0.295668i
$262$	−8.82165	+	4.84974i	−0.545003	+	0.299618i
$263$	−1.07146	+	2.27697i	−0.0660691	+	0.140404i	−0.935134	−	0.354294i	$-0.884721\pi$
$263$	−1.07146	+	2.27697i	−0.0660691	+	0.140404i	0.869065	+	0.494698i	$0.164721\pi$
$264$	0.631600	+	1.34222i	0.0388723	+	0.0826078i
$265$	12.3118	−	17.6614i	0.756307	−	1.08493i
$266$	−5.79324	−	0.731857i	−0.355207	−	0.0448730i
$267$	−0.600809	−	9.54958i	−0.0367689	−	0.584425i
$268$	−1.66912	−	5.13703i	−0.101958	−	0.313794i
$269$	−14.7382	+	23.2236i	−0.898601	+	1.41597i	0.0107515	+	0.999942i	$0.496578\pi$
$269$	−14.7382	+	23.2236i	−0.898601	+	1.41597i	−0.909353	+	0.416026i	$0.863422\pi$
$270$	−0.0436891	−	2.23564i	−0.00265883	−	0.136057i
$271$	−2.42830	+	0.623482i	−0.147509	+	0.0378738i	−0.321722	−	0.946834i	$-0.604262\pi$
$271$	−2.42830	+	0.623482i	−0.147509	+	0.0378738i	0.174213	+	0.984708i	$0.444262\pi$
$272$	−0.330830	+	5.25839i	−0.0200595	+	0.318837i
$273$	−4.83712	+	25.3571i	−0.292756	+	1.53468i
$274$	−1.23975	+	3.81556i	−0.0748960	+	0.230506i
$275$	−4.21585	−	6.10231i	−0.254225	−	0.367983i
$276$	−2.08705	−	6.42329i	−0.125626	−	0.386637i
$277$	−29.4499	+	3.72038i	−1.76947	+	0.223536i	−0.941448	−	0.337158i	$-0.890534\pi$
$277$	−29.4499	+	3.72038i	−1.76947	+	0.223536i	−0.828023	+	0.560694i	$0.810534\pi$
$278$	−21.3164	−	8.43977i	−1.27847	−	0.506183i
$279$	4.56876	+	1.80890i	0.273525	+	0.108296i
$280$	4.70229	−	8.96397i	0.281016	−	0.535700i
$281$	1.68378	+	26.7629i	0.100446	+	1.59654i	0.649242	+	0.760582i	$0.275086\pi$
$281$	1.68378	+	26.7629i	0.100446	+	1.59654i	−0.548796	+	0.835956i	$0.684914\pi$
$282$	7.61597	−	5.53333i	0.453524	−	0.329505i
$283$	−18.9672	−	4.86996i	−1.12749	−	0.289489i	−0.361516	−	0.932366i	$-0.617741\pi$
$283$	−18.9672	−	4.86996i	−1.12749	−	0.289489i	−0.765969	+	0.642877i	$0.777741\pi$
$284$	6.98227	+	6.55679i	0.414321	+	0.389074i
$285$	−2.18606	+	1.88161i	−0.129491	+	0.111457i
$286$	−7.41264	−	4.07513i	−0.438319	−	0.240968i
$287$	6.35068	+	0.802277i	0.374869	+	0.0473569i
$288$	0.187381	+	0.982287i	0.0110415	+	0.0578818i
$289$	−10.6753	+	1.34860i	−0.627959	+	0.0793297i
$290$	7.24819	−	13.8172i	0.425628	−	0.811374i
$291$	1.79487	+	9.40903i	0.105217	+	0.551567i
$292$	−4.70419	+	7.41261i	−0.275292	+	0.433790i
$293$	18.3689	+	13.3458i	1.07312	+	0.779670i	0.976471	−	0.215648i	$-0.0691864\pi$
$293$	18.3689	+	13.3458i	1.07312	+	0.779670i	0.0966528	+	0.995318i	$0.469186\pi$
$294$	8.60067	+	10.3964i	0.501601	+	0.606331i
$295$	4.33851	−	11.6160i	0.252598	−	0.676307i
$296$	4.16892	+	6.56916i	0.242313	+	0.381825i
$297$	−0.945553	+	1.14298i	−0.0548665	+	0.0663222i
$298$	3.41538	+	7.25806i	0.197848	+	0.420448i
$299$	31.1579	+	22.6376i	1.80191	+	1.30916i
$300$	−1.72969	−	4.69129i	−0.0998637	−	0.270852i
$301$	44.4554	−	32.2987i	2.56237	−	1.86167i
$302$	−7.91865	−	4.35331i	−0.455667	−	0.250505i
$303$	10.9723	−	2.81721i	0.630342	−	0.161844i
$304$	0.822219	−	0.993891i	0.0471575	−	0.0570036i
$305$	14.6245	+	25.4127i	0.837396	+	1.45513i
$306$	−4.89880	+	1.93957i	−0.280046	+	0.110878i
$307$	8.71027			0.497121			0.248561	−	0.968616i	$-0.420043\pi$
$307$	8.71027			0.497121			0.248561	+	0.968616i	$0.420043\pi$
$308$	−6.24363	+	2.47203i	−0.355764	+	0.140857i
$309$	8.80356	−	4.83980i	0.500817	−	0.275327i
$310$	10.9774	+	0.475532i	0.623472	+	0.0270084i
$311$	5.02197	−	26.3261i	0.284770	−	1.49281i	−0.496179	−	0.868220i	$-0.665264\pi$
$311$	5.02197	−	26.3261i	0.284770	−	1.49281i	0.780949	−	0.624595i	$-0.214736\pi$
$312$	−4.15689	−	3.90358i	−0.235337	−	0.220997i
$313$	−10.0114	−	9.40135i	−0.565879	−	0.531396i	0.347940	−	0.937517i	$-0.386881\pi$
$313$	−10.0114	−	9.40135i	−0.565879	−	0.531396i	−0.913819	+	0.406121i	$0.866881\pi$
$314$	0.347988	−	1.82422i	0.0196381	−	0.102947i
$315$	10.1130	+	0.438087i	0.569802	+	0.0246834i
$316$	9.62665	−	5.29229i	0.541541	−	0.297715i
$317$	−25.9570	+	10.2771i	−1.45789	+	0.577221i	−0.957463	−	0.288556i	$-0.906825\pi$
$317$	−25.9570	+	10.2771i	−1.45789	+	0.577221i	−0.500430	+	0.865777i	$0.666825\pi$
$318$	−9.62812			−0.539918
$319$	−9.62403	+	3.81042i	−0.538842	+	0.213343i
$320$	1.11531	+	1.93806i	0.0623479	+	0.108341i
$321$	−8.03088	+	9.70767i	−0.448240	+	0.541829i
$322$	29.6135	−	7.60345i	1.65029	−	0.423724i
$323$	5.95561	+	3.27412i	0.331379	+	0.182177i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	23.7039	+	15.8450i	1.31486	+	0.878923i
$326$	−8.81322	−	6.40318i	−0.488119	−	0.354639i
$327$	−2.81156	−	5.97487i	−0.155480	−	0.330411i
$328$	−0.901333	+	1.08952i	−0.0497678	+	0.0601589i
$329$	22.8346	+	35.9816i	1.25891	+	1.98373i
$330$	−1.16057	+	3.10731i	−0.0638873	+	0.171052i
$331$	3.57521	+	4.32168i	0.196511	+	0.237541i	0.859560	−	0.511035i	$-0.170738\pi$
$331$	3.57521	+	4.32168i	0.196511	+	0.237541i	−0.663049	+	0.748576i	$0.730738\pi$
$332$	−2.04315	−	1.48444i	−0.112133	−	0.0814690i
$333$	−4.16892	+	6.56916i	−0.228455	+	0.359988i
$334$	−0.696455	−	3.65094i	−0.0381083	−	0.199771i
$335$	5.61066	−	10.6956i	0.306543	−	0.584363i
$336$	−4.49121	+	0.567371i	−0.245015	+	0.0309526i
$337$	3.28717	+	17.2319i	0.179063	+	0.938683i	0.952438	+	0.304733i	$0.0985674\pi$
$337$	3.28717	+	17.2319i	0.179063	+	0.938683i	−0.773374	+	0.633950i	$0.781433\pi$
$338$	19.3637	+	2.44621i	1.05325	+	0.133056i
$339$	7.39810	+	4.06714i	0.401810	+	0.220897i
$340$	−8.92924	+	7.68566i	−0.484256	+	0.416813i
$341$	−5.31357	−	4.98977i	−0.287746	−	0.270211i
$342$	1.24938	+	0.320787i	0.0675589	+	0.0173462i
$343$	−23.7790	+	17.2765i	−1.28395	+	0.932842i
$344$	0.762184	+	12.1146i	0.0410942	+	0.653173i
$345$	7.01552	−	13.3737i	0.377703	−	0.720014i
$346$	10.4740	+	4.14695i	0.563086	+	0.222942i
$347$	7.14491	+	2.82887i	0.383559	+	0.151862i	0.551988	−	0.833852i	$-0.313869\pi$
$347$	7.14491	+	2.82887i	0.383559	+	0.151862i	−0.168429	+	0.985714i	$0.553869\pi$
$348$	−6.92282	+	0.874556i	−0.371102	+	0.0468811i
$349$	−5.56830	−	17.1375i	−0.298064	−	0.917348i	−0.982175	−	0.187970i	$-0.939809\pi$
$349$	−5.56830	−	17.1375i	−0.298064	−	0.917348i	0.684110	−	0.729378i	$-0.260191\pi$
$350$	21.6868	−	6.48121i	1.15921	−	0.346435i
$351$	1.76215	−	5.42333i	0.0940564	−	0.289476i
$352$	0.277961	−	1.45712i	0.0148154	−	0.0776648i
$353$	0.374178	−	5.94740i	0.0199155	−	0.316548i	−0.975439	−	0.220270i	$-0.929306\pi$
$353$	0.374178	−	5.94740i	0.0199155	−	0.316548i	0.995354	−	0.0962781i	$-0.0306938\pi$
$354$	−5.37111	+	1.37907i	−0.285471	+	0.0732965i
$355$	0.418466	+	21.4136i	0.0222099	+	1.13652i
$356$	−5.12704	+	8.07892i	−0.271732	+	0.428182i
$357$	−7.37046	−	22.6839i	−0.390086	−	1.20056i
$358$	−0.532717	−	8.46729i	−0.0281549	−	0.447510i
$359$	0.856084	+	0.108149i	0.0451824	+	0.00570786i	0.147892	−	0.989004i	$-0.452751\pi$
