LMFDB - Embedded newform 670.2.k.c.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (of order $11$, degree $10$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	670.91
Dual form			670.2.k.c.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(0.490330 - 0.315116i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.0829491 + 0.576924i) q^{6} +(-0.0825464 + 0.180751i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-1.10512 + 2.41987i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(0.490330 - 0.315116i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.0829491 + 0.576924i) q^{6} +(-0.0825464 + 0.180751i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-1.10512 + 2.41987i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.0791468 - 0.550478i) q^{11} +(-0.559247 - 0.164210i) q^{12} +(-2.74470 - 0.805915i) q^{13} +(-0.130126 - 0.150174i) q^{14} +(0.242127 + 0.530185i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.34272 + 3.85770i) q^{17} +(-1.74211 - 2.01050i) q^{18} +(2.52122 + 5.52069i) q^{19} +(0.841254 - 0.540641i) q^{20} +(0.0164827 + 0.114639i) q^{21} +(0.467854 + 0.300672i) q^{22} +(2.44070 - 1.56855i) q^{23} +(0.381690 - 0.440493i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(1.87327 - 2.16187i) q^{26} +(0.469515 + 3.26555i) q^{27} +(0.190659 - 0.0559826i) q^{28} -6.39403 q^{29} -0.582856 q^{30} +(-2.66367 + 0.782125i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.134656 - 0.294857i) q^{33} +(-2.12047 - 4.64319i) q^{34} +(-0.167164 - 0.107430i) q^{35} +(2.55252 - 0.749487i) q^{36} +9.65024 q^{37} -6.06915 q^{38} +(-1.59976 + 0.469733i) q^{39} +(0.142315 + 0.989821i) q^{40} +(-5.41603 + 6.25043i) q^{41} +(-0.111127 - 0.0326298i) q^{42} +(-4.56554 + 5.26891i) q^{43} +(-0.467854 + 0.300672i) q^{44} +(-2.23797 - 1.43826i) q^{45} +(0.412894 + 2.87174i) q^{46} +(-0.436918 + 0.280790i) q^{47} +(0.242127 + 0.530185i) q^{48} +(4.55817 + 5.26041i) q^{49} +(0.654861 - 0.755750i) q^{50} +(-0.423411 + 2.94489i) q^{51} +(1.18832 + 2.60206i) q^{52} +(-1.13902 - 1.31449i) q^{53} +(-3.16549 - 0.929472i) q^{54} +(0.533612 + 0.156682i) q^{55} +(-0.0282791 + 0.196686i) q^{56} +(2.97589 + 1.91249i) q^{57} +(2.65618 - 5.81622i) q^{58} +(-10.2741 + 3.01674i) q^{59} +(0.242127 - 0.530185i) q^{60} +(-1.59068 - 11.0634i) q^{61} +(0.395084 - 2.74787i) q^{62} +(-0.346172 - 0.399504i) q^{63} +(0.841254 - 0.540641i) q^{64} +(1.18832 - 2.60206i) q^{65} +0.324149 q^{66} +(1.52035 + 8.04292i) q^{67} +5.10447 q^{68} +(0.702477 - 1.53821i) q^{69} +(0.167164 - 0.107430i) q^{70} +(10.1923 + 11.7625i) q^{71} +(-0.378597 + 2.63320i) q^{72} +(-2.39685 - 16.6705i) q^{73} +(-4.00885 + 8.77816i) q^{74} +(-0.559247 + 0.164210i) q^{75} +(2.52122 - 5.52069i) q^{76} +(0.0929664 + 0.0597459i) q^{77} +(0.237282 - 1.65033i) q^{78} +(-4.69400 - 1.37828i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-3.96709 - 4.57827i) q^{81} +(-3.43569 - 7.52312i) q^{82} +(1.40352 - 9.76169i) q^{83} +(0.0758449 - 0.0875297i) q^{84} +(-3.34272 - 3.85770i) q^{85} +(-2.89618 - 6.34174i) q^{86} +(-3.13519 + 2.01486i) q^{87} +(-0.0791468 - 0.550478i) q^{88} +(7.30033 + 4.69164i) q^{89} +(2.23797 - 1.43826i) q^{90} +(0.372235 - 0.429582i) q^{91} +(-2.78375 - 0.817382i) q^{92} +(-1.05962 + 1.22287i) q^{93} +(-0.0739134 - 0.514079i) q^{94} +(-5.82331 + 1.70988i) q^{95} -0.582856 q^{96} -0.370829 q^{97} +(-6.67857 + 1.96100i) q^{98} +(1.24462 + 0.799870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	0.490330	−	0.315116i	0.283092	−	0.181932i	−0.391387	−	0.920226i	$-0.628005\pi$
$3$	0.490330	−	0.315116i	0.283092	−	0.181932i	0.674479	+	0.738294i	$0.264368\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$	0.0829491	+	0.576924i	0.0338638	+	0.235528i
$7$	−0.0825464	+	0.180751i	−0.0311996	+	0.0683176i	−0.924590	−	0.380963i	$-0.875592\pi$
$7$	−0.0825464	+	0.180751i	−0.0311996	+	0.0683176i	0.893391	+	0.449281i	$0.148320\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−1.10512	+	2.41987i	−0.368373	+	0.806625i
$10$	−0.841254	−	0.540641i	−0.266028	−	0.170966i
$11$	0.0791468	−	0.550478i	0.0238637	−	0.165975i	−0.974405	−	0.224802i	$-0.927827\pi$
$11$	0.0791468	−	0.550478i	0.0238637	−	0.165975i	0.998268	+	0.0588260i	$0.0187357\pi$
$12$	−0.559247	−	0.164210i	−0.161441	−	0.0474032i
$13$	−2.74470	−	0.805915i	−0.761242	−	0.223521i	−0.122004	−	0.992530i	$-0.538932\pi$
$13$	−2.74470	−	0.805915i	−0.761242	−	0.223521i	−0.639238	+	0.769009i	$0.720750\pi$
$14$	−0.130126	−	0.150174i	−0.0347777	−	0.0401356i
$15$	0.242127	+	0.530185i	0.0625170	+	0.136893i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−3.34272	+	3.85770i	−0.810728	+	0.935630i	−0.998918	−	0.0465027i	$-0.985192\pi$
$17$	−3.34272	+	3.85770i	−0.810728	+	0.935630i	0.188190	+	0.982133i	$0.439738\pi$
$18$	−1.74211	−	2.01050i	−0.410620	−	0.473880i
$19$	2.52122	+	5.52069i	0.578407	+	1.26653i	0.942199	+	0.335054i	$0.108755\pi$
$19$	2.52122	+	5.52069i	0.578407	+	1.26653i	−0.363792	+	0.931480i	$0.618518\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	0.0164827	+	0.114639i	0.00359681	+	0.0250164i
$22$	0.467854	+	0.300672i	0.0997468	+	0.0641034i
$23$	2.44070	−	1.56855i	0.508922	−	0.327064i	−0.260854	−	0.965378i	$-0.584004\pi$
$23$	2.44070	−	1.56855i	0.508922	−	0.327064i	0.769776	+	0.638314i	$0.220368\pi$
$24$	0.381690	−	0.440493i	0.0779121	−	0.0899154i
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	1.87327	−	2.16187i	0.367379	−	0.423978i
$27$	0.469515	+	3.26555i	0.0903582	+	0.628455i
$28$	0.190659	−	0.0559826i	0.0360312	−	0.0105797i
$29$	−6.39403			−1.18734			−0.593671	−	0.804708i	$-0.702322\pi$
$29$	−6.39403			−1.18734			−0.593671	+	0.804708i	$0.702322\pi$
$30$	−0.582856			−0.106415
$31$	−2.66367	+	0.782125i	−0.478410	+	0.140474i	−0.512042	−	0.858960i	$-0.671111\pi$
$31$	−2.66367	+	0.782125i	−0.478410	+	0.140474i	0.0336320	+	0.999434i	$0.489293\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.134656	−	0.294857i	−0.0234407	−	0.0513279i
$34$	−2.12047	−	4.64319i	−0.363658	−	0.796300i
$35$	−0.167164	−	0.107430i	−0.0282559	−	0.0181589i
$36$	2.55252	−	0.749487i	0.425420	−	0.124915i
$37$	9.65024			1.58649			0.793245	−	0.608903i	$-0.208390\pi$
$37$	9.65024			1.58649			0.793245	+	0.608903i	$0.208390\pi$
$38$	−6.06915			−0.984546
$39$	−1.59976	+	0.469733i	−0.256167	+	0.0752175i
$40$	0.142315	+	0.989821i	0.0225020	+	0.156505i
$41$	−5.41603	+	6.25043i	−0.845842	+	0.976154i	−0.999929	−	0.0119036i	$-0.996211\pi$
$41$	−5.41603	+	6.25043i	−0.845842	+	0.976154i	0.154087	+	0.988057i	$0.450756\pi$
$42$	−0.111127	−	0.0326298i	−0.0171473	−	0.00503489i
$43$	−4.56554	+	5.26891i	−0.696238	+	0.803501i	−0.988239	−	0.152917i	$-0.951133\pi$
$43$	−4.56554	+	5.26891i	−0.696238	+	0.803501i	0.292001	+	0.956418i	$0.405679\pi$
$44$	−0.467854	+	0.300672i	−0.0705316	+	0.0453279i
$45$	−2.23797	−	1.43826i	−0.333617	−	0.214402i
$46$	0.412894	+	2.87174i	0.0608779	+	0.423415i
$47$	−0.436918	+	0.280790i	−0.0637310	+	0.0409575i	−0.572118	−	0.820171i	$-0.693878\pi$
$47$	−0.436918	+	0.280790i	−0.0637310	+	0.0409575i	0.508387	+	0.861129i	$0.330242\pi$
$48$	0.242127	+	0.530185i	0.0349481	+	0.0765256i
$49$	4.55817	+	5.26041i	0.651167	+	0.751487i
$50$	0.654861	−	0.755750i	0.0926113	−	0.106879i
$51$	−0.423411	+	2.94489i	−0.0592894	+	0.412367i
$52$	1.18832	+	2.60206i	0.164791	+	0.360841i
$53$	−1.13902	−	1.31449i	−0.156456	−	0.180560i	0.672110	−	0.740451i	$-0.265388\pi$
$53$	−1.13902	−	1.31449i	−0.156456	−	0.180560i	−0.828566	+	0.559892i	$0.810843\pi$
$54$	−3.16549	−	0.929472i	−0.430769	−	0.126485i
$55$	0.533612	+	0.156682i	0.0719522	+	0.0211271i
$56$	−0.0282791	+	0.196686i	−0.00377896	+	0.0262832i
$57$	2.97589	+	1.91249i	0.394166	+	0.253315i
$58$	2.65618	−	5.81622i	0.348773	−	0.763706i
$59$	−10.2741	+	3.01674i	−1.33757	+	0.392746i	−0.870802	−	0.491635i	$-0.836400\pi$
$59$	−10.2741	+	3.01674i	−1.33757	+	0.392746i	−0.466767	+	0.884380i	$0.654581\pi$
$60$	0.242127	−	0.530185i	0.0312585	−	0.0684466i
$61$	−1.59068	−	11.0634i	−0.203665	−	1.41652i	−0.793289	−	0.608845i	$-0.791633\pi$
$61$	−1.59068	−	11.0634i	−0.203665	−	1.41652i	0.589624	−	0.807678i	$-0.299276\pi$
$62$	0.395084	−	2.74787i	0.0501757	−	0.348980i
$63$	−0.346172	−	0.399504i	−0.0436136	−	0.0503327i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	1.18832	−	2.60206i	0.147393	−	0.322746i