$359$	0.856084	+	0.108149i	0.0451824	+	0.00570786i	−0.102710	+	0.994711i	$0.532751\pi$
$360$	−1.27873	+	1.83435i	−0.0673951	+	0.0966788i
$361$	7.38137	+	15.6862i	0.388493	+	0.825590i
$362$	4.86510	−	10.3389i	0.255704	−	0.543399i
$363$	−7.71109	+	4.23921i	−0.404727	+	0.222501i
$364$	18.8178	−	17.6711i	0.986322	−	0.926218i
$365$	−19.2078	+	4.05457i	−1.00538	+	0.212226i
$366$	5.58301	−	11.8645i	0.291829	−	0.620168i
$367$	4.88974	+	5.91068i	0.255242	+	0.308535i	0.882533	−	0.470250i	$-0.155836\pi$
$367$	4.88974	+	5.91068i	0.255242	+	0.308535i	−0.627291	+	0.778785i	$0.715836\pi$
$368$	−2.08705	+	6.42329i	−0.108795	+	0.334837i
$369$	−1.36960	−	0.351654i	−0.0712985	−	0.0183064i
$370$	−3.99649	+	16.9321i	−0.207768	+	0.880260i
$371$	2.73676	−	43.4996i	0.142085	−	2.25838i
$372$	−2.63296	−	4.14888i	−0.136513	−	0.215110i
$373$	19.6104	−	18.4154i	1.01539	−	0.953512i	0.0164622	−	0.999864i	$-0.494760\pi$
$373$	19.6104	−	18.4154i	1.01539	−	0.953512i	0.998925	+	0.0463523i	$0.0147597\pi$
$374$	7.81571			0.404140
$375$	4.80294	−	10.0961i	0.248023	−	0.521362i
$376$	−9.41386			−0.485483
$377$	29.0061	−	27.2386i	1.49389	−	1.40286i
$378$	−2.42564	−	3.82219i	−0.124761	−	0.196592i
$379$	1.14743	−	18.2379i	0.0589396	−	0.936818i	−0.851808	−	0.523854i	$-0.824494\pi$
$379$	1.14743	−	18.2379i	0.0589396	−	0.936818i	0.910748	−	0.412964i	$-0.135506\pi$
$380$	2.87454	−	0.237317i	0.147461	−	0.0121741i
$381$	2.78176	+	0.714235i	0.142514	+	0.0365914i
$382$	1.12818	−	3.47218i	0.0577228	−	0.177652i
$383$	5.19411	+	6.27860i	0.265407	+	0.320822i	0.886334	−	0.463047i	$-0.153244\pi$
$383$	5.19411	+	6.27860i	0.265407	+	0.320822i	−0.620927	+	0.783868i	$0.713244\pi$
$384$	0.425779	−	0.904827i	0.0217280	−	0.0461743i
$385$	−13.7089	−	6.12666i	−0.698668	−	0.312244i
$386$	−14.6987	+	13.8030i	−0.748145	+	0.702555i
$387$	−10.6371	+	5.84777i	−0.540712	+	0.297259i
$388$	4.07841	−	8.66706i	0.207050	−	0.440003i
$389$	−0.0318028	−	0.0675844i	−0.00161247	−	0.00342667i	0.904019	−	0.427492i	$-0.140603\pi$
$389$	−0.0318028	−	0.0675844i	−0.00161247	−	0.00342667i	−0.905632	+	0.424065i	$0.860603\pi$
$390$	−0.249134	−	12.7486i	−0.0126154	−	0.645549i
$391$	−35.3040	−	4.45994i	−1.78540	−	0.225549i
$392$	−0.847223	−	13.4662i	−0.0427912	−	0.680147i
$393$	3.11083	+	9.57414i	0.156921	+	0.482952i
$394$	3.26500	−	5.14481i	0.164488	−	0.259192i
$395$	23.5059	+	7.13287i	1.18271	+	0.358894i
$396$	1.43679	−	0.368906i	0.0722016	−	0.0185382i
$397$	0.545390	−	8.66873i	0.0273723	−	0.435071i	−0.960344	−	0.278816i	$-0.910058\pi$
$397$	0.545390	−	8.66873i	0.0273723	−	0.435071i	0.987717	−	0.156255i	$-0.0499421\pi$
$398$	2.25739	−	11.8336i	0.113153	−	0.593166i
$399$	−1.80444	+	5.55349i	−0.0903350	+	0.278022i
$400$	−1.35812	+	4.81202i	−0.0679060	+	0.240601i
$401$	−4.12401	−	12.6924i	−0.205943	−	0.633827i	−0.999673	−	0.0255576i	$-0.991864\pi$
$401$	−4.12401	−	12.6924i	−0.205943	−	0.633827i	0.793730	−	0.608270i	$-0.208136\pi$
$402$	−5.35880	+	0.676974i	−0.267273	+	0.0337644i
$403$	26.0530	+	10.3151i	1.29779	+	0.513833i
$404$	−10.5327	−	4.17019i	−0.524021	−	0.207475i
$405$	−2.20423	−	0.376002i	−0.109529	−	0.0186837i
$406$	−1.98343	−	31.5257i	−0.0984359	−	1.56459i
$407$	9.33714	−	6.78383i	0.462825	−	0.336262i
$408$	5.10326	+	1.31029i	0.252649	+	0.0648693i
$409$	−7.66479	−	7.19771i	−0.378999	−	0.355904i	0.471513	−	0.881859i	$-0.343708\pi$
$409$	−7.66479	−	7.19771i	−0.378999	−	0.355904i	−0.850512	+	0.525955i	$0.823708\pi$
$410$	−3.15113	+	0.260152i	−0.155623	+	0.0128480i
$411$	3.51567	+	1.93275i	0.173415	+	0.0953357i
$412$	−9.96699	−	1.25912i	−0.491039	−	0.0620326i
$413$	−4.70386	−	24.6585i	−0.231462	−	1.21337i
$414$	−6.70059	+	0.846482i	−0.329316	+	0.0416023i
$415$	−0.817104	−	5.58770i	−0.0401100	−	0.274290i
$416$	1.06853	+	5.60142i	0.0523889	+	0.274632i
$417$	−12.2846	+	19.3574i	−0.601578	+	0.947935i
$418$	−1.54801	−	1.12470i	−0.0757156	−	0.0550106i
$419$	−6.59837	−	7.97606i	−0.322351	−	0.389656i	0.584299	−	0.811538i	$-0.301370\pi$
$419$	−6.59837	−	7.97606i	−0.322351	−	0.389656i	−0.906651	+	0.421882i	$0.861370\pi$
$420$	−7.92407	−	6.29868i	−0.386655	−	0.307344i
$421$	−12.7865	−	20.1483i	−0.623176	−	0.981967i	−0.998483	−	0.0550670i	$-0.982463\pi$
$421$	−12.7865	−	20.1483i	−0.623176	−	0.981967i	0.375307	−	0.926901i	$-0.377537\pi$
$422$	4.34329	−	5.25013i	0.211428	−	0.255572i
$423$	−4.00823	−	8.51791i	−0.194887	−	0.414155i
$424$	7.78931	+	5.65927i	0.378282	+	0.274838i
$425$	−26.2453	−	2.27813i	−1.27308	−	0.110506i
$426$	7.74900	−	5.62998i	0.375440	−	0.272773i
$427$	52.0165	+	28.5963i	2.51726	+	1.38387i
$428$	12.2031	−	3.13323i	0.589861	−	0.151451i
$429$	−5.39194	+	6.51774i	−0.260325	+	0.314679i
$430$	−18.1902	+	20.1453i	−0.877210	+	0.971493i
$431$	15.1814	−	6.01074i	0.731262	−	0.289527i	0.0271652	−	0.999631i	$-0.491352\pi$
$431$	15.1814	−	6.01074i	0.731262	−	0.289527i	0.704097	+	0.710104i	$0.251352\pi$
$432$	1.00000			0.0481125
$433$	10.1461	−	4.01714i	0.487592	−	0.193051i	−0.111448	−	0.993770i	$-0.535549\pi$
$433$	10.1461	−	4.01714i	0.487592	−	0.193051i	0.599040	+	0.800719i	$0.295549\pi$
$434$	19.4929	−	10.7163i	0.935691	−	0.514401i
$435$	−12.2143	−	9.70889i	−0.585631	−	0.465506i
$436$	−1.23734	+	6.48637i	−0.0592579	+	0.310641i
$437$	6.35066	+	5.96367i	0.303793	+	0.285281i
$438$	6.39984	+	6.00985i	0.305796	+	0.287162i
$439$	−4.98833	+	26.1497i	−0.238080	+	1.24806i	0.639561	+	0.768740i	$0.279116\pi$
$439$	−4.98833	+	26.1497i	−0.238080	+	1.24806i	−0.877641	+	0.479318i	$0.840884\pi$
$440$	2.76535	−	1.83170i	0.131833	−	0.0873231i
$441$	11.8239	−	6.50023i	0.563042	−	0.309535i
$442$	−27.9350	+	11.0603i	−1.32873	+	0.526083i
$443$	−34.3996			−1.63437			−0.817187	−	0.576372i	$-0.804468\pi$
$443$	−34.3996			−1.63437			−0.817187	+	0.576372i	$0.804468\pi$
$444$	7.23398	−	2.86414i	0.343310	−	0.135926i
$445$	−20.9344	+	4.41903i	−0.992386	+	0.209482i
$446$	−1.53732	+	1.85830i	−0.0727943	+	0.0879932i
$447$	7.76948	−	1.99486i	0.367484	−	0.0943538i
$448$	3.96696	+	2.18085i	0.187421	+	0.103036i
$449$	−14.2269	+	10.3364i	−0.671407	+	0.487806i	−0.870496	−	0.492176i	$-0.836202\pi$
$449$	−14.2269	+	10.3364i	−0.671407	+	0.487806i	0.199089	+	0.979981i	$0.436202\pi$
$450$	−4.93230	+	0.819994i	−0.232511	+	0.0386549i
$451$	1.69696	+	1.23291i	0.0799068	+	0.0580557i
$452$	−3.59458	−	7.63888i	−0.169075	−	0.359303i
$453$	−5.76001	+	6.96266i	−0.270629	+	0.327134i
$454$	−2.21502	−	3.49031i	−0.103956	−	0.163808i
$455$	57.6685	+	2.49816i	2.70354	+	0.117116i
$456$	−0.822219	−	0.993891i	−0.0385039	−	0.0465432i
$457$	9.33843	+	6.78476i	0.436833	+	0.317378i	0.784375	−	0.620287i	$-0.212984\pi$
$457$	9.33843	+	6.78476i	0.436833	+	0.317378i	−0.347542	+	0.937664i	$0.612984\pi$