$66$	0.324149			0.0399000
$67$	1.52035	+	8.04292i	0.185740	+	0.982599i
$67$	1.52035	+	8.04292i	0.185740	+	0.982599i
$68$	5.10447			0.619008
$69$	0.702477	−	1.53821i	0.0845683	−	0.185179i
$70$	0.167164	−	0.107430i	0.0199799	−	0.0128403i
$71$	10.1923	+	11.7625i	1.20960	+	1.39595i	0.894606	+	0.446856i	$0.147456\pi$
$71$	10.1923	+	11.7625i	1.20960	+	1.39595i	0.314992	+	0.949094i	$0.397998\pi$
$72$	−0.378597	+	2.63320i	−0.0446181	+	0.310326i
$73$	−2.39685	−	16.6705i	−0.280530	−	1.95113i	−0.307651	−	0.951499i	$-0.599543\pi$
$73$	−2.39685	−	16.6705i	−0.280530	−	1.95113i	0.0271206	−	0.999632i	$-0.491366\pi$
$74$	−4.00885	+	8.77816i	−0.466020	+	1.02044i
$75$	−0.559247	+	0.164210i	−0.0645762	+	0.0189613i
$76$	2.52122	−	5.52069i	0.289203	−	0.633267i
$77$	0.0929664	+	0.0597459i	0.0105945	+	0.00680868i
$78$	0.237282	−	1.65033i	0.0268669	−	0.186863i
$79$	−4.69400	−	1.37828i	−0.528116	−	0.155069i	0.00679542	−	0.999977i	$-0.497837\pi$
$79$	−4.69400	−	1.37828i	−0.528116	−	0.155069i	−0.534912	+	0.844908i	$0.679655\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	−3.96709	−	4.57827i	−0.440788	−	0.508696i
$82$	−3.43569	−	7.52312i	−0.379409	−	0.830790i
$83$	1.40352	−	9.76169i	0.154056	−	1.07148i	−0.755274	−	0.655409i	$-0.772496\pi$
$83$	1.40352	−	9.76169i	0.154056	−	1.07148i	0.909330	−	0.416076i	$-0.136595\pi$
$84$	0.0758449	−	0.0875297i	0.00827536	−	0.00955027i
$85$	−3.34272	−	3.85770i	−0.362569	−	0.418426i
$86$	−2.89618	−	6.34174i	−0.312303	−	0.683848i
$87$	−3.13519	+	2.01486i	−0.336127	+	0.216016i
$88$	−0.0791468	−	0.550478i	−0.00843708	−	0.0586812i
$89$	7.30033	+	4.69164i	0.773834	+	0.497313i	0.866982	−	0.498340i	$-0.166057\pi$
$89$	7.30033	+	4.69164i	0.773834	+	0.497313i	−0.0931482	+	0.995652i	$0.529693\pi$
$90$	2.23797	−	1.43826i	0.235903	−	0.151605i
$91$	0.372235	−	0.429582i	0.0390208	−	0.0450324i
$92$	−2.78375	−	0.817382i	−0.290226	−	0.0852180i
$93$	−1.05962	+	1.22287i	−0.109877	+	0.126805i
$94$	−0.0739134	−	0.514079i	−0.00762359	−	0.0530232i
$95$	−5.82331	+	1.70988i	−0.597459	+	0.175430i
$96$	−0.582856			−0.0594875
$97$	−0.370829			−0.0376520			−0.0188260	−	0.999823i	$-0.505993\pi$
$97$	−0.370829			−0.0376520			−0.0188260	+	0.999823i	$0.505993\pi$
$98$	−6.67857	+	1.96100i	−0.674637	+	0.198091i
$99$	1.24462	+	0.799870i	0.125089	+	0.0803900i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	7.49422	+	16.4101i	0.745703	+	1.63286i	0.773939	+	0.633261i	$0.218284\pi$
$101$	7.49422	+	16.4101i	0.745703	+	1.63286i	−0.0282354	+	0.999601i	$0.508989\pi$
$102$	−2.50287	−	1.60850i	−0.247822	−	0.159265i
$103$	6.48590	−	1.90443i	0.639075	−	0.187649i	0.0538870	−	0.998547i	$-0.482839\pi$
$103$	6.48590	−	1.90443i	0.639075	−	0.187649i	0.585188	+	0.810898i	$0.301021\pi$
$104$	−2.86057			−0.280502
$105$	−0.115818			−0.0113027
$106$	1.66887	−	0.490025i	0.162095	−	0.0475954i
$107$	−2.67139	−	18.5799i	−0.258253	−	1.79619i	−0.545267	−	0.838262i	$-0.683572\pi$
$107$	−2.67139	−	18.5799i	−0.258253	−	1.79619i	0.287014	−	0.957926i	$-0.407337\pi$
$108$	2.16047	−	2.49332i	0.207891	−	0.239919i
$109$	15.7322	+	4.61940i	1.50688	+	0.442459i	0.927882	−	0.372873i	$-0.121627\pi$
$109$	15.7322	+	4.61940i	1.50688	+	0.442459i	0.578994	+	0.815332i	$0.303446\pi$
$110$	−0.364194	+	0.420302i	−0.0347245	+	0.0400742i
$111$	4.73180	−	3.04094i	0.449123	−	0.288634i
$112$	−0.167164	−	0.107430i	−0.0157955	−	0.0101512i
$113$	−0.794136	−	5.52333i	−0.0747060	−	0.519592i	−0.992472	−	0.122470i	$-0.960918\pi$
$113$	−0.794136	−	5.52333i	−0.0747060	−	0.519592i	0.917766	−	0.397121i	$-0.129991\pi$
$114$	−2.97589	+	1.91249i	−0.278717	+	0.179121i
$115$	1.20523	+	2.63909i	0.112388	+	0.246096i
$116$	4.18720	+	4.83229i	0.388772	+	0.448667i
$117$	4.98343	−	5.75119i	0.460718	−	0.531697i
$118$	1.52388	−	10.5988i	0.140284	−	0.975700i
$119$	−0.421356	−	0.922640i	−0.0386256	−	0.0845783i
$120$	0.381690	+	0.440493i	0.0348433	+	0.0402114i
$121$	10.2577	+	3.01192i	0.932515	+	0.273811i
$122$	10.7244	+	3.14897i	0.970943	+	0.285095i
$123$	−0.686031	+	4.77145i	−0.0618574	+	0.430227i
$124$	2.33543	+	1.50089i	0.209727	+	0.134784i
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$	0.507206	−	0.148929i	0.0451855	−	0.0132677i
$127$	−0.367417	+	0.804531i	−0.0326030	+	0.0713906i	−0.925233	−	0.379400i	$-0.876131\pi$
$127$	−0.367417	+	0.804531i	−0.0326030	+	0.0713906i	0.892630	+	0.450790i	$0.148858\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−0.578302	+	4.02218i	−0.0509166	+	0.354133i
$130$	1.87327	+	2.16187i	0.164297	+	0.189609i
$131$	−9.03659	+	5.80746i	−0.789530	+	0.507400i	−0.872184	−	0.489178i	$-0.837297\pi$
$131$	−9.03659	+	5.80746i	−0.789530	+	0.507400i	0.0826536	+	0.996578i	$0.473660\pi$
$132$	−0.134656	+	0.294857i	−0.0117203	+	0.0256640i
$133$	−1.20599			−0.104573
$134$	−7.94767	−	1.95819i	−0.686574	−	0.169162i
$135$	−3.29913			−0.283944
$136$	−2.12047	+	4.64319i	−0.181829	+	0.398150i
$137$	−3.32860	+	2.13916i	−0.284381	+	0.182761i	−0.675053	−	0.737769i	$-0.735879\pi$
$137$	−3.32860	+	2.13916i	−0.284381	+	0.182761i	0.390671	+	0.920530i	$0.372243\pi$
$138$	1.10739	+	1.27799i	0.0942669	+	0.108790i
$139$	2.56371	−	17.8310i	0.217451	−	1.51241i	−0.529946	−	0.848031i	$-0.677788\pi$
$139$	2.56371	−	17.8310i	0.217451	−	1.51241i	0.747398	−	0.664377i	$-0.231303\pi$
$140$	0.0282791	+	0.196686i	0.00239002	+	0.0166230i
$141$	−0.125753	+	0.275360i	−0.0105903	+	0.0231895i
$142$	−14.9335	+	4.38489i	−1.25320	+	0.367971i
$143$	−0.660873	+	1.44711i	−0.0552650	+	0.121013i
$144$	−2.23797	−	1.43826i	−0.186497	−	0.119855i
$145$	0.909965	−	6.32895i	0.0755685	−	0.525591i
$146$	16.1597	+	4.74491i	1.33739	+	0.392692i
$147$	3.89264	+	1.14298i	0.321060	+	0.0942717i
$148$	−6.31956	−	7.29316i	−0.519465	−	0.599494i
$149$	−0.376749	−	0.824965i	−0.0308645	−	0.0675838i	0.893572	−	0.448920i	$-0.148191\pi$
$149$	−0.376749	−	0.824965i	−0.0308645	−	0.0675838i	−0.924436	+	0.381336i	$0.875464\pi$
$150$	0.0829491	−	0.576924i	0.00677277	−	0.0471056i
$151$	−0.773956	+	0.893193i	−0.0629837	+	0.0726870i	−0.786367	−	0.617760i	$-0.788040\pi$
$151$	−0.773956	+	0.893193i	−0.0629837	+	0.0726870i	0.723383	+	0.690447i	$0.242586\pi$
$152$	3.97445	+	4.58676i	0.322370	+	0.372035i
$153$	−5.64105	−	12.3522i	−0.456052	−	0.998614i
$154$	−0.0929664	+	0.0597459i	−0.00749145	+	0.00481446i
$155$	−0.395084	−	2.74787i	−0.0317339	−	0.220714i
$156$	1.40262	+	0.901411i	0.112300	+	0.0721706i
$157$	11.2741	−	7.24541i	0.899770	−	0.578247i	−0.00695234	−	0.999976i	$-0.502213\pi$
$157$	11.2741	−	7.24541i	0.899770	−	0.578247i	0.906722	+	0.421729i	$0.138577\pi$
$158$	3.20369	−	3.69725i	0.254872	−	0.294138i
$159$	−0.972712	−	0.285614i	−0.0771411	−	0.0226507i
$160$	0.654861	−	0.755750i	0.0517713	−	0.0597472i
$161$	0.0820454	+	0.570638i	0.00646608	+	0.0449726i
$162$	5.81253	−	1.70671i	0.456675	−	0.134092i
$163$	9.98546			0.782121			0.391061	−	0.920365i	$-0.372108\pi$
$163$	9.98546			0.782121			0.391061	+	0.920365i	$0.372108\pi$
$164$	8.27051			0.645818
$165$	0.311019	−	0.0913234i	0.0242128	−	0.00710952i
$166$	8.29651	+	5.33184i	0.643934	+	0.413831i
$167$	10.0129	+	21.9252i	0.774821	+	1.69662i	0.715740	+	0.698367i	$0.246090\pi$
$167$	10.0129	+	21.9252i	0.774821	+	1.69662i	0.0590808	+	0.998253i	$0.481183\pi$
$168$	0.0481127	+	0.105352i	0.00371197	+	0.00812809i
$169$	−4.05244	−	2.60435i	−0.311726	−	0.200334i
$170$	4.89770	−	1.43810i	0.375637	−	0.110297i
$171$	−16.1456			−1.23469
$172$	6.97177			0.531592
$173$	14.7169	−	4.32128i	1.11891	−	0.328541i	0.330568	−	0.943782i	$-0.392760\pi$
$173$	14.7169	−	4.32128i	1.11891	−	0.328541i	0.788339	+	0.615241i	$0.210941\pi$
$174$	−0.530379	−	3.68887i	−0.0402079	−	0.279652i
$175$	0.130126	−	0.150174i	0.00983662	−	0.0113521i
$176$	0.533612	+	0.156682i	0.0402225	+	0.0118104i
$177$	−4.08706	+	4.71672i	−0.307202	+	0.354530i
$178$	−7.30033	+	4.69164i	−0.547183	+	0.351653i
$179$	20.6571	+	13.2755i	1.54398	+	0.992258i	0.986814	+	0.161859i	$0.0517491\pi$
$179$	20.6571	+	13.2755i	1.54398	+	0.992258i	0.557170	+	0.830399i	$0.311887\pi$
$180$	0.378597	+	2.63320i	0.0282190	+	0.196267i
$181$	−2.53889	+	1.63164i	−0.188714	+	0.121279i	−0.631586	−	0.775306i	$-0.717596\pi$
$181$	−2.53889	+	1.63164i	−0.188714	+	0.121279i	0.442872	+	0.896585i	$0.353960\pi$
$182$	0.236130	+	0.517052i	0.0175031	+	0.0383264i
$183$	−4.26621	−	4.92347i	−0.315367	−	0.363953i
$184$	1.89993	−	2.19263i	0.140065	−	0.161643i