$458$	14.8697	−	23.4308i	0.694814	−	1.09485i
$459$	0.987273	+	5.17547i	0.0460820	+	0.241570i
$460$	−13.5365	+	6.69591i	−0.631143	+	0.312198i
$461$	13.0094	−	1.64347i	0.605908	−	0.0765440i	0.183607	−	0.983000i	$-0.441223\pi$
$461$	13.0094	−	1.64347i	0.605908	−	0.0765440i	0.422301	+	0.906456i	$0.361223\pi$
$462$	1.25830	+	6.59625i	0.0585415	+	0.306885i
$463$	18.1067	+	2.28741i	0.841491	+	0.106305i	0.534250	−	0.845327i	$-0.320594\pi$
$463$	18.1067	+	2.28741i	0.841491	+	0.106305i	0.307241	+	0.951632i	$0.400594\pi$
$464$	6.11473	+	3.36160i	0.283869	+	0.156058i
$465$	2.52406	−	10.6938i	0.117051	−	0.495914i
$466$	−1.27598	−	1.19822i	−0.0591085	−	0.0555065i
$467$	7.55717	+	1.94035i	0.349704	+	0.0897887i	0.419456	−	0.907776i	$-0.362221\pi$
$467$	7.55717	+	1.94035i	0.349704	+	0.0897887i	−0.0697520	+	0.997564i	$0.522221\pi$
$468$	−4.61336	+	3.35180i	−0.213253	+	0.154937i
$469$	−1.53533	−	24.4033i	−0.0708948	−	1.12684i
$470$	−14.7068	−	15.0603i	−0.678374	−	0.694681i
$471$	−1.72670	−	0.683648i	−0.0795621	−	0.0315009i
$472$	5.15591	+	2.04137i	0.237320	+	0.0939617i
$473$	17.8642	−	2.25678i	0.821399	−	0.103767i
$474$	−3.39470	−	10.4478i	−0.155924	−	0.479884i
$475$	4.87042	+	4.22796i	0.223470	+	0.193992i
$476$	−7.37046	+	22.6839i	−0.337824	+	1.03972i
$477$	−1.80413	+	9.45758i	−0.0826054	+	0.433033i
$478$	−1.13064	+	17.9710i	−0.0517142	+	0.821974i
$479$	11.0355	−	2.83344i	0.504225	−	0.129463i	0.0119950	−	0.999928i	$-0.496182\pi$
$479$	11.0355	−	2.83344i	0.504225	−	0.129463i	0.492230	+	0.870465i	$0.336182\pi$
$480$	2.11272	−	0.732402i	0.0964321	−	0.0334294i
$481$	−23.7729	+	37.4602i	−1.08395	+	1.70804i
$482$	1.39899	+	4.30564i	0.0637221	+	0.196117i
$483$	−1.91976	−	30.5137i	−0.0873520	−	1.38842i
$484$	8.73015	+	1.10287i	0.396825	+	0.0501306i
$485$	20.2371	−	7.01545i	0.918919	−	0.318555i
$486$	0.425779	+	0.904827i	0.0193137	+	0.0410438i
$487$	6.97071	−	14.8135i	0.315873	−	0.671265i	−0.682339	−	0.731036i	$-0.739037\pi$
$487$	6.97071	−	14.8135i	0.315873	−	0.671265i	0.998212	+	0.0597712i	$0.0190371\pi$
$488$	−11.4905	+	6.31697i	−0.520152	+	0.285956i
$489$	−7.94120	+	7.45728i	−0.359113	+	0.337230i
$490$	20.2198	−	22.3930i	0.913436	−	1.01161i
$491$	2.92867	−	6.22374i	0.132169	−	0.280874i	−0.827778	−	0.561056i	$-0.810395\pi$
$491$	2.92867	−	6.22374i	0.132169	−	0.280874i	0.959947	+	0.280183i	$0.0903951\pi$
$492$	0.901333	+	1.08952i	0.0406352	+	0.0491196i
$493$	−11.3609	+	34.9654i	−0.511671	+	1.57476i
$494$	7.12451	+	1.82926i	0.320547	+	0.0823025i
$495$	2.83481	+	1.72227i	0.127415	+	0.0774101i
$496$	−0.308542	+	4.90413i	−0.0138539	+	0.220202i
$497$	23.2334	+	36.6100i	1.04216	+	1.64218i
$498$	−1.84099	+	1.72881i	−0.0824968	+	0.0774697i
$499$	37.4211			1.67520			0.837599	−	0.546286i	$-0.183959\pi$
$499$	37.4211			1.67520			0.837599	+	0.546286i	$0.183959\pi$
$500$	−9.82001	+	5.34484i	−0.439164	+	0.239029i
$501$	−3.71678			−0.166053
$502$	−2.23402	+	2.09788i	−0.0997090	+	0.0936330i
$503$	18.7384	+	29.5270i	0.835505	+	1.31655i	0.946493	+	0.322724i	$0.104598\pi$
$503$	18.7384	+	29.5270i	0.835505	+	1.31655i	−0.110988	+	0.993822i	$0.535402\pi$
$504$	−0.284247	+	4.51797i	−0.0126613	+	0.201246i
$505$	−9.78320	−	23.3651i	−0.435347	−	1.03973i
$506$	9.70388	+	2.49153i	0.431390	+	0.110762i
$507$	6.03128	−	18.5624i	0.267859	−	0.824384i
$508$	−1.83068	−	2.21291i	−0.0812231	−	0.0981819i
$509$	10.0334	−	21.3220i	0.444721	−	0.945081i	−0.549272	−	0.835643i	$-0.685095\pi$
$509$	10.0334	−	21.3220i	0.444721	−	0.945081i	0.993994	−	0.109437i	$-0.0349049\pi$
$510$	5.87635	+	10.2112i	0.260209	+	0.452161i
$511$	−28.9714	+	27.2060i	−1.28162	+	1.20352i
$512$	−0.876307	+	0.481754i	−0.0387276	+	0.0212907i
$513$	0.549216	−	1.16714i	0.0242485	−	0.0515307i
$514$	−0.811023	−	1.72351i	−0.0357727	−	0.0760208i
$515$	−13.5566	−	17.9123i	−0.597374	−	0.789311i
$516$	12.0428	+	1.52136i	0.530155	+	0.0669741i
$517$	0.876837	+	13.9369i	0.0385633	+	0.612945i
$518$	10.8838	+	33.4970i	0.478209	+	1.47178i
$519$	6.03614	−	9.51143i	0.264957	−	0.417505i
$520$	−7.29187	+	10.4602i	−0.319770	+	0.458712i
$521$	−25.4141	+	6.52522i	−1.11341	+	0.285875i	−0.760213	−	0.649674i	$-0.774905\pi$
$521$	−25.4141	+	6.52522i	−1.11341	+	0.285875i	−0.353197	+	0.935549i	$0.614905\pi$
$522$	−0.438142	+	6.96407i	−0.0191770	+	0.304809i
$523$	1.70707	−	8.94877i	0.0746449	−	0.391302i	−0.925283	−	0.379278i	$-0.876172\pi$
$523$	1.70707	−	8.94877i	0.0746449	−	0.391302i	0.999928	−	0.0120243i	$-0.00382755\pi$
$524$	3.11083	−	9.57414i	0.135897	−	0.418248i
$525$	−2.30272	−	22.5171i	−0.100499	−	0.982726i
$526$	−0.777632	−	2.39331i	−0.0339064	−	0.104353i
$527$	−25.6858	+	3.24487i	−1.11889	+	0.141349i
$528$	−1.37923	−	0.546075i	−0.0600232	−	0.0237648i
$529$	−21.0264	−	8.32495i	−0.914192	−	0.361954i
$530$	3.11513	+	21.3026i	0.135312	+	0.925324i
$531$	0.348194	+	5.53438i	0.0151103	+	0.240172i
$532$	4.72408	−	3.43225i	0.204815	−	0.148807i
$533$	−7.81004	−	2.00528i	−0.338290	−	0.0868582i
$534$	6.97511	+	6.55006i	0.301842	+	0.283449i
$535$	24.0769	+	14.6278i	1.04094	+	0.632413i
$536$	4.73328	+	2.60214i	0.204446	+	0.112395i
$537$	−8.41713	−	1.06333i	−0.363226	−	0.0458861i
$538$	−5.15401	−	27.0182i	−0.222205	−	1.16484i
$539$	−19.8574	+	2.50858i	−0.855320	+	0.108052i
$540$	1.56225	+	1.59981i	0.0672285	+	0.0688446i
$541$	3.44905	+	18.0806i	0.148286	+	0.777344i	0.976264	+	0.216583i	$0.0694912\pi$
$541$	3.44905	+	18.0806i	0.148286	+	0.777344i	−0.827978	+	0.560761i	$0.810509\pi$
$542$	1.34335	−	2.11679i	0.0577020	−	0.0909238i
$543$	−9.24411	−	6.71624i	−0.396703	−	0.288221i
$544$	−3.35845	−	4.05967i	−0.143993	−	0.174057i
$545$	−12.3100	+	8.15382i	−0.527301	+	0.349271i
$546$	−13.8320	−	21.7958i	−0.591955	−	0.932772i
$547$	−8.50577	+	10.2817i	−0.363681	+	0.439614i	−0.920336	−	0.391129i	$-0.872084\pi$
$547$	−8.50577	+	10.2817i	−0.363681	+	0.439614i	0.556655	+	0.830744i	$0.312084\pi$
$548$	−1.70819	−	3.63009i	−0.0729703	−	0.155070i
$549$	−10.6082	−	7.70731i	−0.452747	−	0.328940i
$550$	7.25054	+	1.56245i	0.309164	+	0.0666230i
$551$	7.28178	−	5.29052i	0.310214	−	0.225384i
$552$	5.91844	+	3.25369i	0.251906	+	0.138486i
$553$	48.1678	−	12.3674i	2.04830	−	0.525915i
$554$	18.9212	−	22.8719i	0.803887	−	0.971732i
$555$	15.8833	+	7.09847i	0.674211	+	0.301313i
$556$	21.3164	−	8.43977i	0.904017	−	0.357926i
$557$	−23.5865			−0.999391			−0.499695	−	0.866201i	$-0.666555\pi$
$557$	−23.5865			−0.999391			−0.499695	+	0.866201i	$0.666555\pi$
$558$	−4.56876	+	1.80890i	−0.193411	+	0.0765769i
$559$	−60.6570	+	33.3465i	−2.56552	+	1.41041i
$560$	2.70844	+	9.75339i	0.114452	+	0.412156i
$561$	1.46452	−	7.67727i	0.0618320	−	0.324134i
$562$	−19.5479	−	18.3567i	−0.824577	−	0.774329i