$185$	−1.37337	+	9.55201i	−0.100972	+	0.702278i
$186$	−0.672176	−	1.47186i	−0.0492863	−	0.107922i
$187$	1.85902	+	2.14542i	0.135945	+	0.156889i
$188$	0.498328	+	0.146322i	0.0363443	+	0.0106716i
$189$	−0.629009	−	0.184694i	−0.0457537	−	0.0134345i
$190$	0.863730	−	6.00738i	0.0626616	−	0.435821i
$191$	0.622625	+	0.400137i	0.0450516	+	0.0289529i	0.562973	−	0.826475i	$-0.309658\pi$
$191$	0.622625	+	0.400137i	0.0450516	+	0.0289529i	−0.517921	+	0.855428i	$0.673294\pi$
$192$	0.242127	−	0.530185i	0.0174740	−	0.0382628i
$193$	16.3301	−	4.79494i	1.17546	−	0.345148i	0.365041	−	0.930992i	$-0.381055\pi$
$193$	16.3301	−	4.79494i	1.17546	−	0.345148i	0.810424	+	0.585844i	$0.199237\pi$
$194$	0.154048	−	0.337318i	0.0110600	−	0.0242180i
$195$	−0.237282	−	1.65033i	−0.0169921	−	0.118183i
$196$	0.990585	−	6.88967i	0.0707560	−	0.492119i
$197$	0.355117	+	0.409827i	0.0253011	+	0.0291990i	0.768259	−	0.640139i	$-0.221123\pi$
$197$	0.355117	+	0.409827i	0.0253011	+	0.0291990i	−0.742958	+	0.669338i	$0.766578\pi$
$198$	−1.24462	+	0.799870i	−0.0884514	+	0.0568443i
$199$	0.284433	−	0.622821i	0.0201629	−	0.0441506i	−0.899283	−	0.437368i	$-0.855911\pi$
$199$	0.284433	−	0.622821i	0.0201629	−	0.0441506i	0.919446	+	0.393217i	$0.128638\pi$
$200$	−1.00000			−0.0707107
$201$	3.27993	+	3.46460i	0.231348	+	0.244374i
$202$	−18.0403			−1.26931
$203$	0.527804	−	1.15573i	0.0370446	−	0.0811163i
$204$	2.50287	−	1.60850i	0.175236	−	0.112618i
$205$	−5.41603	−	6.25043i	−0.378272	−	0.436549i
$206$	−0.962008	+	6.69091i	−0.0670263	+	0.466178i
$207$	1.09841	+	7.63963i	0.0763450	+	0.530991i
$208$	1.18832	−	2.60206i	0.0823954	−	0.180421i
$209$	3.23857	−	0.950930i	0.224017	−	0.0657772i
$210$	0.0481127	−	0.105352i	0.00332009	−	0.00726998i
$211$	1.04725	+	0.673028i	0.0720958	+	0.0463332i	0.576192	−	0.817314i	$-0.304538\pi$
$211$	1.04725	+	0.673028i	0.0720958	+	0.0463332i	−0.504096	+	0.863647i	$0.668174\pi$
$212$	−0.247532	+	1.72162i	−0.0170006	+	0.118241i
$213$	8.70411	+	2.55576i	0.596396	+	0.175118i
$214$	18.0106	+	5.28840i	1.23118	+	0.361507i
$215$	−4.56554	−	5.26891i	−0.311367	−	0.359337i
$216$	1.37051	+	3.00099i	0.0932513	+	0.204192i
$217$	0.0785064	−	0.546024i	0.00532936	−	0.0370665i
$218$	−10.7374	+	12.3916i	−0.727226	+	0.839264i
$219$	−6.42838	−	7.41875i	−0.434390	−	0.501312i
$220$	−0.231029	−	0.505882i	−0.0155759	−	0.0341066i
$221$	12.2837	−	7.89427i	0.826292	−	0.531026i
$222$	0.800479	+	5.56745i	0.0537246	+	0.373663i
$223$	−4.08444	−	2.62491i	−0.273514	−	0.175777i	0.396692	−	0.917952i	$-0.370158\pi$
$223$	−4.08444	−	2.62491i	−0.273514	−	0.175777i	−0.670206	+	0.742175i	$0.733794\pi$
$224$	0.167164	−	0.107430i	0.0111691	−	0.00717795i
$225$	1.74211	−	2.01050i	0.116141	−	0.134034i
$226$	5.35410	+	1.57210i	0.356149	+	0.104575i
$227$	7.43627	−	8.58191i	0.493563	−	0.569602i	−0.453251	−	0.891383i	$-0.649736\pi$
$227$	7.43627	−	8.58191i	0.493563	−	0.569602i	0.946814	+	0.321781i	$0.104282\pi$
$228$	−0.503431	−	3.50144i	−0.0333405	−	0.231888i
$229$	23.3564	−	6.85805i	1.54343	−	0.453193i	0.604303	−	0.796755i	$-0.293452\pi$
$229$	23.3564	−	6.85805i	1.54343	−	0.453193i	0.939130	+	0.343562i	$0.111634\pi$
$230$	−2.90127			−0.191304
$231$	0.0644111			0.00423794
$232$	−6.13503	+	1.80141i	−0.402784	+	0.118268i
$233$	−12.2578	−	7.87762i	−0.803036	−	0.516080i	0.0735694	−	0.997290i	$-0.476561\pi$
$233$	−12.2578	−	7.87762i	−0.803036	−	0.516080i	−0.876605	+	0.481210i	$0.840197\pi$
$234$	3.16127	+	6.92222i	0.206659	+	0.452519i
$235$	−0.215752	−	0.472431i	−0.0140741	−	0.0308180i
$236$	9.00797	+	5.78907i	0.586369	+	0.376837i
$237$	−2.73593	+	0.803341i	−0.177718	+	0.0521826i
$238$	1.01430			0.0657473
$239$	−0.350871			−0.0226960			−0.0113480	−	0.999936i	$-0.503612\pi$
$239$	−0.350871			−0.0226960			−0.0113480	+	0.999936i	$0.503612\pi$
$240$	−0.559247	+	0.164210i	−0.0360992	+	0.0105997i
$241$	0.685994	+	4.77120i	0.0441888	+	0.307340i	0.999914	+	0.0130806i	$0.00416380\pi$
$241$	0.685994	+	4.77120i	0.0441888	+	0.307340i	−0.955726	+	0.294259i	$0.904927\pi$
$242$	−7.00093	+	8.07950i	−0.450037	+	0.519370i
$243$	−12.8843	−	3.78318i	−0.826531	−	0.242691i
$244$	−7.31949	+	8.44714i	−0.468582	+	0.540773i
$245$	−5.85556	+	3.76314i	−0.374098	+	0.240418i
$246$	−4.05528	−	2.60617i	−0.258555	−	0.166163i
$247$	−2.47076	−	17.1845i	−0.157211	−	1.09342i
$248$	−2.33543	+	1.50089i	−0.148300	+	0.0953064i
$249$	−2.38788	−	5.22872i	−0.151326	−	0.331357i
$250$	0.654861	+	0.755750i	0.0414170	+	0.0477978i
$251$	−11.8950	+	13.7276i	−0.750808	+	0.866479i	−0.994646	−	0.103337i	$-0.967048\pi$
$251$	−11.8950	+	13.7276i	−0.750808	+	0.866479i	0.243838	+	0.969816i	$0.421593\pi$
$252$	−0.0752304	+	0.523239i	−0.00473907	+	0.0329609i
$253$	−0.670276	−	1.46770i	−0.0421399	−	0.0922735i
$254$	−0.579196	−	0.668428i	−0.0363420	−	0.0419409i
$255$	−2.85466	−	0.838203i	−0.178766	−	0.0524903i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	0.533479	−	3.71043i	0.0332775	−	0.231450i	−0.966394	−	0.257064i	$-0.917245\pi$
$257$	0.533479	−	3.71043i	0.0332775	−	0.231450i	0.999672	+	0.0256138i	$0.00815403\pi$
$258$	−3.41847	−	2.19692i	−0.212824	−	0.136774i
$259$	−0.796592	+	1.74429i	−0.0494978	+	0.108385i
$260$	−2.74470	+	0.805915i	−0.170219	+	0.0499807i
$261$	7.06617	−	15.4728i	0.437385	−	0.957739i
$262$	−1.52872	−	10.6325i	−0.0944446	−	0.656877i
$263$	−3.07672	+	21.3990i	−0.189719	+	1.31952i	0.643018	+	0.765851i	$0.277682\pi$
$263$	−3.07672	+	21.3990i	−0.189719	+	1.31952i	−0.832736	+	0.553670i	$0.813227\pi$
$264$	−0.212273	−	0.244976i	−0.0130645	−	0.0150772i
$265$	1.46321	−	0.940350i	0.0898845	−	0.0577653i
$266$	0.500986	−	1.09701i	0.0307174	−	0.0672618i
$267$	5.05798			0.309543
$268$	5.08281	−	6.41600i	0.310482	−	0.391919i
$269$	−21.0790			−1.28521			−0.642606	−	0.766197i	$-0.722147\pi$
$269$	−21.0790			−1.28521			−0.642606	+	0.766197i	$0.722147\pi$
$270$	1.37051	−	3.00099i	0.0834065	−	0.182635i
$271$	−21.5147	+	13.8266i	−1.30692	+	0.839908i	−0.993948	−	0.109853i	$-0.964962\pi$
$271$	−21.5147	+	13.8266i	−1.30692	+	0.839908i	−0.312975	+	0.949761i	$0.601326\pi$
$272$	−3.34272	−	3.85770i	−0.202682	−	0.233907i
$273$	0.0471498	−	0.327934i	0.00285364	−	0.0198475i
$274$	−0.563099	−	3.91644i	−0.0340181	−	0.236601i
$275$	−0.231029	+	0.505882i	−0.0139315	+	0.0305058i
$276$	−1.62253	+	0.476417i	−0.0976646	+	0.0286769i
$277$	−1.00662	+	2.20419i	−0.0604820	+	0.132437i	−0.937460	−	0.348094i	$-0.886829\pi$
$277$	−1.00662	+	2.20419i	−0.0604820	+	0.132437i	0.876978	+	0.480531i	$0.159556\pi$
$278$	15.1547	+	9.73931i	0.908917	+	0.584125i
$279$	1.05103	−	7.31010i	0.0629237	−	0.437644i
$280$	−0.190659	−	0.0559826i	−0.0113941	−	0.00334560i
$281$	−12.0317	−	3.53282i	−0.717750	−	0.210750i	−0.0975908	−	0.995227i	$-0.531114\pi$
$281$	−12.0317	−	3.53282i	−0.717750	−	0.210750i	−0.620159	+	0.784476i	$0.712932\pi$
$282$	−0.198236	−	0.228777i	−0.0118048	−	0.0136235i
$283$	−1.19958	−	2.62671i	−0.0713076	−	0.156142i	0.870622	−	0.491953i	$-0.163717\pi$
$283$	−1.19958	−	2.62671i	−0.0713076	−	0.156142i	−0.941929	+	0.335811i	$0.890990\pi$
$284$	2.21499	−	15.4056i	0.131435	−	0.914153i
$285$	−2.31653	+	2.67342i	−0.137220	+	0.158360i
$286$	−1.04180	−	1.20230i	−0.0616030	−	0.0710936i
$287$	−0.682701	−	1.49491i	−0.0402985	−	0.0882415i
$288$	2.23797	−	1.43826i	0.131874	−	0.0847500i
$289$	−1.28875	−	8.96344i	−0.0758087	−	0.527261i
$290$	5.37900	+	3.45687i	0.315866	+	0.202995i
$291$	−0.181829	+	0.116854i	−0.0106590	+	0.00685012i
$292$	−11.0291	+	12.7283i	−0.645429	+	0.744865i
$293$	−22.8214	−	6.70098i	−1.33324	−	0.391476i	−0.463989	−	0.885841i	$-0.653582\pi$
$293$	−22.8214	−	6.70098i	−1.33324	−	0.391476i	−0.869254	+	0.494365i	$0.835401\pi$
$294$	−2.65676	+	3.06606i	−0.154945	+	0.178816i
$295$	−1.52388	−	10.5988i	−0.0887237	−	0.617087i
$296$	9.25933	−	2.71879i	0.538188	−	0.158026i
$297$	1.83477			0.106464
$298$	0.906922			0.0525366
$299$	−7.96310	+	2.33818i	−0.460518	+	0.135220i
$300$	0.490330	+	0.315116i	0.0283092	+	0.0181932i
$301$	−0.575494	−	1.26016i	−0.0331709	−	0.0726342i
$302$	−0.490964	−	1.07506i	−0.0282518	−	0.0618628i
$303$	8.84571	+	5.68480i	0.508173	+	0.326583i
$304$	−5.82331	+	1.70988i	−0.333990	+	0.0980682i
$305$	11.1772			0.640003
$306$	13.5793			0.776278
$307$	−20.5230	+	6.02611i	−1.17131	+	0.343928i	−0.808818	−	0.588058i	$-0.799893\pi$
$307$	−20.5230	+	6.02611i	−1.17131	+	0.343928i	−0.362493	+	0.931986i	$0.618074\pi$
$308$	−0.0157271	−	0.109385i	−0.000896136	−	0.00623277i
$309$	2.58011	−	2.97761i	0.146778	−	0.169390i
$310$	2.66367	+	0.782125i	0.151286	+	0.0444217i
$311$	−8.27728	+	9.55250i	−0.469362	+	0.541672i	−0.940234	−	0.340529i	$-0.889394\pi$
$311$	−8.27728	+	9.55250i	−0.469362	+	0.541672i	0.470872	+	0.882201i	$0.343939\pi$
$312$	−1.40262	+	0.901411i	−0.0794079	+	0.0510323i
$313$	−22.7327	−	14.6094i	−1.28493	−	0.825773i	−0.293440	−	0.955977i	$-0.594800\pi$
$313$	−22.7327	−	14.6094i	−1.28493	−	0.825773i	−0.991487	+	0.130205i	$0.958437\pi$
$314$	1.90724	+	13.2651i	0.107632	+	0.748594i
$315$	0.444703	−	0.285793i	0.0250562	−	0.0161026i
$316$	2.03228	+	4.45007i	0.114325	+	0.250336i
$317$	−0.919376	−	1.06102i	−0.0516373	−	0.0595926i	0.729343	−	0.684148i	$-0.239826\pi$
$317$	−0.919376	−	1.06102i	−0.0516373	−	0.0595926i	−0.780981	+	0.624555i	$0.785280\pi$
$318$	0.663883	−	0.766161i	0.0372287	−	0.0429642i
$319$	−0.506067	+	3.51978i	−0.0283343	+	0.197070i
$320$	0.415415	+	0.909632i	0.0232224	+	0.0508500i
$321$	−7.16469	−	8.26849i	−0.399894	−	0.461502i
$322$	−0.553154	−	0.162421i	−0.0308261	−	0.00905135i
$323$	−29.7249	−	8.72802i	−1.65394	−	0.485640i
$324$	−0.862131	+	5.99626i	−0.0478962	+	0.333125i
$325$	2.40646	+	1.54654i	0.133487	+	0.0857866i
$326$	−4.14811	+	9.08309i	−0.229742	+	0.503066i
$327$	9.16964	−	2.69245i	0.507082	−	0.148893i
$328$	−3.43569	+	7.52312i	−0.189704	+	0.415395i
$329$	−0.0146872	−	0.102152i	−0.000809732	−	0.00563181i
$330$	−0.0461312	+	0.320850i	−0.00253944	+	0.0176622i
$331$	−2.91023	−	3.35859i	−0.159961	−	0.184605i	0.670111	−	0.742261i	$-0.266246\pi$
$331$	−2.91023	−	3.35859i	−0.159961	−	0.184605i	−0.830072	+	0.557656i	$0.811701\pi$
$332$	−8.29651	+	5.33184i	−0.455330	+	0.292623i
$333$	−10.6647	+	23.3524i	−0.584420	+	1.27970i
$334$	−24.1033			−1.31888
$335$	−8.17742	+	0.360249i	−0.446780	+	0.0196825i
$336$	−0.115818			−0.00631841
$337$	2.36653	−	5.18198i	0.128913	−	0.282280i	−0.834159	−	0.551524i	$-0.814046\pi$
$337$	2.36653	−	5.18198i	0.128913	−	0.282280i	0.963072	+	0.269244i	$0.0867737\pi$
$338$	4.05244	−	2.60435i	0.220424	−	0.141658i
$339$	−2.12988	−	2.45801i	−0.115679	−	0.133501i
$340$	−0.726442	+	5.05251i	−0.0393968	+	0.274011i
$341$	0.219722	+	1.52820i	0.0118986	+	0.0827565i
$342$	6.70714	−	14.6866i	0.362680	−	0.794159i
$343$	−2.66170	+	0.781546i	−0.143718	+	0.0421995i
$344$	−2.89618	+	6.34174i	−0.156151	+	0.341924i
$345$	1.42258	+	0.914237i	0.0765891	+	0.0492208i
$346$	−2.18286	+	15.1821i	−0.117351	+	0.816195i
$347$	21.7048	+	6.37312i	1.16518	+	0.342127i	0.806442	−	0.591313i	$-0.201390\pi$
$347$	21.7048	+	6.37312i	1.16518	+	0.342127i	0.358735	+	0.933440i	$0.383208\pi$
$348$	3.57584	+	1.04996i	0.191685	+	0.0562838i
$349$	17.8103	+	20.5541i	0.953362	+	1.10024i	0.994876	+	0.101100i	$0.0322362\pi$
$349$	17.8103	+	20.5541i	0.953362	+	1.10024i	−0.0415148	+	0.999138i	$0.513218\pi$
$350$	0.0825464	+	0.180751i	0.00441229	+	0.00966157i
$351$	1.34308	−	9.34133i	0.0716883	−	0.498603i
$352$	−0.364194	+	0.420302i	−0.0194116	+	0.0224022i
$353$	−6.71462	−	7.74908i	−0.357383	−	0.412442i	0.548378	−	0.836230i	$-0.315245\pi$
$353$	−6.71462	−	7.74908i	−0.357383	−	0.412442i	−0.905761	+	0.423788i	$0.860700\pi$
$354$	−2.59265	−	5.67711i	−0.137798	−	0.301735i
$355$	−13.0933	+	8.41453i	−0.694919	+	0.446597i
$356$	−1.23500	−	8.58959i	−0.0654547	−	0.455248i
$357$	−0.497342	−	0.319622i	−0.0263221	−	0.0169162i
$358$	−20.6571	+	13.2755i	−1.09176	+	0.701632i
$359$	−1.11351	+	1.28505i	−0.0587686	+	0.0678225i	−0.784373	−	0.620290i	$-0.787015\pi$
$359$	−1.11351	+	1.28505i	−0.0587686	+	0.0678225i	0.725604	+	0.688112i	$0.241560\pi$
$360$	−2.55252	−	0.749487i	−0.134530	−	0.0395014i
$361$	−11.6792	+	13.4785i	−0.614693	+	0.709394i
$362$	−0.429504	−	2.98726i	−0.0225742	−	0.157007i
$363$	5.97874	−	1.75552i	0.313803	−	0.0921408i
$364$	−0.568418			−0.0297932
$365$	16.8419			0.881545
$366$	6.25079	−	1.83540i	0.326734	−	0.0959378i
$367$	1.59139	+	1.02273i	0.0830700	+	0.0533858i	0.581516	−	0.813535i	$-0.302460\pi$
$367$	1.59139	+	1.02273i	0.0830700	+	0.0533858i	−0.498446	+	0.866920i	$0.666096\pi$
$368$	1.20523	+	2.63909i	0.0628270	+	0.137572i
$369$	−9.13990	−	20.0136i	−0.475804	−	1.04187i
$370$	−8.11830	−	5.21731i	−0.422050	−	0.271235i
$371$	0.331618	−	0.0973719i	0.0172168	−	0.00505530i
$372$	1.61808			0.0838937
$373$	1.95991			0.101480			0.0507402	−	0.998712i	$-0.483842\pi$
$373$	1.95991			0.101480			0.0507402	+	0.998712i	$0.483842\pi$
$374$	−2.72380	+	0.799781i	−0.140845	+	0.0413557i
$375$	−0.0829491	−	0.576924i	−0.00428347	−	0.0297922i
$376$	−0.340112	+	0.392510i	−0.0175399	+	0.0202422i
$377$	17.5497	+	5.15305i	0.903854	+	0.265395i
$378$	0.429303	−	0.495442i	0.0220810	−	0.0254828i
$379$	−13.8231	+	8.88355i	−0.710043	+	0.456317i	−0.845161	−	0.534513i	$-0.820495\pi$
$379$	−13.8231	+	8.88355i	−0.710043	+	0.456317i	0.135117	+	0.990830i	$0.456859\pi$
$380$	5.10569	+	3.28123i	0.261917	+	0.168324i
$381$	0.0733650	+	0.510264i	0.00375860	+	0.0261416i
$382$	−0.622625	+	0.400137i	−0.0318563	+	0.0204728i
$383$	10.3636	+	22.6931i	0.529555	+	1.15956i	0.965694	+	0.259684i	$0.0836183\pi$
$383$	10.3636	+	22.6931i	0.529555	+	1.15956i	−0.436139	+	0.899879i	$0.643654\pi$
$384$	0.381690	+	0.440493i	0.0194780	+	0.0224788i
$385$	−0.0723683	+	0.0835174i	−0.00368823	+	0.00425644i
$386$	−2.42212	+	16.8462i	−0.123283	+	0.857451i
$387$	−7.70464	−	16.8708i	−0.391649	−	0.857591i
$388$	0.242842	+	0.280254i	0.0123284	+	0.0142278i
$389$	8.31882	+	2.44262i	0.421781	+	0.123846i	0.485734	−	0.874107i	$-0.338553\pi$
$389$	8.31882	+	2.44262i	0.421781	+	0.123846i	−0.0639529	+	0.997953i	$0.520371\pi$
$390$	1.59976	+	0.469733i	0.0810072	+	0.0237858i
$391$	−2.10760	+	14.6587i	−0.106586	+	0.741323i
$392$	5.85556	+	3.76314i	0.295750	+	0.190067i
$393$	−2.60089	+	5.69515i	−0.131197	+	0.287282i
$394$	−0.520313	+	0.152778i	−0.0262130	+	0.00769683i
$395$	2.03228	−	4.45007i	0.102255	−	0.223907i
$396$	−0.210553	−	1.46443i	−0.0105807	−	0.0735902i
$397$	−1.57220	+	10.9349i	−0.0789062	+	0.548805i	0.911573	+	0.411139i	$0.134869\pi$
$397$	−1.57220	+	10.9349i	−0.0789062	+	0.548805i	−0.990479	+	0.137666i	$0.956040\pi$
$398$	0.448381	+	0.517459i	0.0224753	+	0.0259379i
$399$	−0.591333	+	0.380027i	−0.0296037	+	0.0190251i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	−24.3963			−1.21829			−0.609146	−	0.793058i	$-0.708488\pi$
$401$	−24.3963			−1.21829			−0.609146	+	0.793058i	$0.708488\pi$
$402$	−4.51404	+	1.54428i	−0.225140	+	0.0770217i
$403$	7.94130			0.395584
$404$	7.49422	−	16.4101i	0.372852	−	0.816431i
$405$	5.09624	−	3.27516i	0.253234	−	0.162744i
$406$	0.832031	+	0.960215i	0.0412930	+	0.0476547i
$407$	0.763786	−	5.31225i	0.0378595	−	0.263318i
$408$	0.423411	+	2.94489i	0.0209620	+	0.145794i
$409$	9.14016	−	20.0142i	0.451952	−	0.989637i	−0.537297	−	0.843393i	$-0.680554\pi$
$409$	9.14016	−	20.0142i	0.451952	−	0.989637i	0.989249	−	0.146244i	$-0.0467183\pi$
$410$	7.93549	−	2.33007i	0.391906	−	0.115074i
$411$	−0.958028	+	2.09779i	−0.0472561	+	0.103476i
$412$	−5.68664	−	3.65458i	−0.280160	−	0.180048i
$413$	0.302807	−	2.10607i	0.0149002	−	0.103633i
$414$	−7.40555	−	2.17446i	−0.363963	−	0.106869i
$415$	9.46259	+	2.77847i	0.464500	+	0.136390i
$416$	1.87327	+	2.16187i	0.0918448	+	0.105995i
$417$	−4.36178	−	9.55096i	−0.213597	−	0.467712i
$418$	−0.480354	+	3.34094i	−0.0234949	+	0.163411i
$419$	−4.73506	+	5.46455i	−0.231323	+	0.266961i	−0.859530	−	0.511085i	$-0.829244\pi$
$419$	−4.73506	+	5.46455i	−0.231323	+	0.266961i	0.628207	+	0.778046i	$0.283789\pi$
$420$	0.0758449	+	0.0875297i	0.00370085	+	0.00427101i
$421$	−3.90514	−	8.55106i	−0.190325	−	0.416753i	0.790281	−	0.612745i	$-0.209935\pi$
$421$	−3.90514	−	8.55106i	−0.190325	−	0.416753i	−0.980606	+	0.195992i	$0.937207\pi$
$422$	−1.04725	+	0.673028i	−0.0509794	+	0.0327625i
$423$	−0.196630	−	1.36759i	−0.00956049	−	0.0664947i
$424$	−1.46321	−	0.940350i	−0.0710599	−	0.0456674i
$425$	4.29415	−	2.75968i	0.208297	−	0.133864i
$426$	−5.94062	+	6.85584i	−0.287824	+	0.332167i
$427$	2.13103	+	0.625727i	0.103128	+	0.0302810i
$428$	−12.2924	+	14.1862i	−0.594175	+	0.685714i
$429$	0.131962	+	0.917813i	0.00637117	+	0.0443124i
$430$	6.68936	−	1.96417i	0.322590	−	0.0947209i
$431$	−1.22487			−0.0589997			−0.0294999	−	0.999565i	$-0.509391\pi$