$563$	−0.770248	−	0.723311i	−0.0324621	−	0.0304839i	0.668146	−	0.744030i	$-0.267088\pi$
$563$	−0.770248	−	0.723311i	−0.0324621	−	0.0304839i	−0.700608	+	0.713546i	$0.747088\pi$
$564$	−1.76398	+	9.24711i	−0.0742770	+	0.389374i
$565$	6.60508	−	17.6845i	0.277878	−	0.743991i
$566$	17.1602	−	9.43392i	0.721298	−	0.396537i
$567$	−4.20901	+	1.66646i	−0.176762	+	0.0699849i
$568$	−9.57829			−0.401896
$569$	−24.6923	+	9.77638i	−1.03516	+	0.409847i	−0.823391	−	0.567474i	$-0.807921\pi$
$569$	−24.6923	+	9.77638i	−1.03516	+	0.409847i	−0.211764	+	0.977321i	$0.567921\pi$
$570$	0.305522	−	2.86810i	0.0127969	−	0.120131i
$571$	−1.76415	+	2.13250i	−0.0738276	+	0.0892422i	−0.806134	−	0.591733i	$-0.798444\pi$
$571$	−1.76415	+	2.13250i	−0.0738276	+	0.0892422i	0.732306	+	0.680975i	$0.238444\pi$
$572$	8.19320	−	2.10366i	0.342575	−	0.0879583i
$573$	−3.19928	−	1.75882i	−0.133652	−	0.0734758i
$574$	−5.17864	+	3.76250i	−0.216152	+	0.157044i
$575$	−31.8596	−	11.1951i	−1.32864	−	0.466868i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	8.12975	+	17.2766i	0.338446	+	0.719234i	0.999517	−	0.0310893i	$-0.00989761\pi$
$577$	8.12975	+	17.2766i	0.338446	+	0.719234i	−0.661071	+	0.750324i	$0.729898\pi$
$578$	6.85878	−	8.29084i	0.285288	−	0.344853i
$579$	10.8043	+	17.0248i	0.449010	+	0.707526i
$580$	4.17483	+	15.0340i	0.173350	+	0.624254i
$581$	−7.28740	−	8.80895i	−0.302332	−	0.365457i
$582$	−7.74932	−	5.63021i	−0.321220	−	0.233380i
$583$	7.65285	−	12.0590i	0.316949	−	0.499431i
$584$	−1.64508	−	8.62380i	−0.0680738	−	0.356855i
$585$	−12.5694	−	2.14412i	−0.519683	−	0.0886486i
$586$	−22.5262	+	2.84572i	−0.930549	+	0.117556i
$587$	7.82238	+	41.0064i	0.322864	+	1.69251i	0.660168	+	0.751118i	$0.270485\pi$
$587$	7.82238	+	41.0064i	0.322864	+	1.69251i	−0.337304	+	0.941396i	$0.609515\pi$
$588$	−13.3865	−	1.69110i	−0.552048	−	0.0697399i
$589$	5.55437	+	3.05354i	0.228864	+	0.125819i
$590$	4.78903	+	11.4376i	0.197161	+	0.470878i
$591$	−4.44188	−	4.17121i	−0.182715	−	0.171581i
$592$	−7.53591	−	1.93489i	−0.309724	−	0.0795236i
$593$	−5.77199	+	4.19360i	−0.237027	+	0.172210i	−0.699958	−	0.714184i	$-0.746798\pi$
$593$	−5.77199	+	4.19360i	−0.237027	+	0.172210i	0.462931	+	0.886395i	$0.346798\pi$
$594$	−0.0931432	−	1.48047i	−0.00382171	−	0.0607444i
$595$	−47.8044	+	23.6467i	−1.95979	+	0.969419i
$596$	−7.45819	−	2.95291i	−0.305499	−	0.120956i
$597$	−11.2010	−	4.43480i	−0.458428	−	0.181504i
$598$	−38.2096	+	4.82700i	−1.56251	+	0.197391i
$599$	3.95206	+	12.1632i	0.161477	+	0.496975i	0.998759	−	0.0497956i	$-0.0158570\pi$
$599$	3.95206	+	12.1632i	0.161477	+	0.496975i	−0.837282	+	0.546771i	$0.815857\pi$
$600$	4.47230	+	2.23575i	0.182581	+	0.0912740i
$601$	1.95689	−	6.02270i	0.0798233	−	0.245671i	−0.903179	−	0.429264i	$-0.858773\pi$
$601$	1.95689	−	6.02270i	0.0798233	−	0.245671i	0.983002	+	0.183593i	$0.0587729\pi$
$602$	−10.2966	+	53.9766i	−0.419657	+	2.19992i
$603$	−0.339156	+	5.39073i	−0.0138115	+	0.219528i
$604$	8.75249	−	2.24726i	0.356134	−	0.0914396i
$605$	11.8743	+	15.6895i	0.482758	+	0.637869i
$606$	−6.06995	+	9.56471i	−0.246575	+	0.388540i
$607$	−9.88140	−	30.4118i	−0.401074	−	1.23438i	−0.924130	−	0.382079i	$-0.875208\pi$
$607$	−9.88140	−	30.4118i	−0.401074	−	1.23438i	0.523056	−	0.852298i	$-0.324792\pi$
$608$	0.0809940	+	1.28736i	0.00328474	+	0.0522095i
$609$	−31.3389	−	3.95903i	−1.26992	−	0.160428i
$610$	−28.0570	−	8.51392i	−1.13600	−	0.344719i
$611$	−22.8566	−	48.5727i	−0.924679	−	1.96504i
$612$	2.24334	−	4.76734i	0.0906817	−	0.192708i
$613$	7.17639	−	3.94525i	0.289852	−	0.159347i	−0.330194	−	0.943913i	$-0.607114\pi$
$613$	7.17639	−	3.94525i	0.289852	−	0.159347i	0.620045	+	0.784566i	$0.287114\pi$
$614$	−6.34951	+	5.96259i	−0.256245	+	0.240630i
$615$	−0.334920	+	3.14407i	−0.0135053	+	0.126781i
$616$	2.85919	−	6.07609i	0.115200	−	0.244813i
$617$	−6.42210	−	7.76298i	−0.258544	−	0.312526i	0.625230	−	0.780441i	$-0.285005\pi$
$617$	−6.42210	−	7.76298i	−0.258544	−	0.312526i	−0.883773	+	0.467915i	$0.845005\pi$
$618$	−3.10445	+	9.55451i	−0.124879	+	0.384339i
$619$	−29.3271	−	7.52993i	−1.17876	−	0.302653i	−0.392029	−	0.919953i	$-0.628227\pi$
$619$	−29.3271	−	7.52993i	−1.17876	−	0.302653i	−0.786728	+	0.617300i	$0.788227\pi$
$620$	−8.32768	+	7.16788i	−0.334448	+	0.287869i
$621$	−0.424078	+	6.74052i	−0.0170177	+	0.270488i
$622$	14.3606	+	22.6287i	0.575807	+	0.907327i
$623$	−31.5756	+	29.6515i	−1.26505	+	1.18796i
$624$	5.70242			0.228280
$625$	−23.8920	−	7.36012i	−0.955681	−	0.294405i
$626$	13.7337			0.548908
$627$	−1.39484	+	1.30984i	−0.0557046	+	0.0523101i
$628$	0.995090	+	1.56801i	0.0397084	+	0.0625705i
$629$	2.57397	−	40.9121i	0.102631	−	1.63127i
$630$	−7.67194	+	6.60346i	−0.305657	+	0.263088i
$631$	3.16762	+	0.813308i	0.126101	+	0.0323773i	0.311213	−	0.950340i	$-0.399265\pi$
$631$	3.16762	+	0.813308i	0.126101	+	0.0323773i	−0.185112	+	0.982717i	$0.559265\pi$
$632$	−3.39470	+	10.4478i	−0.135034	+	0.415592i
$633$	−4.34329	−	5.25013i	−0.172630	−	0.208674i
$634$	11.8867	−	25.2605i	0.472081	−	1.00322i
$635$	0.680247	−	6.38584i	0.0269948	−	0.253414i
$636$	7.01860	−	6.59090i	0.278305	−	0.261346i
$637$	67.4247	−	37.0671i	2.67147	−	1.46865i
$638$	4.40720	−	9.36578i	0.174483	−	0.370795i
$639$	−4.07824	−	8.66669i	−0.161333	−	0.342849i
$640$	−2.13972	−	0.649300i	−0.0845799	−	0.0256658i
$641$	23.6443	+	2.98697i	0.933895	+	0.117978i	0.577531	−	0.816369i	$-0.304016\pi$
$641$	23.6443	+	2.98697i	0.933895	+	0.117978i	0.356364	+	0.934347i	$0.384016\pi$
$642$	−0.791095	−	12.5741i	−0.0312220	−	0.496260i
$643$	0.513594	+	1.58068i	0.0202542	+	0.0623359i	0.960673	−	0.277683i	$-0.0895665\pi$
$643$	0.513594	+	1.58068i	0.0202542	+	0.0623359i	−0.940419	+	0.340019i	$0.889567\pi$
$644$	−16.3824	+	25.8145i	−0.645556	+	1.01723i
$645$	16.3800	+	21.6429i	0.644961	+	0.852187i
$646$	−6.58274	+	1.69016i	−0.258994	+	0.0664985i
$647$	−0.230664	+	3.66629i	−0.00906833	+	0.144137i	0.990887	+	0.134695i	$0.0430055\pi$
$647$	−0.230664	+	3.66629i	−0.00906833	+	0.144137i	−0.999955	+	0.00944185i	$0.996995\pi$
$648$	0.187381	−	0.982287i	0.00736103	−	0.0385879i
$649$	2.54195	−	7.82331i	0.0997802	−	0.307092i
$650$	−28.1261	+	4.67595i	−1.10320	+	0.183406i
$651$	−6.87391	−	21.1557i	−0.269410	−	0.829158i
$652$	10.8078	−	1.36535i	0.423268	−	0.0534712i
$653$	−14.7050	−	5.82212i	−0.575451	−	0.227837i	0.0623292	−	0.998056i	$-0.480147\pi$
$653$	−14.7050	−	5.82212i	−0.575451	−	0.227837i	−0.637780	+	0.770219i	$0.720147\pi$
$654$	6.13962	+	2.43085i	0.240078	+	0.0950537i
$655$	20.1767	−	9.98049i	0.788367	−	0.389970i
$656$	−0.0887873	−	1.41123i	−0.00346656	−	0.0550994i
$657$	7.10261	−	5.16035i	0.277099	−	0.201324i
$658$	−41.2768	−	10.5981i	−1.60914	−	0.413156i
$659$	21.0282	+	19.7468i	0.819144	+	0.769227i	0.975856	−	0.218417i	$-0.0700893\pi$
$659$	21.0282	+	19.7468i	0.819144	+	0.769227i	−0.156712	+	0.987644i	$0.550089\pi$
$660$	−1.28108	−	3.05960i	−0.0498661	−	0.119095i
$661$	25.2382	+	13.8748i	0.981654	+	0.539669i	0.889921	−	0.456115i	$-0.150759\pi$
$661$	25.2382	+	13.8748i	0.981654	+	0.539669i	0.0917330	+	0.995784i	$0.470759\pi$
$662$	−5.56461	−	0.702974i	−0.216275	−	0.0273218i
$663$	5.62985	+	29.5127i	0.218645	+	1.14618i
$664$	2.50556	−	0.316526i	0.0972346	−	0.0122836i
$665$	12.8711	+	2.19559i	0.499121	+	0.0851412i
$666$	−1.45789	−	7.64254i	−0.0564922	−	0.296142i
$667$	−25.2521	+	39.7909i	−0.977764	+	1.54071i
$668$	3.00694	+	2.18467i	0.116342	+	0.0845273i
$669$	1.53732	+	1.85830i	0.0594363	+	0.0718462i
$670$	3.23164	+	11.6375i	0.124849	+	0.449596i
$671$	10.4224	+	16.4230i	0.402350	+	0.634003i
$672$	2.88556	−	3.48804i	0.111313	−	0.134554i
$673$	−12.0798	−	25.6708i	−0.465640	−	0.989536i	−0.990393	−	0.138281i	$-0.955842\pi$
$673$	−12.0798	−	25.6708i	−0.465640	−	0.989536i	0.524753	−	0.851255i	$-0.324158\pi$
$674$	−14.1923	−	10.3113i	−0.546667	−	0.397177i
$675$	−0.118752	+	4.99859i	−0.00457077	+	0.192396i
$676$	−15.7901	+	11.4722i	−0.607312	+	0.441238i
$677$	31.2308	+	17.1693i	1.20030	+	0.659869i	0.951190	−	0.308607i	$-0.0998628\pi$
$677$	31.2308	+	17.1693i	1.20030	+	0.659869i	0.249107	+	0.968476i	$0.419863\pi$
$678$	−8.17713	+	2.09953i	−0.314041	+	0.0806320i
$679$	27.6399	−	33.4108i	1.06072	−	1.28219i
$680$	1.24794	−	11.7151i	0.0478564	−	0.449253i
$681$	−3.84354	+	1.52177i	−0.147285	+	0.0583142i
$682$	7.28916			0.279116
$683$	−43.0702	+	17.0527i	−1.64803	+	0.652503i	−0.994533	−	0.104423i	$-0.966701\pi$
$683$	−43.0702	+	17.0527i	−1.64803	+	0.652503i	−0.653501	+	0.756926i	$0.726701\pi$
$684$	−1.13036	+	0.621418i	−0.0432202	+	0.0237605i
$685$	3.13881	−	8.40387i	0.119928	−	0.321096i
$686$	5.50760	−	28.8719i	0.210281	−	1.10233i
$687$	−20.2295	−	18.9968i	−0.771804	−	0.724773i
$688$	−8.84860	−	8.30938i	−0.337350	−	0.316792i
$689$	−10.2879	+	53.9311i	−0.391938	+	2.05461i
$690$	4.04081	+	14.5514i	0.153831	+	0.553964i
$691$	34.4273	−	18.9266i	1.30968	−	0.720001i	0.334704	−	0.942323i	$-0.391364\pi$
$691$	34.4273	−	18.9266i	1.30968	−	0.720001i	0.974973	+	0.222323i	$0.0713638\pi$
$692$	−10.4740	+	4.14695i	−0.398162	+	0.157644i
$693$	6.71519			0.255089
$694$	−7.14491	+	2.82887i	−0.271217	+	0.107382i
$695$	46.8035	+	20.9171i	1.77536	+	0.793430i
$696$	4.44784	−	5.37652i	0.168595	−	0.203796i
$697$	7.21614	−	1.85279i	0.273331	−	0.0701794i
$698$	15.7905	+	8.68092i	0.597680	+	0.328578i
$699$	−1.41609	+	1.02885i	−0.0535615	+	0.0389147i
$700$	−11.3723	+	19.5702i	−0.429831	+	0.739684i
$701$	−11.2396	−	8.16602i	−0.424513	−	0.308426i	0.354938	−	0.934890i	$-0.384502\pi$
$701$	−11.2396	−	8.16602i	−0.424513	−	0.308426i	−0.779451	+	0.626463i	$0.784502\pi$
$702$	2.42797	+	5.15971i	0.0916380	+	0.194741i
$703$	−6.39715	+	7.73282i	−0.241273	+	0.291649i
$704$	0.794844	+	1.25247i	0.0299568	+	0.0472044i
$705$	−17.5494	+	11.6243i	−0.660947	+	0.437795i
$706$	3.79851	+	4.59161i	0.142959	+	0.172807i
$707$	−41.4877	−	30.1426i	−1.56031	−	1.13363i
$708$	2.97133	−	4.68207i	0.111670	−	0.175963i
$709$	−2.10726	−	11.0467i	−0.0791399	−	0.414866i	−0.999705	−	0.0242774i	$-0.992272\pi$
$709$	−2.10726	−	11.0467i	−0.0791399	−	0.414866i	0.920565	−	0.390589i	$-0.127728\pi$
$710$	−14.9637	−	15.3234i	−0.561577	−	0.575077i
$711$	−10.8989	+	1.37685i	−0.408739	+	0.0516357i
$712$	−1.79295	−	9.39898i	−0.0671937	−	0.352242i
$713$	−32.9256	−	4.15947i	−1.23307	−	0.155773i
$714$	20.9011	+	11.4905i	0.782202	+	0.430019i
$715$	16.1653	+	9.82109i	0.604547	+	0.367288i
$716$	6.18459	+	5.80772i	0.231129	+	0.217045i
$717$	17.4408	+	4.47804i	0.651339	+	0.167236i
$718$	−0.698091	+	0.507193i	−0.0260525	+	0.0189283i
$719$	−2.61650	−	41.5881i	−0.0975791	−	1.55098i	−0.677022	−	0.735963i	$-0.736730\pi$
$719$	−2.61650	−	41.5881i	−0.0975791	−	1.55098i	0.579443	−	0.815013i	$-0.303270\pi$
$720$	−0.323545	−	2.21254i	−0.0120578	−	0.0824564i
$721$	−42.2846	−	16.7416i	−1.57476	−	0.623492i
$722$	−16.1187	−	6.38186i	−0.599877	−	0.237508i
$723$	4.49152	−	0.567411i	0.167041	−	0.0211022i
$724$	3.53094	+	10.8671i	0.131226	+	0.403873i
$725$	−17.5294	+	30.1658i	−0.651026	+	1.12033i
$726$	2.71921	−	8.36885i	0.100919	−	0.310597i
$727$	5.20194	−	27.2695i	0.192929	−	1.01137i	−0.745658	−	0.666329i	$-0.767865\pi$
$727$	5.20194	−	27.2695i	0.192929	−	1.01137i	0.938587	−	0.345042i	$-0.112135\pi$
$728$	−1.62089	+	25.7634i	−0.0600743	+	0.954854i
$729$	0.968583	−	0.248690i	0.0358735	−	0.00921074i
$730$	11.2264	−	16.1043i	0.415507	−	0.596048i
$731$	34.2690	−	53.9992i	1.26748	−	1.99723i
$732$	4.05197	+	12.4707i	0.149765	+	0.460930i
$733$	−0.495690	−	7.87876i	−0.0183087	−	0.291009i	−0.996517	−	0.0833847i	$-0.973427\pi$
$733$	−0.495690	−	7.87876i	−0.0183087	−	0.291009i	0.978209	−	0.207624i	$-0.0665730\pi$
$734$	−7.61060	−	0.961443i	−0.280912	−	0.0354875i
$735$	−18.2075	−	24.0576i	−0.671596	−	0.887379i
$736$	−2.87565	−	6.11107i	−0.105998	−	0.225257i
$737$	3.41152	−	7.24984i	0.125665	−	0.267051i
$738$	1.23912	−	0.681212i	0.0456126	−	0.0250757i
$739$	11.6550	−	10.9448i	0.428736	−	0.402610i	−0.439911	−	0.898041i	$-0.644990\pi$
$739$	11.6550	−	10.9448i	0.428736	−	0.402610i	0.868647	+	0.495431i	$0.164990\pi$
$740$	−8.67752	−	15.0788i	−0.318992	−	0.554307i
$741$	3.13186	−	6.65555i	0.115052	−	0.244498i
$742$	27.7825	+	33.5833i	1.01993	+	1.23288i
$743$	3.53626	−	10.8835i	0.129733	−	0.399276i	−0.865001	−	0.501770i	$-0.832682\pi$
$743$	3.53626	−	10.8835i	0.129733	−	0.399276i	0.994734	+	0.102494i	$0.0326823\pi$
$744$	4.75945	+	1.22202i	0.174490	+	0.0448014i
$745$	−6.92748	−	16.5448i	−0.253803	−	0.606155i
$746$	−1.68916	+	26.8485i	−0.0618446	+	0.982992i
$747$	1.35322	+	2.13233i	0.0495116	+	0.0780178i
$748$	−5.69740	+	5.35022i	−0.208318	+	0.195623i
$749$	57.0343			2.08399
$750$	3.41009	+	10.6476i	0.124519	+	0.388795i
$751$	−2.09025			−0.0762745			−0.0381372	−	0.999273i	$-0.512142\pi$
$751$	−2.09025			−0.0762745			−0.0381372	+	0.999273i	$0.512142\pi$
$752$	6.86241	−	6.44423i	0.250246	−	0.234997i
$753$	1.64211	+	2.58755i	0.0598418	+	0.0942955i
$754$	−2.49847	+	39.7121i	−0.0909891	+	1.44623i
$755$	17.2688	+	10.4915i	0.628474	+	0.381825i
$756$	4.38468	+	1.12579i	0.159469	+	0.0409448i
$757$	−5.09922	+	15.6938i	−0.185334	+	0.570400i	−0.999954	−	0.00959538i	$-0.996946\pi$
$757$	−5.09922	+	15.6938i	−0.185334	+	0.570400i	0.814620	+	0.579995i	$0.196946\pi$
$758$	11.6483	+	14.0803i	0.423084	+	0.511420i
$759$	4.26573	−	9.06513i	0.154836	−	0.329044i
$760$	−1.93300	+	2.14076i	−0.0701172	+	0.0776534i