$431$	−1.22487			−0.0589997			−0.0294999	+	0.999565i	$0.509391\pi$
$432$	−3.29913			−0.158729
$433$	20.5305	−	6.02828i	0.986630	−	0.289701i	0.251672	−	0.967813i	$-0.419020\pi$
$433$	20.5305	−	6.02828i	0.986630	−	0.289701i	0.734959	+	0.678112i	$0.237201\pi$
$434$	0.464068	+	0.298239i	0.0222760	+	0.0143159i
$435$	−1.54817	−	3.39002i	−0.0742290	−	0.162539i
$436$	−6.81132	−	14.9147i	−0.326203	−	0.714285i
$437$	14.8130	+	9.51974i	0.708602	+	0.455391i
$438$	9.41878	−	2.76560i	0.450047	−	0.132146i
$439$	−4.51786			−0.215626			−0.107813	−	0.994171i	$-0.534385\pi$
$439$	−4.51786			−0.215626			−0.107813	+	0.994171i	$0.534385\pi$
$440$	0.556139			0.0265129
$441$	−17.7668	+	5.21682i	−0.846040	+	0.248420i
$442$	2.07804	+	14.4531i	0.0988421	+	0.687462i
$443$	−20.8293	+	24.0383i	−0.989629	+	1.14209i	0.000224500		1.00000i	$0.499929\pi$
$443$	−20.8293	+	24.0383i	−0.989629	+	1.14209i	−0.989853	+	0.142093i	$0.954617\pi$
$444$	−5.39686	−	1.58466i	−0.256124	−	0.0752047i
$445$	−5.68283	+	6.55834i	−0.269392	+	0.310895i
$446$	4.08444	−	2.62491i	0.193404	−	0.124293i
$447$	−0.444691	−	0.285786i	−0.0210332	−	0.0135172i
$448$	0.0282791	+	0.196686i	0.00133606	+	0.00929252i
$449$	27.1265	−	17.4332i	1.28018	−	0.822722i	0.289270	−	0.957247i	$-0.406587\pi$
$449$	27.1265	−	17.4332i	1.28018	−	0.822722i	0.990910	+	0.134525i	$0.0429510\pi$
$450$	1.10512	+	2.41987i	0.0520958	+	0.114074i
$451$	3.01207	+	3.47611i	0.141833	+	0.163684i
$452$	−3.65421	+	4.21718i	−0.171880	+	0.198360i
$453$	−0.0980346	+	0.681845i	−0.00460607	+	0.0320359i
$454$	4.71724	+	10.3293i	0.221391	+	0.484779i
$455$	0.372235	+	0.429582i	0.0174506	+	0.0201391i
$456$	3.39415	+	0.996613i	0.158946	+	0.0466707i
$457$	0.650862	+	0.191110i	0.0304460	+	0.00893976i	0.296920	−	0.954902i	$-0.404040\pi$
$457$	0.650862	+	0.191110i	0.0304460	+	0.00893976i	−0.266474	+	0.963842i	$0.585859\pi$
$458$	−3.46429	+	24.0946i	−0.161876	+	1.12587i
$459$	−14.1670	−	9.10456i	−0.661257	−	0.424964i
$460$	1.20523	−	2.63909i	0.0561942	−	0.123048i
$461$	19.1355	−	5.61870i	0.891231	−	0.261689i	0.196110	−	0.980582i	$-0.437169\pi$
$461$	19.1355	−	5.61870i	0.891231	−	0.261689i	0.695121	+	0.718893i	$0.255351\pi$
$462$	−0.0267573	+	0.0585904i	−0.00124486	+	0.00272587i
$463$	0.0830064	+	0.577322i	0.00385764	+	0.0268304i	0.991659	−	0.128887i	$-0.0411403\pi$
$463$	0.0830064	+	0.577322i	0.00385764	+	0.0268304i	−0.987802	+	0.155717i	$0.950231\pi$
$464$	0.909965	−	6.32895i	0.0422441	−	0.293814i
$465$	−1.05962	−	1.22287i	−0.0491386	−	0.0567090i
$466$	12.2578	−	7.87762i	0.567832	−	0.364923i
$467$	−4.17095	+	9.13311i	−0.193009	+	0.422630i	−0.981251	−	0.192735i	$-0.938264\pi$
$467$	−4.17095	+	9.13311i	−0.193009	+	0.422630i	0.788242	+	0.615365i	$0.210991\pi$
$468$	−7.60991			−0.351768
$469$	−1.57927	−	0.389108i	−0.0729238	−	0.0179674i
$470$	0.519365			0.0239565
$471$	3.24487	−	7.10529i	0.149516	−	0.327394i
$472$	−9.00797	+	5.78907i	−0.414626	+	0.266464i
$473$	2.53907	+	2.93025i	0.116747	+	0.134733i
$474$	0.405801	−	2.82241i	0.0186391	−	0.129637i
$475$	−0.863730	−	6.00738i	−0.0396307	−	0.275637i
$476$	−0.421356	+	0.922640i	−0.0193128	+	0.0422891i
$477$	4.43966	−	1.30360i	0.203278	−	0.0596878i
$478$	0.145757	−	0.319164i	0.00666678	−	0.0145982i
$479$	−22.2596	−	14.3054i	−1.01707	−	0.653629i	−0.0778535	−	0.996965i	$-0.524807\pi$
$479$	−22.2596	−	14.3054i	−1.01707	−	0.653629i	−0.939213	+	0.343336i	$0.888443\pi$
$480$	0.0829491	−	0.576924i	0.00378609	−	0.0263328i
$481$	−26.4870	−	7.77727i	−1.20770	−	0.354613i
$482$	−4.62501	−	1.35802i	−0.210663	−	0.0618563i
$483$	0.220047	+	0.253947i	0.0100125	+	0.0115550i
$484$	−4.44108	−	9.72461i	−0.201867	−	0.442028i
$485$	0.0527745	−	0.367055i	0.00239637	−	0.0166671i
$486$	8.79366	−	10.1484i	0.398888	−	0.460342i
$487$	−7.15037	−	8.25197i	−0.324014	−	0.373933i	0.570250	−	0.821471i	$-0.306846\pi$
$487$	−7.15037	−	8.25197i	−0.324014	−	0.373933i	−0.894265	+	0.447538i	$0.852301\pi$
$488$	−4.64316	−	10.1671i	−0.210186	−	0.460243i
$489$	4.89617	−	3.14658i	0.221412	−	0.142293i
$490$	−0.990585	−	6.88967i	−0.0447500	−	0.311243i
$491$	28.2458	+	18.1525i	1.27471	+	0.819209i	0.990226	−	0.139471i	$-0.0445400\pi$
$491$	28.2458	+	18.1525i	1.27471	+	0.819209i	0.284488	+	0.958680i	$0.408176\pi$
$492$	4.05528	−	2.60617i	0.182826	−	0.117495i
$493$	21.3734	−	24.6663i	0.962611	−	1.11091i
$494$	16.6580	+	4.89122i	0.749477	+	0.220066i
$495$	−0.968857	+	1.11812i	−0.0435469	+	0.0502558i
$496$	−0.395084	−	2.74787i	−0.0177398	−	0.123383i
$497$	−2.96742	+	0.871313i	−0.133107	+	0.0390837i
$498$	5.74817			0.257582
$499$	33.0315			1.47869			0.739347	−	0.673324i	$-0.235134\pi$
$499$	33.0315			1.47869			0.739347	+	0.673324i	$0.235134\pi$
$500$	−0.959493	+	0.281733i	−0.0429098	+	0.0125995i
$501$	11.8186	+	7.59535i	0.528016	+	0.339335i
$502$	−7.54569	−	16.5228i	−0.336781	−	0.737447i
$503$	6.49787	+	14.2284i	0.289726	+	0.634411i	0.997395	−	0.0721330i	$-0.0229806\pi$
$503$	6.49787	+	14.2284i	0.289726	+	0.634411i	−0.707669	+	0.706544i	$0.750253\pi$
$504$	−0.444703	−	0.285793i	−0.0198086	−	0.0127302i
$505$	−17.3096	+	5.08255i	−0.770266	+	0.226170i
$506$	1.61351			0.0717293
$507$	−2.80771			−0.124695
$508$	0.848631	−	0.249180i	0.0376519	−	0.0110556i
$509$	4.67177	+	32.4929i	0.207072	+	1.44022i	0.782644	+	0.622469i	$0.213870\pi$
$509$	4.67177	+	32.4929i	0.207072	+	1.44022i	−0.575572	+	0.817751i	$0.695221\pi$
$510$	1.94832	−	2.24849i	0.0862732	−	0.0995646i
$511$	3.21106	+	0.942853i	0.142049	+	0.0417094i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−16.8443	+	10.8252i	−0.743696	+	0.477944i
$514$	3.15351	+	2.02664i	0.139095	+	0.0893911i
$515$	0.962008	+	6.69091i	0.0423911	+	0.294837i
$516$	3.41847	−	2.19692i	0.150490	−	0.0967138i
$517$	0.119988	+	0.262738i	0.00527708	+	0.0115552i
$518$	−1.25575	−	1.44921i	−0.0551744	−	0.0636747i
$519$	5.85445	−	6.75639i	0.256982	−	0.296573i
$520$	0.407101	−	2.83145i	0.0178526	−	0.124167i
$521$	−7.95850	−	17.4267i	−0.348668	−	0.763477i	−0.999989	−	0.00467475i	$-0.998512\pi$
$521$	−7.95850	−	17.4267i	−0.348668	−	0.763477i	0.651321	−	0.758803i	$-0.274215\pi$
$522$	11.1391	+	12.8552i	0.487546	+	0.562658i
$523$	41.3157	+	12.1314i	1.80661	+	0.530469i	0.998300	−	0.0582883i	$-0.0185643\pi$
$523$	41.3157	+	12.1314i	1.80661	+	0.530469i	0.808310	+	0.588757i	$0.200382\pi$
$524$	10.3067	+	3.02632i	0.450250	+	0.132205i
$525$	0.0164827	−	0.114639i	0.000719363	−	0.00500328i
$526$	−18.1871	−	11.6882i	−0.792997	−	0.509628i
$527$	5.88670	−	12.8901i	0.256429	−	0.561501i
$528$	0.311019	−	0.0913234i	0.0135354	−	0.00397434i
$529$	−6.05784	+	13.2648i	−0.263384	+	0.576732i
$530$	0.247532	+	1.72162i	0.0107521	+	0.0747825i
$531$	4.05394	−	28.1958i	0.175926	−	1.22359i
$532$	0.789756	+	0.911427i	0.0342402	+	0.0395154i
$533$	19.9027	−	12.7907i	0.862081	−	0.554026i
$534$	−2.10116	+	4.60090i	−0.0909262	+	0.199101i
$535$	18.7710			0.811540
$536$	3.72472	+	7.28879i	0.160883	+	0.314828i
$537$	14.3121			0.617613
$538$	8.75655	−	19.1742i	0.377522	−	0.826657i
$539$	3.25650	−	2.09283i	0.140268	−	0.0901445i
$540$	2.16047	+	2.49332i	0.0929718	+	0.107295i
$541$	4.69485	−	32.6534i	0.201847	−	1.40388i	−0.596949	−	0.802279i	$-0.703621\pi$
$541$	4.69485	−	32.6534i	0.201847	−	1.40388i	0.798797	−	0.601601i	$-0.205470\pi$
$542$	−3.63963	−	25.3142i	−0.156336	−	1.08734i
$543$	−0.730736	+	1.60009i	−0.0313589	+	0.0686664i
$544$	4.89770	−	1.43810i	0.209987	−	0.0616578i
$545$	−6.81132	+	14.9147i	−0.291765	+	0.638876i
$546$	0.278713	+	0.179118i	0.0119278	+	0.00766553i
$547$	−3.03278	+	21.0935i	−0.129672	+	0.901891i	0.816296	+	0.577633i	$0.196024\pi$
$547$	−3.03278	+	21.0935i	−0.129672	+	0.901891i	−0.945969	+	0.324258i	$0.894885\pi$
$548$	3.79644	+	1.11474i	0.162176	+	0.0476191i
$549$	28.5299	+	8.37714i	1.21763	+	0.357528i
$550$	−0.364194	−	0.420302i	−0.0155293	−	0.0179217i
$551$	−16.1207	−	35.2995i	−0.686766	−	1.50381i
$552$	0.240658	−	1.67381i	0.0102431	−	0.0712422i
$553$	0.636599	−	0.734675i	0.0270710	−	0.0312415i
$554$	−1.58684	−	1.83131i	−0.0674184	−	0.0778049i
$555$	2.33659	+	5.11641i	0.0991825	+	0.217179i
$556$	−15.1547	+	9.73931i	−0.642701	+	0.413039i
$557$	1.56551	+	10.8884i	0.0663328	+	0.461354i	0.995733	+	0.0922810i	$0.0294158\pi$
$557$	1.56551	+	10.8884i	0.0663328	+	0.461354i	−0.929400	+	0.369073i	$0.879675\pi$
$558$	6.21288	+	3.99278i	0.263012	+	0.169028i
$559$	16.7773	−	10.7821i	0.709604	−	0.456035i
$560$	0.130126	−	0.150174i	0.00549884	−	0.00634600i
$561$	1.58759	+	0.466158i	0.0670280	+	0.0196812i
$562$	8.21170	−	9.47681i	0.346390	−	0.399755i
$563$	2.14982	+	14.9524i	0.0906043	+	0.630167i	0.983635	+	0.180171i	$0.0576652\pi$
$563$	2.14982	+	14.9524i	0.0906043	+	0.630167i	−0.893031	+	0.449995i	$0.851426\pi$
$564$	0.290453	−	0.0852848i	0.0122303	−	0.00359114i
$565$	5.58013			0.234758
$566$	2.88767			0.121378
$567$	1.15500	−	0.339138i	0.0485053	−	0.0142424i
$568$	13.0933	+	8.41453i	0.549381	+	0.353066i
$569$	8.62119	+	18.8778i	0.361419	+	0.791398i	0.999766	+	0.0216484i	$0.00689144\pi$
$569$	8.62119	+	18.8778i	0.361419	+	0.791398i	−0.638346	+	0.769749i	$0.720381\pi$
$570$	−1.46951	−	3.21777i	−0.0615509	−	0.134778i
$571$	−21.0017	−	13.4969i	−0.878892	−	0.564830i	0.0215684	−	0.999767i	$-0.493134\pi$
$571$	−21.0017	−	13.4969i	−0.878892	−	0.564830i	−0.900461	+	0.434938i	$0.856770\pi$
$572$	1.52643	−	0.448201i	0.0638233	−	0.0187402i
$573$	0.431381			0.0180212
$574$	1.64342			0.0685949
$575$	−2.78375	+	0.817382i	−0.116090	+	0.0340872i
$576$	0.378597	+	2.63320i	0.0157749	+	0.109717i
$577$	−24.3221	+	28.0692i	−1.01254	+	1.16854i	−0.0269087	+	0.999638i	$0.508566\pi$
$577$	−24.3221	+	28.0692i	−1.01254	+	1.16854i	−0.985634	+	0.168898i	$0.945979\pi$
$578$	8.68880	+	2.55126i	0.361406	+	0.106118i
$579$	6.49616	−	7.49697i	0.269971	−	0.311563i
$580$	−5.37900	+	3.45687i	−0.223351	+	0.143539i
$581$	1.64858	+	1.05948i	0.0683948	+	0.0439547i
$582$	−0.0307600	−	0.213940i	−0.00127504	−	0.00886811i
$583$	−0.813750	+	0.522966i	−0.0337021	+	0.0216590i
$584$	−6.99638	−	15.3199i	−0.289512	−	0.633943i
$585$	4.98343	+	5.75119i	0.206039	+	0.237782i
$586$	15.5758	−	17.9754i	0.643430	−	0.742558i
$587$	−0.0269025	+	0.187111i	−0.00111039	+	0.00772290i	−0.990369	−	0.138452i	$-0.955787\pi$
$587$	−0.0269025	+	0.187111i	−0.00111039	+	0.00772290i	0.989259	+	0.146175i	$0.0466963\pi$
$588$	−1.68533	−	3.69036i	−0.0695019	−	0.152188i
$589$	−11.0336	−	12.7334i	−0.454630	−	0.524671i
$590$	10.2741	+	3.01674i	0.422976	+	0.124197i
$591$	0.303268	+	0.0890475i	0.0124748	+	0.00366292i
$592$	−1.37337	+	9.55201i	−0.0564452	+	0.392585i
$593$	19.9218	+	12.8029i	0.818089	+	0.525754i	0.881472	−	0.472236i	$-0.156553\pi$
$593$	19.9218	+	12.8029i	0.818089	+	0.525754i	−0.0633838	+	0.997989i	$0.520189\pi$
$594$	−0.762193	+	1.66897i	−0.0312732	+	0.0684787i
$595$	0.973214	−	0.285761i	0.0398979	−	0.0117151i
$596$	−0.376749	+	0.824965i	−0.0154322	+	0.0337919i
$597$	−0.0567949	−	0.395017i	−0.00232446	−	0.0161670i
$598$	1.18111	−	8.21481i	0.0482992	−	0.335929i
$599$	−21.1109	−	24.3633i	−0.862569	−	0.995458i	−0.999988	−	0.00494484i	$-0.998426\pi$
$599$	−21.1109	−	24.3633i	−0.862569	−	0.995458i	0.137419	−	0.990513i	$-0.456119\pi$
$600$	−0.490330	+	0.315116i	−0.0200176	+	0.0128646i
$601$	−6.13237	+	13.4280i	−0.250144	+	0.547740i	−0.992497	−	0.122270i	$-0.960983\pi$
$601$	−6.13237	+	13.4280i	−0.250144	+	0.547740i	0.742352	+	0.670010i	$0.233710\pi$
$602$	1.38535			0.0564626
$603$	−21.1430	−	5.20933i	−0.861010	−	0.212140i
$604$	1.18186			0.0480894
$605$	−4.44108	+	9.72461i	−0.180556	+	0.395362i
$606$	−8.84571	+	5.68480i	−0.359333	+	0.230929i
$607$	26.9936	+	31.1523i	1.09564	+	1.26443i	0.961896	+	0.273415i	$0.0881534\pi$
$607$	26.9936	+	31.1523i	1.09564	+	1.26443i	0.133740	+	0.991016i	$0.457301\pi$
$608$	0.863730	−	6.00738i	0.0350289	−	0.243631i
$609$	−0.105391	−	0.733008i	−0.00427065	−	0.0297030i
$610$	−4.64316	+	10.1671i	−0.187996	+	0.411654i
$611$	1.42550	−	0.418565i	0.0576696	−	0.0169333i
$612$	−5.64105	+	12.3522i	−0.228026	+	0.499307i
$613$	11.6486	+	7.48608i	0.470481	+	0.302360i	0.754314	−	0.656514i	$-0.227970\pi$
$613$	11.6486	+	7.48608i	0.470481	+	0.302360i	−0.283833	+	0.958874i	$0.591606\pi$
$614$	3.04404	−	21.1717i	0.122847	−	0.854422i
$615$	−4.62525	−	1.35810i	−0.186508	−	0.0547638i
$616$	0.106033	+	0.0311341i	0.00427219	+	0.00125443i
$617$	−22.7714	−	26.2796i	−0.916742	−	1.05798i	−0.998120	−	0.0612938i	$-0.980477\pi$
$617$	−22.7714	−	26.2796i	−0.916742	−	1.05798i	0.0813773	−	0.996683i	$-0.474068\pi$
$618$	1.63671	+	3.58390i	0.0658382	+	0.144166i
$619$	−2.68881	+	18.7011i	−0.108072	+	0.751660i	0.861659	+	0.507487i	$0.169426\pi$
$619$	−2.68881	+	18.7011i	−0.108072	+	0.751660i	−0.969732	+	0.244173i	$0.921484\pi$
$620$	−1.81798	+	2.09806i	−0.0730117	+	0.0842600i
$621$	6.26811	+	7.23378i	0.251531	+	0.290282i
$622$	−5.25075	−	11.4975i	−0.210536	−	0.461009i
$623$	−1.45064	+	0.932267i	−0.0581185	+	0.0373505i
$624$	−0.237282	−	1.65033i	−0.00949887	−	0.0660661i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	22.7327	−	14.6094i	0.908581	−	0.583910i
$627$	1.28831	−	1.48679i	0.0514503	−	0.0593768i
$628$	−12.8587	−	3.77565i	−0.513117	−	0.150665i
$629$	−32.2580	+	37.2277i	−1.28621	+	1.48437i
$630$	0.0752304	+	0.523239i	0.00299725	+	0.0208463i
$631$	33.2640	−	9.76718i	1.32422	−	0.388825i	0.458204	−	0.888847i	$-0.348493\pi$
$631$	33.2640	−	9.76718i	1.32422	−	0.388825i	0.866013	+	0.500022i	$0.166675\pi$
$632$	−4.89217			−0.194600
$633$	0.725581			0.0288393
$634$	1.34706	−	0.395532i	0.0534985	−	0.0157086i
$635$	−0.744053	−	0.478174i	−0.0295268	−	0.0189757i
$636$	0.421138	+	0.922164i	0.0166992	+	0.0365662i
$637$	−8.27134	−	18.1117i	−0.327722	−	0.717612i
$638$	−2.99147	−	1.92250i	−0.118434	−	0.0761126i
$639$	−39.7274	+	11.6650i	−1.57159	+	0.461461i
$640$	−1.00000			−0.0395285
$641$	−15.5030			−0.612333			−0.306167	−	0.951978i	$-0.599047\pi$
$641$	−15.5030			−0.612333			−0.306167	+	0.951978i	$0.599047\pi$
$642$	10.4976	−	3.08238i	0.414308	−	0.121652i
$643$	4.95744	+	34.4797i	0.195502	+	1.35975i	0.817138	+	0.576442i	$0.195559\pi$
$643$	4.95744	+	34.4797i	0.195502	+	1.35975i	−0.621636	+	0.783306i	$0.713532\pi$
$644$	0.377531	−	0.435694i	0.0148768	−	0.0171688i
$645$	−3.89894	−	1.14483i	−0.153521	−	0.0450777i
$646$	20.2875	−	23.4130i	0.798199	−	0.921171i
$647$	−12.6812	+	8.14973i	−0.498550	+	0.320399i	−0.765636	−	0.643274i	$-0.777576\pi$
$647$	−12.6812	+	8.14973i	−0.498550	+	0.320399i	0.267086	+	0.963673i	$0.413939\pi$
$648$	−5.09624	−	3.27516i	−0.200199	−	0.128660i
$649$	0.847489	+	5.89441i	0.0332668	+	0.231376i
$650$	−2.40646	+	1.54654i	−0.0943893	+	0.0606603i
$651$	−0.133567	−	0.292471i	−0.00523490	−	0.0114628i
$652$	−6.53908	−	7.54650i	−0.256090	−	0.295544i
$653$	21.1941	−	24.4593i	0.829388	−	0.957165i	−0.170213	−	0.985407i	$-0.554446\pi$
$653$	21.1941	−	24.4593i	0.829388	−	0.957165i	0.999601	+	0.0282427i	$0.00899112\pi$
$654$	−1.36007	+	9.45948i	−0.0531829	+	0.369895i
$655$	−4.46231	−	9.77110i	−0.174357	−	0.381788i
$656$	−5.41603	−	6.25043i	−0.211460	−	0.244038i
$657$	42.9893	+	12.6228i	1.67717	+	0.492462i
$658$	0.0990218	+	0.0290754i	0.00386027	+	0.00113348i
$659$	5.22494	−	36.3403i	0.203535	−	1.41562i	−0.590154	−	0.807291i	$-0.700933\pi$
$659$	5.22494	−	36.3403i	0.203535	−	1.41562i	0.793688	−	0.608324i	$-0.208158\pi$
$660$	−0.272692	−	0.175248i	−0.0106145	−	0.00682153i
$661$	2.20840	−	4.83572i	0.0858968	−	0.188088i	−0.861809	−	0.507233i	$-0.830668\pi$
$661$	2.20840	−	4.83572i	0.0858968	−	0.188088i	0.947706	+	0.319145i	$0.103396\pi$
$662$	4.26403	−	1.25203i	0.165726	−	0.0486617i
$663$	3.53547	−	7.74159i	0.137306	−	0.300659i
$664$	−1.40352	−	9.76169i	−0.0544671	−	0.378827i
$665$	0.171630	−	1.19371i	0.00665554	−	0.0462903i
$666$	−16.8118	−	19.4018i	−0.651444	−	0.751806i
$667$	−15.6059	+	10.0293i	−0.604264	+	0.388337i
$668$	10.0129	−	21.9252i	0.387410	−	0.848310i
$669$	−2.82987			−0.109409
$670$	3.06933	−	7.58810i	0.118579	−	0.293154i
$671$	−6.21606			−0.239968
$672$	0.0481127	−	0.105352i	0.00185599	−	0.00406404i
$673$	−33.9409	+	21.8125i	−1.30833	+	0.840810i	−0.994092	−	0.108536i	$-0.965384\pi$
$673$	−33.9409	+	21.8125i	−1.30833	+	0.840810i	−0.314233	+	0.949346i	$0.601747\pi$
$674$	3.73060	+	4.30534i	0.143697	+	0.165836i
$675$	0.469515	−	3.26555i	0.0180716	−	0.125691i
$676$	0.685552	+	4.76812i	0.0263674	+	0.183389i
$677$	12.8184	−	28.0684i	0.492652	−	1.07876i	−0.486137	−	0.873883i	$-0.661594\pi$
$677$	12.8184	−	28.0684i	0.492652	−	1.07876i	0.978788	−	0.204874i	$-0.0656784\pi$
$678$	3.12067	−	0.916311i	0.119849	−	0.0351907i
$679$	0.0306106	−	0.0670279i	0.00117473	−	0.00257230i
$680$	−4.29415	−	2.75968i	−0.164673	−	0.105829i
$681$	0.941929	−	6.55126i	0.0360948	−	0.251045i
$682$	−1.48137	−	0.434970i	−0.0567247	−	0.0166559i