$761$	2.10913	−	1.98061i	0.0764561	−	0.0717970i	−0.645377	−	0.763864i	$-0.723300\pi$
$761$	2.10913	−	1.98061i	0.0764561	−	0.0717970i	0.721833	+	0.692067i	$0.243300\pi$
$762$	−2.51675	+	1.38359i	−0.0911721	+	0.0501223i
$763$	−12.7277	+	27.0477i	−0.460772	+	0.979191i
$764$	1.55446	+	3.30341i	0.0562386	+	0.119513i
$765$	11.1315	−	3.85887i	0.402460	−	0.139518i
$766$	−8.08435	−	1.02129i	−0.292099	−	0.0369007i
$767$	1.98555	+	31.5594i	0.0716940	+	1.13954i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	16.8500	−	26.5514i	0.607628	−	0.957468i	−0.391674	−	0.920104i	$-0.628104\pi$
$769$	16.8500	−	26.5514i	0.607628	−	0.957468i	0.999302	−	0.0373641i	$-0.0118961\pi$
$770$	14.1873	−	4.91822i	0.511276	−	0.177240i
$771$	−1.84495	+	0.473704i	−0.0664444	+	0.0170600i
$772$	1.26609	−	20.1239i	0.0455676	−	0.724276i
$773$	2.65302	−	13.9076i	0.0954225	−	0.500222i	−0.902201	−	0.431316i	$-0.858049\pi$
$773$	2.65302	−	13.9076i	0.0954225	−	0.500222i	0.997623	−	0.0689057i	$-0.0219508\pi$
$774$	3.75101	−	11.5444i	0.134827	−	0.414955i
$775$	−24.4771	−	2.12465i	−0.879244	−	0.0763197i
$776$	2.95998	+	9.10988i	0.106257	+	0.327026i
$777$	34.9431	−	4.41435i	1.25358	−	0.158364i
$778$	0.0694480	+	0.0274964i	0.00248983	+	0.000985793i
$779$	−1.69588	−	0.671445i	−0.0607611	−	0.0240570i
$780$	8.90861	+	9.12277i	0.318979	+	0.326647i
$781$	0.892153	+	14.1804i	0.0319237	+	0.507413i
$782$	28.7886	−	20.9161i	1.02948	−	0.747959i
$783$	6.75862	+	1.73532i	0.241533	+	0.0620152i
$784$	9.83586	+	9.23649i	0.351281	+	0.329875i
$785$	−0.953933	+	4.04157i	−0.0340473	+	0.144250i
$786$	−8.82165	−	4.84974i	−0.314658	−	0.172985i
$787$	−18.0436	−	2.27944i	−0.643186	−	0.0812533i	−0.203027	−	0.979173i	$-0.565078\pi$
$787$	−18.0436	−	2.27944i	−0.643186	−	0.0812533i	−0.440159	+	0.897920i	$0.645078\pi$
$788$	1.14179	+	5.98545i	0.0406744	+	0.213223i
$789$	−2.49663	+	0.315398i	−0.0888823	+	0.0112284i
$790$	−22.0178	+	10.8912i	−0.783359	+	0.387493i
$791$	−7.16130	−	37.5408i	−0.254626	−	1.33480i
$792$	−0.794844	+	1.25247i	−0.0282435	+	0.0445047i
$793$	−60.4925	−	43.9503i	−2.14815	−	1.56072i
$794$	5.53658	+	6.69258i	0.196486	+	0.237511i
$795$	21.5090	+	0.931754i	0.762844	+	0.0330459i
$796$	6.45511	+	10.1716i	0.228795	+	0.360524i
$797$	20.0216	−	24.2020i	0.709202	−	0.857278i	−0.285680	−	0.958325i	$-0.592219\pi$
$797$	20.0216	−	24.2020i	0.709202	−	0.857278i	0.994882	+	0.101047i	$0.0322193\pi$
$798$	−2.48625	−	5.28355i	−0.0880122	−	0.187036i
$799$	40.1269	+	29.1539i	1.41959	+	1.03139i
$800$	−2.30403	−	4.43751i	−0.0814596	−	0.156890i
$801$	7.74105	−	5.62420i	0.273517	−	0.198721i
$802$	11.6948	+	6.42927i	0.412958	+	0.227026i
$803$	−12.6140	+	3.23874i	−0.445140	+	0.114292i
$804$	3.44298	−	4.16184i	0.121424	−	0.146777i
$805$	−66.8915	+	14.1201i	−2.35762	+	0.497667i
$806$	−26.0530	+	10.3151i	−0.917679	+	0.363335i
$807$	−27.5054			−0.968237
$808$	10.5327	−	4.17019i	0.370539	−	0.146707i
$809$	22.1350	−	12.1688i	0.778225	−	0.427833i	−0.0425429	−	0.999095i	$-0.513546\pi$
$809$	22.1350	−	12.1688i	0.778225	−	0.427833i	0.820768	+	0.571262i	$0.193546\pi$
$810$	1.86420	−	1.23480i	0.0655015	−	0.0433866i
$811$	−3.46700	+	18.1747i	−0.121743	+	0.638199i	0.868141	+	0.496318i	$0.165315\pi$
$811$	−3.46700	+	18.1747i	−0.121743	+	0.638199i	−0.989884	+	0.141881i	$0.954685\pi$
$812$	23.0267	+	21.6235i	0.808078	+	0.758836i
$813$	−1.82757	−	1.71621i	−0.0640958	−	0.0601899i
$814$	−2.16263	+	11.3369i	−0.0758002	+	0.397359i
$815$	19.0688	+	15.1574i	0.667952	+	0.530941i
$816$	−4.61708	+	2.53826i	−0.161630	+	0.0888568i
$817$	−14.5580	+	5.76394i	−0.509321	+	0.201655i
$818$	10.5146			0.367633
$819$	−24.0015	+	9.50288i	−0.838682	+	0.332058i
$820$	2.11899	−	2.34674i	0.0739984	−	0.0819518i
$821$	−22.9409	+	27.7307i	−0.800642	+	0.967809i	−0.999926	−	0.0121323i	$-0.996138\pi$
$821$	−22.9409	+	27.7307i	−0.800642	+	0.967809i	0.199285	+	0.979942i	$0.436138\pi$
$822$	−3.88587	+	0.997722i	−0.135535	+	0.0347996i
$823$	26.0761	+	14.3355i	0.908956	+	0.499703i	0.866377	−	0.499391i	$-0.166443\pi$
$823$	26.0761	+	14.3355i	0.908956	+	0.499703i	0.0425786	+	0.999093i	$0.486443\pi$
$824$	8.12756	−	5.90501i	0.283137	−	0.205711i
$825$	2.89339	−	6.82934i	0.100735	−	0.237767i
$826$	20.3089	+	14.7553i	0.706636	+	0.513401i
$827$	9.27247	+	19.7050i	0.322435	+	0.685210i	0.998674	−	0.0514721i	$-0.0163913\pi$
$827$	9.27247	+	19.7050i	0.322435	+	0.685210i	−0.676239	+	0.736682i	$0.736391\pi$
$828$	4.30507	−	5.20393i	0.149611	−	0.180849i
$829$	18.6975	+	29.4626i	0.649391	+	1.02328i	0.996347	+	0.0853956i	$0.0272154\pi$
$829$	18.6975	+	29.4626i	0.649391	+	1.02328i	−0.346956	+	0.937881i	$0.612785\pi$
$830$	4.42069	+	3.51392i	0.153444	+	0.121970i
$831$	−18.9212	−	22.8719i	−0.656371	−	0.793416i
$832$	−4.61336	−	3.35180i	−0.159939	−	0.116203i
$833$	−38.0925	+	60.0241i	−1.31983	+	2.07971i
$834$	−4.29598	−	22.5203i	−0.148757	−	0.779814i
$835$	1.20254	+	8.22351i	0.0416158	+	0.284586i
$836$	1.89836	−	0.239818i	0.0656561	−	0.00829429i
$837$	0.920760	+	4.82679i	0.0318261	+	0.166838i
$838$	10.2700	+	1.29740i	0.354771	+	0.0448180i
$839$	−18.2131	−	10.0127i	−0.628786	−	0.345678i	0.135288	−	0.990806i	$-0.456804\pi$
$839$	−18.2131	−	10.0127i	−0.628786	−	0.345678i	−0.764074	+	0.645128i	$0.776804\pi$
$840$	10.0881	−	0.832859i	0.348074	−	0.0287364i
$841$	14.3536	+	13.4789i	0.494952	+	0.464791i
$842$	23.1134	+	5.93451i	0.796541	+	0.204517i
$843$	−21.6944	+	15.7619i	−0.747195	+	0.542869i
$844$	0.427843	+	6.80037i	0.0147270	+	0.234078i
$845$	−43.0213	−	7.33867i	−1.47998	−	0.252458i
$846$	8.75278	+	3.46547i	0.300927	+	0.119145i
$847$	37.0373	+	14.6641i	1.27262	+	0.503865i
$848$	−9.55220	+	1.20672i	−0.328024	+	0.0414390i
$849$	−6.05131	−	18.6240i	−0.207680	−	0.639175i
$850$	20.6915	−	16.3054i	0.709711	−	0.559272i
$851$	16.2380	−	49.9754i	0.556632	−	1.71314i
$852$	−1.79479	+	9.40863i	−0.0614886	+	0.322334i
$853$	−0.570077	+	9.06112i	−0.0195191	+	0.310247i	0.976138	+	0.217151i	$0.0696763\pi$
$853$	−0.570077	+	9.06112i	−0.0195191	+	0.310247i	−0.995657	+	0.0930960i	$0.970324\pi$
$854$	−57.4940	+	14.7619i	−1.96740	+	0.505143i
$855$	−2.76004	−	0.837538i	−0.0943915	−	0.0286432i
$856$	−6.75086	+	10.6377i	−0.230740	+	0.363588i
$857$	−11.6748	−	35.9315i	−0.398805	−	1.22740i	−0.925958	−	0.377626i	$-0.876741\pi$
$857$	−11.6748	−	35.9315i	−0.398805	−	1.22740i	0.527153	−	0.849770i	$-0.323259\pi$
$858$	−0.531142	−	8.44226i	−0.0181329	−	0.288214i
$859$	11.1492	+	1.40847i	0.380405	+	0.0480563i	0.313211	−	0.949684i	$-0.398595\pi$
$859$	11.1492	+	1.40847i	0.380405	+	0.0480563i	0.0671941	+	0.997740i	$0.478595\pi$
$860$	−0.530320	−	27.1374i	−0.0180838	−	0.925376i
$861$	2.72548	+	5.79194i	0.0928840	+	0.197389i
$862$	−6.95213	+	14.7740i	−0.236790	+	0.503205i