$683$	40.2626	+	11.8222i	1.54060	+	0.452362i	0.938276	−	0.345887i	$-0.112422\pi$
$683$	40.2626	+	11.8222i	1.54060	+	0.452362i	0.602328	+	0.798249i	$0.294240\pi$
$684$	10.5731	+	12.2021i	0.404274	+	0.466557i
$685$	−1.64368	−	3.59915i	−0.0628017	−	0.137517i
$686$	0.394791	−	2.74583i	0.0150732	−	0.104836i
$687$	9.29125	−	10.7227i	0.354483	−	0.409096i
$688$	−4.56554	−	5.26891i	−0.174059	−	0.200875i
$689$	2.06688	+	4.52584i	0.0787419	+	0.172421i
$690$	−1.42258	+	0.914237i	−0.0541567	+	0.0348044i
$691$	1.48696	+	10.3420i	0.0565666	+	0.393429i	0.998361	+	0.0572385i	$0.0182295\pi$
$691$	1.48696	+	10.3420i	0.0565666	+	0.393429i	−0.941794	+	0.336191i	$0.890861\pi$
$692$	−12.9033	−	8.29247i	−0.490511	−	0.315233i
$693$	−0.247317	+	0.158941i	−0.00939478	+	0.00603766i
$694$	−14.8137	+	17.0959i	−0.562321	+	0.648953i
$695$	17.2847	+	5.07524i	0.655645	+	0.192515i
$696$	−2.44054	+	2.81653i	−0.0925083	+	0.106760i
$697$	−6.00804	−	41.7869i	−0.227571	−	1.58279i
$698$	−26.0954	+	7.66229i	−0.987724	+	0.290022i
$699$	−8.49273			−0.321225
$700$	−0.198708			−0.00751047
$701$	−30.1259	+	8.84576i	−1.13784	+	0.334100i	−0.795784	−	0.605580i	$-0.792941\pi$
$701$	−30.1259	+	8.84576i	−1.13784	+	0.334100i	−0.342055	+	0.939680i	$0.611123\pi$
$702$	7.93923	+	5.10224i	0.299647	+	0.192571i
$703$	24.3303	+	53.2760i	0.917636	+	2.00934i
$704$	−0.231029	−	0.505882i	−0.00870722	−	0.0190661i
$705$	−0.254660	−	0.163660i	−0.00959107	−	0.00616381i
$706$	9.83817	−	2.88875i	0.370264	−	0.108719i
$707$	−3.58476			−0.134819
$708$	6.24111			0.234555
$709$	11.0087	−	3.23244i	0.413440	−	0.121397i	−0.0683962	−	0.997658i	$-0.521788\pi$
$709$	11.0087	−	3.23244i	0.413440	−	0.121397i	0.481836	+	0.876261i	$0.339970\pi$
$710$	−2.21499	−	15.4056i	−0.0831270	−	0.578161i
$711$	8.52270	−	9.83572i	0.319626	−	0.368868i
$712$	8.32641	+	2.44485i	0.312045	+	0.0916247i
$713$	−5.27444	+	6.08703i	−0.197529	+	0.227961i
$714$	0.497342	−	0.319622i	0.0186125	−	0.0119616i
$715$	−1.33833	−	0.860091i	−0.0500506	−	0.0321656i
$716$	−3.49456	−	24.3052i	−0.130598	−	0.908328i
$717$	−0.172043	+	0.110565i	−0.00642505	+	0.00412913i
$718$	−0.706359	−	1.54671i	−0.0263611	−	0.0577227i
$719$	14.9628	+	17.2680i	0.558019	+	0.643988i	0.962733	−	0.270455i	$-0.0871742\pi$
$719$	14.9628	+	17.2680i	0.558019	+	0.643988i	−0.404714	+	0.914443i	$0.632629\pi$
$720$	1.74211	−	2.01050i	0.0649247	−	0.0749271i
$721$	−0.191159	+	1.32954i	−0.00711913	+	0.0495146i
$722$	−7.40876	−	16.2229i	−0.275725	−	0.603754i
$723$	1.83984	+	2.12329i	0.0684245	+	0.0789661i
$724$	2.89573	+	0.850264i	0.107619	+	0.0315998i
$725$	6.13503	+	1.80141i	0.227849	+	0.0669026i
$726$	−0.886785	+	6.16772i	−0.0329117	+	0.228906i
$727$	−24.6295	−	15.8284i	−0.913456	−	0.587042i	−0.00270387	−	0.999996i	$-0.500861\pi$
$727$	−24.6295	−	15.8284i	−0.913456	−	0.587042i	−0.910752	+	0.412954i	$0.864497\pi$
$728$	0.236130	−	0.517052i	0.00875154	−	0.0191632i
$729$	9.92786	−	2.91508i	0.367699	−	0.107966i
$730$	−6.99638	+	15.3199i	−0.258948	+	0.567016i
$731$	−5.06458	−	35.2250i	−0.187320	−	1.30284i
$732$	−0.927136	+	6.44837i	−0.0342679	+	0.238339i
$733$	−2.38773	−	2.75558i	−0.0881926	−	0.101780i	0.709938	−	0.704264i	$-0.248723\pi$
$733$	−2.38773	−	2.75558i	−0.0881926	−	0.101780i	−0.798131	+	0.602485i	$0.794178\pi$
$734$	−1.59139	+	1.02273i	−0.0587393	+	0.0377495i
$735$	−1.68533	+	3.69036i	−0.0621644	+	0.136121i
$736$	−2.90127			−0.106942
$737$	4.54778	−	0.200349i	0.167520	−	0.00737994i
$738$	22.0019			0.809899
$739$	13.6519	−	29.8936i	0.502195	−	1.09965i	−0.473555	−	0.880764i	$-0.657030\pi$
$739$	13.6519	−	29.8936i	0.502195	−	1.09965i	0.975750	−	0.218889i	$-0.0702432\pi$
$740$	8.11830	−	5.21731i	0.298434	−	0.191792i
$741$	−6.62660	−	7.64750i	−0.243434	−	0.280938i
$742$	−0.0491866	+	0.342100i	−0.00180570	+	0.0125589i
$743$	−1.79047	−	12.4530i	−0.0656858	−	0.456855i	−0.995946	−	0.0899541i	$-0.971328\pi$
$743$	−1.79047	−	12.4530i	−0.0656858	−	0.456855i	0.930260	−	0.366901i	$-0.119581\pi$
$744$	−0.672176	+	1.47186i	−0.0246432	+	0.0539610i
$745$	0.870185	−	0.255509i	0.0318811	−	0.00936114i
$746$	−0.814176	+	1.78280i	−0.0298091	+	0.0652729i
$747$	22.0710	+	14.1842i	0.807536	+	0.518972i
$748$	0.404003	−	2.80990i	0.0147718	−	0.102740i
$749$	3.57886	+	1.05085i	0.130769	+	0.0383971i
$750$	0.559247	+	0.164210i	0.0204208	+	0.00599609i
$751$	15.0805	+	17.4038i	0.550296	+	0.635075i	0.960952	−	0.276715i	$-0.0892459\pi$
$751$	15.0805	+	17.4038i	0.550296	+	0.635075i	−0.410656	+	0.911790i	$0.634700\pi$
$752$	−0.215752	−	0.472431i	−0.00786767	−	0.0172278i
$753$	−1.50671	+	10.4794i	−0.0549074	+	0.381890i
$754$	−11.9778	+	13.8231i	−0.436205	+	0.503407i
$755$	−0.773956	−	0.893193i	−0.0281672	−	0.0325066i
$756$	0.272331	+	0.596322i	0.00990459	+	0.0216880i
$757$	20.8549	−	13.4026i	0.757985	−	0.487127i	−0.103676	−	0.994611i	$-0.533061\pi$
$757$	20.8549	−	13.4026i	0.757985	−	0.487127i	0.861661	+	0.507484i	$0.169424\pi$
$758$	−2.33845	−	16.2643i	−0.0849363	−	0.590745i
$759$	−0.791152	−	0.508443i	−0.0287170	−	0.0184553i
$760$	−5.10569	+	3.28123i	−0.185203	+	0.119023i
$761$	−4.03017	+	4.65106i	−0.146094	+	0.168601i	−0.824080	−	0.566473i	$-0.808307\pi$
$761$	−4.03017	+	4.65106i	−0.146094	+	0.168601i	0.677986	+	0.735074i	$0.262853\pi$
$762$	−0.494630	−	0.145236i	−0.0179185	−	0.00526136i
$763$	−2.13360	+	2.46231i	−0.0772416	+	0.0891416i
$764$	−0.105329	−	0.732582i	−0.00381069	−	0.0265039i
$765$	13.0293	−	3.82573i	0.471074	−	0.138320i
$766$	−24.9476			−0.901392
$767$	30.6304			1.10600
$768$	−0.559247	+	0.164210i	−0.0201801	+	0.00592540i
$769$	1.48449	+	0.954022i	0.0535320	+	0.0344029i	0.567133	−	0.823626i	$-0.308053\pi$
$769$	1.48449	+	0.954022i	0.0535320	+	0.0344029i	−0.513601	+	0.858029i	$0.671689\pi$
$770$	−0.0459073	−	0.100523i	−0.00165438	−	0.00362259i
$771$	−0.907634	−	1.98744i	−0.0326876	−	0.0715759i
$772$	−14.3177	−	9.20143i	−0.515305	−	0.331167i
$773$	7.90706	−	2.32172i	0.284397	−	0.0835066i	−0.136423	−	0.990651i	$-0.543561\pi$
$773$	7.90706	−	2.32172i	0.284397	−	0.0835066i	0.420820	+	0.907144i	$0.361742\pi$
$774$	18.5468			0.666652
$775$	2.77613			0.0997214
$776$	−0.355808	+	0.104475i	−0.0127728	+	0.00375042i
$777$	0.159062	+	1.10630i	0.00570631	+	0.0396882i
$778$	−5.67765	+	6.55236i	−0.203554	+	0.234913i
$779$	−48.1617	−	14.1416i	−1.72557	−	0.506674i
$780$	−1.09185	+	1.26006i	−0.0390945	+	0.0451174i
$781$	7.28168	−	4.67965i	0.260559	−	0.167451i
$782$	−12.4585	−	8.00659i	−0.445515	−	0.286315i
$783$	−3.00209	−	20.8800i	−0.107286	−	0.746191i
$784$	−5.85556	+	3.76314i	−0.209127	+	0.134398i
$785$	5.56719	+	12.1905i	0.198702	+	0.435096i
$786$	−4.10004	−	4.73170i	−0.146244	−	0.168774i
$787$	−13.7004	+	15.8111i	−0.488365	+	0.563604i	−0.945428	−	0.325831i	$-0.894356\pi$
$787$	−13.7004	+	15.8111i	−0.488365	+	0.563604i	0.457063	+	0.889434i	$0.348901\pi$
$788$	0.0771744	−	0.536760i	0.00274922	−	0.0191213i
$789$	5.23457	+	11.4621i	0.186356	+	0.408062i
$790$	3.20369	+	3.69725i	0.113982	+	0.131542i
$791$	1.06390	+	0.312390i	0.0378280	+	0.0111073i
$792$	1.41956	+	0.416819i	0.0504417	+	0.0148110i
$793$	−4.55024	+	31.6476i	−0.161584	+	1.12384i
$794$	−9.29359	−	5.97262i	−0.329817	−	0.211961i
$795$	0.421138	−	0.922164i	0.0149362	−	0.0327058i
$796$	−0.656961	+	0.192901i	−0.0232854	+	0.00683720i
$797$	−3.76228	+	8.23825i	−0.133267	+	0.291814i	−0.964487	−	0.264129i	$-0.914915\pi$
$797$	−3.76228	+	8.23825i	−0.133267	+	0.291814i	0.831220	+	0.555943i	$0.187643\pi$
$798$	−0.100036	−	0.695764i	−0.00354123	−	0.0246298i
$799$	0.377289	−	2.62410i	0.0133475	−	0.0928340i
$800$	0.654861	+	0.755750i	0.0231528	+	0.0267198i
$801$	−19.4209	+	12.4811i	−0.686204	+	0.440997i
$802$	10.1346	−	22.1916i	0.357864	−	0.783614i
$803$	−9.36644			−0.330534
$804$	0.470474	−	4.74763i	0.0165923	−	0.167436i
$805$	−0.576506			−0.0203192
$806$	−3.29893	+	7.22366i	−0.116200	+	0.254443i
$807$	−10.3357	+	6.64234i	−0.363833	+	0.233821i
$808$	11.8139	+	13.6340i	0.415612	+	0.479641i
$809$	−3.49128	+	24.2824i	−0.122747	+	0.853722i	0.831675	+	0.555262i	$0.187382\pi$
$809$	−3.49128	+	24.2824i	−0.122747	+	0.853722i	−0.954422	+	0.298460i	$0.903527\pi$
$810$	0.862131	+	5.99626i	0.0302922	+	0.210687i
$811$	22.0670	−	48.3199i	0.774876	−	1.69674i	0.0592667	−	0.998242i	$-0.481124\pi$
$811$	22.0670	−	48.3199i	0.774876	−	1.69674i	0.715610	−	0.698500i	$-0.246149\pi$
$812$	−1.21908	+	0.357954i	−0.0427813	+	0.0125617i