$863$	31.5936	−	17.3687i	1.07546	−	0.591238i	0.157339	−	0.987545i	$-0.449708\pi$
$863$	31.5936	−	17.3687i	1.07546	−	0.591238i	0.918118	+	0.396307i	$0.129708\pi$
$864$	−0.728969	+	0.684547i	−0.0248000	+	0.0232888i
$865$	−22.9973	−	10.2778i	−0.781933	−	0.349456i
$866$	−4.64629	+	9.87387i	−0.157887	+	0.335528i
$867$	−6.85878	−	8.29084i	−0.232936	−	0.281572i
$868$	−6.87391	+	21.1557i	−0.233316	+	0.718072i
$869$	15.7839	+	4.05260i	0.535431	+	0.137475i
$870$	15.5500	−	1.28378i	0.527195	−	0.0435243i
$871$	−1.93401	+	30.7402i	−0.0655315	+	1.04159i
$872$	−3.53824	−	5.57538i	−0.119820	−	0.188806i
$873$	−6.98257	+	6.55707i	−0.236324	+	0.221923i
$874$	−8.71185			−0.294683
$875$	−49.0748	+	12.3801i	−1.65903	+	0.418525i
$876$	−8.77930			−0.296625
$877$	19.6395	−	18.4427i	0.663179	−	0.622767i	−0.278037	−	0.960570i	$-0.589684\pi$
$877$	19.6395	−	18.4427i	0.663179	−	0.622767i	0.941217	+	0.337803i	$0.109684\pi$
$878$	−14.2644	−	22.4771i	−0.481400	−	0.758564i
$879$	−1.42567	+	22.6604i	−0.0480868	+	0.764317i
$880$	−0.761969	+	3.22827i	−0.0256860	+	0.108825i
$881$	37.6006	+	9.65419i	1.26680	+	0.325258i	0.821543	−	0.570147i	$-0.193114\pi$
$881$	37.6006	+	9.65419i	1.26680	+	0.325258i	0.445253	+	0.895405i	$0.353114\pi$
$882$	−4.16952	+	12.8325i	−0.140395	+	0.432091i
$883$	−23.8964	−	28.8858i	−0.804177	−	0.972083i	0.195786	−	0.980647i	$-0.437274\pi$
$883$	−23.8964	−	28.8858i	−0.804177	−	0.972083i	−0.999963	+	0.00856342i	$0.997274\pi$
$884$	12.7925	−	27.1854i	0.430258	−	0.914345i
$885$	12.1324	−	2.56101i	0.407825	−	0.0860875i
$886$	25.0762	−	23.5482i	0.842453	−	0.791116i
$887$	17.5873	−	9.66869i	0.590523	−	0.324643i	−0.158322	−	0.987388i	$-0.550608\pi$
$887$	17.5873	−	9.66869i	0.590523	−	0.324643i	0.748846	+	0.662745i	$0.230608\pi$
$888$	−3.31271	+	7.03987i	−0.111167	+	0.236243i
$889$	−5.53565	−	11.7639i	−0.185660	−	0.394547i
$890$	12.2355	−	17.5519i	0.410135	−	0.588342i
$891$	−1.47170	−	0.185919i	−0.0493038	−	0.00622852i
$892$	−0.151437	−	2.40701i	−0.00507047	−	0.0805928i
$893$	−3.75240	−	11.5487i	−0.125569	−	0.386462i
$894$	−4.29813	+	6.77276i	−0.143751	+	0.226515i
$895$	0.370659	+	18.9672i	0.0123898	+	0.634005i
$896$	−4.38468	+	1.12579i	−0.146482	+	0.0376102i
$897$	−2.41827	+	38.4373i	−0.0807437	+	1.28338i
$898$	3.29517	−	17.2739i	0.109961	−	0.576437i
$899$	−10.5956	+	32.6098i	−0.353382	+	1.08760i
$900$	3.03417	−	3.97414i	0.101139	−	0.132471i
$901$	−15.6760	−	48.2457i	−0.522243	−	1.60730i
$902$	−2.08102	+	0.262894i	−0.0692904	+	0.00875341i
$903$	51.0911	+	20.2284i	1.70021	+	0.673159i
$904$	7.84951	+	3.10784i	0.261071	+	0.103365i
$905$	−11.8690	+	22.6259i	−0.394540	+	0.752112i
$906$	−0.567400	−	9.01856i	−0.0188506	−	0.299621i
$907$	18.8904	−	13.7247i	0.627246	−	0.455721i	−0.228199	−	0.973614i	$-0.573284\pi$
$907$	18.8904	−	13.7247i	0.627246	−	0.455721i	0.855445	+	0.517894i	$0.173284\pi$
$908$	4.00396	+	1.02804i	0.132876	+	0.0341168i
$909$	8.25790	+	7.75468i	0.273897	+	0.257207i
$910$	−43.7486	+	37.6557i	−1.45025	+	1.24827i
$911$	23.4146	+	12.8723i	0.775761	+	0.426478i	0.819871	−	0.572549i	$-0.194045\pi$
$911$	23.4146	+	12.8723i	0.775761	+	0.426478i	−0.0441101	+	0.999027i	$0.514045\pi$
$912$	1.27974	+	0.161668i	0.0423763	+	0.00535338i
$913$	−0.701983	−	3.67992i	−0.0232322	−	0.121788i
$914$	−11.4519	+	1.44671i	−0.378795	+	0.0478530i
$915$	−13.6205	+	25.9647i	−0.450279	+	0.858366i
$916$	5.20000	+	27.2593i	0.171813	+	0.900674i
$917$	24.4185	−	38.4774i	0.806370	−	1.27064i
$918$	−4.26254	−	3.09692i	−0.140685	−	0.102214i
$919$	−5.39818	−	6.52528i	−0.178069	−	0.215249i	0.673925	−	0.738800i	$-0.264607\pi$
$919$	−5.39818	−	6.52528i	−0.178069	−	0.215249i	−0.851995	+	0.523551i	$0.824607\pi$
$920$	5.28403	−	14.1475i	0.174209	−	0.466429i
$921$	4.66719	+	7.35432i	0.153789	+	0.242333i
$922$	−8.35841	+	10.1036i	−0.275270	+	0.332744i
$923$	−23.2558	−	49.4212i	−0.765475	−	1.62672i
$924$	−5.43270	−	3.94709i	−0.178723	−	0.129850i
$925$	10.5666	−	37.4392i	0.347429	−	1.23099i
$926$	−14.7651	+	10.7275i	−0.485211	+	0.352526i
$927$	8.80356	+	4.83980i	0.289147	+	0.158960i
$928$	−6.75862	+	1.73532i	−0.221863	+	0.0569646i
$929$	0.864952	−	1.04555i	0.0283781	−	0.0343033i	−0.756133	−	0.654418i	$-0.772914\pi$
$929$	0.864952	−	1.04555i	0.0283781	−	0.0343033i	0.784511	+	0.620114i	$0.212914\pi$
$930$	5.48046	+	9.52330i	0.179711	+	0.312281i
$931$	16.1823	−	6.40704i	0.530354	−	0.209982i
$932$	1.75039			0.0573358
$933$	24.9187	−	9.86603i	0.815803	−	0.322999i
$934$	−6.83720	+	3.75878i	−0.223720	+	0.122991i
$935$	−17.4601	−	0.756359i	−0.571005	−	0.0247356i
$936$	1.06853	−	5.60142i	0.0349259	−	0.183088i
$937$	36.0318	+	33.8361i	1.17711	+	1.10538i	0.992460	+	0.122572i	$0.0391142\pi$
$937$	36.0318	+	33.8361i	1.17711	+	1.10538i	0.184647	+	0.982805i	$0.440886\pi$
$938$	17.8244	+	16.7383i	0.581988	+	0.546523i
$939$	2.57344	−	13.4904i	0.0839809	−	0.440243i
$940$	21.0303	+	0.911019i	0.685933	+	0.0297141i
$941$	−33.1077	+	18.2011i	−1.07928	+	0.593340i	−0.919211	−	0.393766i	$-0.871172\pi$
$941$	−33.1077	+	18.2011i	−1.07928	+	0.593340i	−0.160070	+	0.987106i	$0.551172\pi$
$942$	1.72670	−	0.683648i	0.0562589	−	0.0222745i
$943$	9.55011			0.310994
$944$	−5.15591	+	2.04137i	−0.167811	+	0.0664409i
$945$	5.04892	+	8.77341i	0.164241	+	0.285399i
$946$	−11.4776	+	13.8740i	−0.373169	+	0.451084i
$947$	−14.1740	+	3.63928i	−0.460594	+	0.118261i	−0.471855	−	0.881676i	$-0.656416\pi$
$947$	−14.1740	+	3.63928i	−0.460594	+	0.118261i	0.0112608	+	0.999937i	$0.496416\pi$
$948$	9.62665	+	5.29229i	0.312659	+	0.171886i
$949$	40.5021	−	29.4265i	1.31475	−	0.955224i
$950$	−6.44462	+	0.251979i	−0.209091	+	0.00817527i
$951$	−22.5857	−	16.4095i	−0.732393	−	0.532115i
$952$	−10.1554	−	21.5813i	−0.329138	−	0.699454i
$953$	−26.8631	+	32.4719i	−0.870181	+	1.05187i	0.128011	+	0.991773i	$0.459141\pi$
$953$	−26.8631	+	32.4719i	−0.870181	+	1.05187i	−0.998193	+	0.0600959i	$0.980859\pi$
$954$	−5.15900	−	8.12929i	−0.167029	−	0.263195i
$955$	−2.85634	+	7.64759i	−0.0924291	+	0.247470i
$956$	−11.4778	−	13.8743i	−0.371218	−	0.448726i
$957$	−8.37406	−	6.08411i	−0.270695	−	0.196671i
$958$	−6.10492	+	9.61981i	−0.197241	+	0.310802i
$959$	−3.40313	−	17.8399i	−0.109893	−	0.576079i
$960$	−1.03874	+	1.98015i	−0.0335253	+	0.0639092i
$961$	6.80022	−	0.859067i	0.219362	−	0.0277119i
$962$	−8.31352	−	43.5810i	−0.268039	−	1.40511i
$963$	−12.4996	−	1.57907i	−0.402795	−	0.0508848i
$964$	−3.96723	−	2.18100i	−0.127776	−	0.0702454i
$965$	34.1723	−	29.4131i	1.10005	−	0.946842i
$966$	22.2875	+	20.9294i	0.717089	+	0.673391i
$967$	−18.4183	−	4.72903i	−0.592294	−	0.152075i	−0.0593666	−	0.998236i	$-0.518908\pi$
$967$	−18.4183	−	4.72903i	−0.592294	−	0.152075i	−0.532927	+	0.846161i	$0.678908\pi$
$968$	−7.11897	+	5.17224i	−0.228812	+	0.166242i
$969$	0.426740	+	6.78285i	0.0137089	+	0.217896i
$970$	−9.94980	+	18.9673i	−0.319469	+	0.609003i
$971$	−40.3431	−	15.9730i	−1.29467	−	0.512597i	−0.383088	−	0.923712i	$-0.625139\pi$
$971$	−40.3431	−	15.9730i	−1.29467	−	0.512597i	−0.911583	+	0.411115i	$0.865139\pi$
$972$	−0.929776	−	0.368125i	−0.0298226	−	0.0118076i
$973$	102.967	−	13.0078i	3.30097	−	0.417010i
$974$	5.05912	+	15.5704i	0.162105	+	0.498907i
$975$	−0.677175	+	28.5041i	−0.0216870	+	0.912861i
$976$	4.05197	−	12.4707i	0.129700	−	0.399177i
$977$	−6.27905	+	32.9159i	−0.200885	+	1.05307i	0.728803	+	0.684724i	$0.240077\pi$
$977$	−6.27905	+	32.9159i	−0.200885	+	1.05307i	−0.929687	+	0.368350i	$0.879923\pi$
$978$	0.684024	−	10.8722i	0.0218727	−	0.347656i
$979$	−13.7479	+	3.52986i	−0.439385	+	0.112815i
$980$	0.589490	+	30.1652i	0.0188306	+	0.963591i
$981$	3.53824	−	5.57538i	0.112967	−	0.178008i
$982$	2.12554	+	6.54173i	0.0678286	+	0.208755i
$983$	−1.55039	−	24.6427i	−0.0494496	−	0.785979i	−0.942121	−	0.335272i	$-0.891172\pi$
$983$	−1.55039	−	24.6427i	−0.0494496	−	0.785979i	0.892672	−	0.450707i	$-0.148828\pi$
$984$	−1.40287	−	0.177224i	−0.0447220	−	0.00564970i
$985$	−7.79180	+	11.1774i	−0.248267	+	0.356142i
$986$	−15.6537	−	33.2658i	−0.498515	−	1.05940i
$987$	−18.1448	+	38.5598i	−0.577557	+	1.22737i
$988$	−6.44577	+	3.54359i	−0.205067	+	0.112737i
$989$	59.7621	−	56.1203i	1.90032	−	1.78452i
$990$	−3.24546	+	0.685081i	−0.103147	+	0.0217733i
$991$	15.7680	−	33.5087i	0.500887	−	1.06444i	−0.481304	−	0.876554i	$-0.659837\pi$
$991$	15.7680	−	33.5087i	0.500887	−	1.06444i	0.982191	−	0.187886i	$-0.0601635\pi$
$992$	−3.13219	−	3.78617i	−0.0994472	−	0.120211i
$993$	−1.73323	+	5.33432i	−0.0550023	+	0.169280i
$994$	−41.9977	−	10.7832i	−1.33209	−	0.342022i
$995$	−6.18813	+	26.2176i	−0.196177	+	0.831152i
$996$	0.158576	−	2.52049i	0.00502467	−	0.0798648i
$997$	−7.27993	−	11.4713i	−0.230558	−	0.363301i	0.709277	−	0.704930i	$-0.249021\pi$
$997$	−7.27993	−	11.4713i	−0.230558	−	0.363301i	−0.939835	+	0.341629i	$0.889021\pi$
$998$	−27.2788	+	25.6165i	−0.863495	+	0.810876i
$999$	−7.78035			−0.246159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.d.511.6	yes	140
125.91	even	25	inner	750.2.m.d.91.6	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.d.91.6	✓	140	125.91	even	25	inner
750.2.m.d.511.6	yes	140	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.728969 + 0.684547i) q^{2} +(0.535827 + 0.844328i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(1.69474 - 1.45871i) q^{5} +(-0.968583 - 0.248690i) q^{6} +(1.39889 - 4.30534i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.425779 + 0.904827i) q^{9} +O(q^{10})\)	\(q+(-0.728969 + 0.684547i) q^{2} +(0.535827 + 0.844328i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(1.69474 - 1.45871i) q^{5} +(-0.968583 - 0.248690i) q^{6} +(1.39889 - 4.30534i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.425779 + 0.904827i) q^{9} +(-0.236856 + 2.22349i) q^{10} +(1.08135 - 1.01545i) q^{11} +(0.876307 - 0.481754i) q^{12} +(-2.42797 + 5.15971i) q^{13} +(1.92746 + 4.09606i) q^{14} +(2.13972 + 0.649300i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.330830 - 5.25839i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.691167 + 1.08911i) q^{19} +(-1.34942 - 1.78299i) q^{20} +(4.38468 - 1.12579i) q^{21} +(-0.0931432 + 1.48047i) q^{22} +(1.26555 - 6.63422i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(0.744305 - 4.94429i) q^{25} +(-1.76215 - 5.42333i) q^{26} +(-0.992115 + 0.125333i) q^{27} +(-4.20901 - 1.66646i) q^{28} +(-6.48783 - 2.56872i) q^{29} +(-2.00427 + 0.991421i) q^{30} +(-0.308542 - 4.90413i) q^{31} +(0.809017 - 0.587785i) q^{32} +(1.43679 + 0.368906i) q^{33} +(3.84078 + 3.60674i) q^{34} +(-3.90950 - 9.33702i) q^{35} +(0.876307 + 0.481754i) q^{36} +(7.71900 + 0.975136i) q^{37} +(-0.241705 - 1.26706i) q^{38} +(-5.65746 + 0.714703i) q^{39} +(2.20423 + 0.376002i) q^{40} +(0.264962 + 1.38898i) q^{41} +(-2.42564 + 3.82219i) q^{42} +(9.82026 + 7.13484i) q^{43} +(-0.945553 - 1.14298i) q^{44} +(0.598298 + 2.15454i) q^{45} +(3.61889 + 5.70246i) q^{46} +(-6.00062 + 7.25350i) q^{47} +(-0.425779 - 0.904827i) q^{48} +(-10.9159 - 7.93090i) q^{49} +(2.84202 + 4.11374i) q^{50} +(4.26254 - 3.09692i) q^{51} +(4.99707 + 2.74716i) q^{52} +(9.32563 - 2.39442i) q^{53} +(0.637424 - 0.770513i) q^{54} +(0.351351 - 3.29831i) q^{55} +(4.20901 - 1.66646i) q^{56} -1.28991 q^{57} +(6.48783 - 2.56872i) q^{58} +(4.85940 - 2.67148i) q^{59} +(0.782373 - 2.09473i) q^{60} +(-2.45703 + 12.8802i) q^{61} +(3.58203 + 3.36375i) q^{62} +(3.29997 + 3.09888i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(3.41175 + 12.2861i) q^{65} +(-1.29991 + 0.714632i) q^{66} +(5.02209 - 1.98838i) q^{67} -5.26879 q^{68} +(6.27957 - 2.48626i) q^{69} +(9.24154 + 4.13016i) q^{70} +(-6.10543 + 7.38020i) q^{71} +(-0.968583 + 0.248690i) q^{72} +(-7.69336 - 4.22946i) q^{73} +(-6.29443 + 4.57317i) q^{74} +(4.57342 - 2.02085i) q^{75} +(1.04356 + 0.758189i) q^{76} +(-2.85919 - 6.07609i) q^{77} +(3.63486 - 4.39379i) q^{78} +(5.88631 + 9.27534i) q^{79} +(-1.86420 + 1.23480i) q^{80} +(-0.637424 - 0.770513i) q^{81} +(-1.14397 - 0.831143i) q^{82} +(1.35322 - 2.13233i) q^{83} +(-0.848257 - 4.44672i) q^{84} +(-8.23117 - 8.42904i) q^{85} +(-12.0428 + 1.52136i) q^{86} +(-1.30752 - 6.85425i) q^{87} +(1.47170 + 0.185919i) q^{88} +(-8.38491 - 4.60964i) q^{89} +(-1.91102 - 1.16103i) q^{90} +(18.8178 + 17.6711i) q^{91} +(-6.54167 - 1.67961i) q^{92} +(3.97537 - 2.88828i) q^{93} +(-0.591101 - 9.39528i) q^{94} +(0.417343 + 2.85397i) q^{95} +(0.929776 + 0.368125i) q^{96} +(8.90604 + 3.52615i) q^{97} +(13.3865 - 1.69110i) q^{98} +(0.458395 + 1.41079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{5} + 5 q^{7}+O(q^{10}) \) 140 * q - 20 * q^5 + 5 * q^7	\( 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32} - 15 q^{34} - 25 q^{37} + 35 q^{38} - 10 q^{39} + 5 q^{40} + 55 q^{41} + 35 q^{43} + 25 q^{44} + 20 q^{46} + 10 q^{47} - 60 q^{49} - 5 q^{51} + 40 q^{52} + 40 q^{55} + 20 q^{57} - 25 q^{58} + 75 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 35 q^{65} + 20 q^{66} - 95 q^{67} + 20 q^{68} - 20 q^{69} + 65 q^{70} - 50 q^{71} + 20 q^{73} + 30 q^{74} + 35 q^{75} - 5 q^{76} + 15 q^{77} + 5 q^{78} + 70 q^{79} - 15 q^{82} + 25 q^{83} + 5 q^{84} - 95 q^{85} - 5 q^{86} - 5 q^{88} - 105 q^{89} - 5 q^{90} - 65 q^{91} + 55 q^{92} - 30 q^{93} - 10 q^{94} + 125 q^{95} - 5 q^{97} + 70 q^{98} - 10 q^{99}+O(q^{100}) \) 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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