$813$	−6.19229	+	13.5592i	−0.217173	+	0.475543i
$814$	4.51490	+	2.90155i	0.158247	+	0.101699i
$815$	−1.42108	+	9.88382i	−0.0497782	+	0.346215i
$816$	−2.85466	−	0.838203i	−0.0999330	−	0.0293430i
$817$	−40.5987	−	11.9209i	−1.42037	−	0.417058i
$818$	14.4086	+	16.6284i	0.503784	+	0.581397i
$819$	0.628170	+	1.37550i	0.0219501	+	0.0480639i
$820$	−1.17702	+	8.18633i	−0.0411032	+	0.285879i
$821$	−10.6031	+	12.2367i	−0.370052	+	0.427063i	−0.909983	−	0.414647i	$-0.863905\pi$
$821$	−10.6031	+	12.2367i	−0.370052	+	0.427063i	0.539930	+	0.841710i	$0.318451\pi$
$822$	−1.51024	−	1.74291i	−0.0526756	−	0.0607908i
$823$	9.25553	+	20.2668i	0.322627	+	0.706455i	0.999562	−	0.0295876i	$-0.00941939\pi$
$823$	9.25553	+	20.2668i	0.322627	+	0.706455i	−0.676935	+	0.736043i	$0.736692\pi$
$824$	5.68664	−	3.65458i	0.198103	−	0.127313i
$825$	0.0461312	+	0.320850i	0.00160608	+	0.0111706i
$826$	1.78996	+	1.15034i	0.0622806	+	0.0400253i
$827$	−22.4018	+	14.3967i	−0.778986	+	0.500624i	−0.868697	−	0.495344i	$-0.835042\pi$
$827$	−22.4018	+	14.3967i	−0.778986	+	0.500624i	0.0897110	+	0.995968i	$0.471406\pi$
$828$	5.05434	−	5.83302i	0.175650	−	0.202711i
$829$	17.6545	+	5.18382i	0.613165	+	0.180041i	0.573546	−	0.819173i	$-0.305567\pi$
$829$	17.6545	+	5.18382i	0.613165	+	0.180041i	0.0396189	+	0.999215i	$0.487386\pi$
$830$	−6.45829	+	7.45326i	−0.224170	+	0.258706i
$831$	0.201000	+	1.39799i	0.00697261	+	0.0484956i
$832$	−2.74470	+	0.805915i	−0.0951552	+	0.0279401i
$833$	−35.5297			−1.23103
$834$	10.4998			0.363578
$835$	−23.1270	+	6.79069i	−0.800342	+	0.235002i
$836$	−2.83948	−	1.82482i	−0.0982053	−	0.0631127i
$837$	−3.80470	−	8.33114i	−0.131510	−	0.287966i
$838$	−3.00371	−	6.57722i	−0.103762	−	0.227206i
$839$	−25.0953	−	16.1278i	−0.866387	−	0.556793i	0.0302585	−	0.999542i	$-0.490367\pi$
$839$	−25.0953	−	16.1278i	−0.866387	−	0.556793i	−0.896646	+	0.442749i	$0.854003\pi$
$840$	−0.111127	+	0.0326298i	−0.00383424	+	0.00112584i
$841$	11.8836			0.409780
$842$	9.40057			0.323965
$843$	−7.01274	+	2.05913i	−0.241532	+	0.0709201i
$844$	−0.177164	−	1.23220i	−0.00609822	−	0.0424141i
$845$	3.15456	−	3.64056i	0.108520	−	0.125239i
$846$	1.32569	+	0.389258i	0.0455782	+	0.0133830i
$847$	−1.39114	+	1.60546i	−0.0478002	+	0.0551644i
$848$	1.46321	−	0.940350i	0.0502470	−	0.0322918i
$849$	−1.41591	−	0.909950i	−0.0485939	−	0.0312294i
$850$	0.726442	+	5.05251i	0.0249167	+	0.173300i
$851$	23.5534	−	15.1368i	0.807399	−	0.518884i
$852$	−3.76847	−	8.25180i	−0.129106	−	0.282702i
$853$	−20.0479	−	23.1365i	−0.686428	−	0.792180i	0.300424	−	0.953806i	$-0.402872\pi$
$853$	−20.0479	−	23.1365i	−0.686428	−	0.792180i	−0.986852	+	0.161625i	$0.948326\pi$
$854$	−1.45444	+	1.67852i	−0.0497700	+	0.0574376i
$855$	2.29776	−	15.9813i	0.0785818	−	0.546549i
$856$	−7.79775	−	17.0747i	−0.266522	−	0.583601i
$857$	−34.4313	−	39.7358i	−1.17615	−	1.35735i	−0.920578	−	0.390559i	$-0.872282\pi$
$857$	−34.4313	−	39.7358i	−1.17615	−	1.35735i	−0.255572	−	0.966790i	$-0.582264\pi$
$858$	−0.889691	−	0.261237i	−0.0303735	−	0.00891848i
$859$	31.7544	+	9.32394i	1.08345	+	0.318129i	0.774257	−	0.632872i	$-0.218124\pi$
$859$	31.7544	+	9.32394i	1.08345	+	0.318129i	0.309190	+	0.951000i	$0.399942\pi$
$860$	−0.992186	+	6.90081i	−0.0338333	+	0.235315i
$861$	−0.805817	−	0.517867i	−0.0274622	−	0.0176489i
$862$	0.508828	−	1.11418i	0.0173307	−	0.0379490i
$863$	39.5818	−	11.6223i	1.34738	−	0.395626i	0.473082	−	0.881018i	$-0.343141\pi$
$863$	39.5818	−	11.6223i	1.34738	−	0.395626i	0.874296	+	0.485392i	$0.161323\pi$
$864$	1.37051	−	3.00099i	0.0466256	−	0.102096i
$865$	2.18286	+	15.1821i	0.0742194	+	0.516207i
$866$	−3.04514	+	21.1794i	−0.103478	+	0.719705i
$867$	−3.45643	−	3.98894i	−0.117387	−	0.135471i
$868$	−0.464068	+	0.298239i	−0.0157515	+	0.0101229i
$869$	−1.13023	+	2.47486i	−0.0383404	+	0.0839538i
$870$	3.72680			0.126350
$871$	2.30901	−	23.3006i	0.0782379	−	0.789512i
$872$	16.3964			0.555253
$873$	0.409811	−	0.897361i	0.0138700	−	0.0303711i
$874$	−14.8130	+	9.51974i	−0.501057	+	0.322010i
$875$	0.130126	+	0.150174i	0.00439907	+	0.00507680i
$876$	−1.39702	+	9.71649i	−0.0472010	+	0.328290i
$877$	3.65426	+	25.4160i	0.123396	+	0.858236i	0.953664	+	0.300873i	$0.0972779\pi$
$877$	3.65426	+	25.4160i	0.123396	+	0.858236i	−0.830269	+	0.557363i	$0.811813\pi$
$878$	1.87679	−	4.10959i	0.0633385	−	0.138692i
$879$	−13.3016	+	3.90571i	−0.448653	+	0.131736i
$880$	−0.231029	+	0.505882i	−0.00778797	+	0.0170533i
$881$	42.6996	+	27.4414i	1.43859	+	0.924523i	0.999662	+	0.0259989i	$0.00827665\pi$
$881$	42.6996	+	27.4414i	1.43859	+	0.924523i	0.438924	+	0.898524i	$0.355360\pi$
$882$	2.63523	−	18.3284i	0.0887328	−	0.617150i
$883$	43.1123	+	12.6589i	1.45085	+	0.426007i	0.909821	−	0.415000i	$-0.136219\pi$
$883$	43.1123	+	12.6589i	1.45085	+	0.426007i	0.541024	+	0.841007i	$0.318037\pi$
$884$	−14.0102	−	4.11377i	−0.471215	−	0.138361i
$885$	−4.08706	−	4.71672i	−0.137385	−	0.158551i
$886$	−13.2132	−	28.9328i	−0.443906	−	0.972018i
$887$	8.03339	−	55.8735i	0.269735	−	1.87605i	−0.181135	−	0.983458i	$-0.557977\pi$
$887$	8.03339	−	55.8735i	0.269735	−	1.87605i	0.450870	−	0.892590i	$-0.351114\pi$
$888$	3.68340	−	4.25087i	0.123607	−	0.142650i
$889$	−0.115091	−	0.132822i	−0.00386003	−	0.00445471i
$890$	−3.60494	−	7.89372i	−0.120838	−	0.264598i
$891$	−2.83422	+	1.82144i	−0.0949500	+	0.0610206i
$892$	0.690964	+	4.80576i	0.0231352	+	0.160909i
$893$	−2.65172	−	1.70416i	−0.0887365	−	0.0570275i
$894$	0.444691	−	0.285786i	0.0148727	−	0.00955810i
$895$	−16.0802	+	18.5575i	−0.537502	+	0.620310i
$896$	−0.190659	−	0.0559826i	−0.00636948	−	0.00187025i
$897$	−3.16775	+	3.65578i	−0.105768	+	0.122063i
$898$	4.58900	+	31.9172i	0.153137	+	1.06509i
$899$	17.0316	−	5.00093i	0.568036	−	0.166790i
$900$	−2.66028			−0.0886759
$901$	8.87833			0.295780
$902$	−4.41324	+	1.29584i	−0.146945	+	0.0431469i
$903$	−0.679277	−	0.436545i	−0.0226049	−	0.0145273i
$904$	−2.31807	−	5.07587i	−0.0770979	−	0.168821i
$905$	−1.25372	−	2.74525i	−0.0416749	−	0.0912553i
$906$	−0.579503	−	0.372424i	−0.0192527	−	0.0123730i
$907$	15.0298	−	4.41313i	0.499055	−	0.146536i	−0.0225113	−	0.999747i	$-0.507166\pi$
$907$	15.0298	−	4.41313i	0.499055	−	0.146536i	0.521566	+	0.853211i	$0.325348\pi$
$908$	−11.3555			−0.376845
$909$	−47.9923			−1.59180
$910$	−0.545394	+	0.160142i	−0.0180796	+	0.00530866i
$911$	3.03257	+	21.0920i	0.100474	+	0.698809i	0.976338	+	0.216251i	$0.0693830\pi$
$911$	3.03257	+	21.0920i	0.100474	+	0.698809i	−0.875864	+	0.482558i	$0.839708\pi$
$912$	−2.31653	+	2.67342i	−0.0767081	+	0.0885258i
$913$	−5.26252	−	1.54521i	−0.174164	−	0.0511391i
$914$	−0.444218	+	0.512655i	−0.0146934	+	0.0169571i
$915$	5.48050	−	3.52210i	0.181180	−	0.116437i
$916$	−20.4781	−	13.1605i	−0.676617	−	0.434835i
$917$	−0.303769	−	2.11276i	−0.0100313	−	0.0697695i
$918$	14.1670	−	9.10456i	0.467580	−	0.300495i
$919$	16.1735	+	35.4150i	0.533514	+	1.16823i	0.964065	+	0.265666i	$0.0855920\pi$
$919$	16.1735	+	35.4150i	0.533514	+	1.16823i	−0.430551	+	0.902566i	$0.641681\pi$
$920$	1.89993	+	2.19263i	0.0626388	+	0.0722890i
$921$	−8.16414	+	9.42192i	−0.269017	+	0.310463i
$922$	−2.83824	+	19.7404i	−0.0934724	+	0.650115i
$923$	−18.4951	−	40.4985i	−0.608772	−	1.33303i
$924$	−0.0421803	−	0.0486787i	−0.00138763	−	0.00160141i
$925$	−9.25933	−	2.71879i	−0.304445	−	0.0893931i
$926$	−0.559633	−	0.164323i	−0.0183907	−	0.00539999i
$927$	−2.55921	+	17.7997i	−0.0840555	+	0.584619i
$928$	5.37900	+	3.45687i	0.176574	+	0.113477i
$929$	3.31964	−	7.26900i	0.108914	−	0.238488i	−0.847325	−	0.531074i	$-0.821789\pi$
$929$	3.31964	−	7.26900i	0.108914	−	0.238488i	0.956239	+	0.292586i	$0.0945158\pi$
$930$	1.55254	−	0.455867i	0.0509098	−	0.0149485i
$931$	−17.5490	+	38.4269i	−0.575144	+	1.25939i
$932$	2.07365	+	14.4226i	0.0679248	+	0.472427i
$933$	−1.04846	+	7.29218i	−0.0343249	+	0.238735i
$934$	−6.57509	−	7.58806i	−0.215144	−	0.248289i
$935$	−2.38815	+	1.53477i	−0.0781007	+	0.0501923i
$936$	3.16127	−	6.92222i	0.103329	−	0.226260i
$937$	−2.12458			−0.0694071			−0.0347036	−	0.999398i	$-0.511049\pi$
$937$	−2.12458			−0.0694071			−0.0347036	+	0.999398i	$0.511049\pi$
$938$	1.01000	−	1.27491i	0.0329776	−	0.0416273i
$939$	−15.7502			−0.513988
$940$	−0.215752	+	0.472431i	−0.00703706	+	0.0154090i
$941$	8.59698	−	5.52495i	0.280254	−	0.180108i	−0.392961	−	0.919555i	$-0.628549\pi$
$941$	8.59698	−	5.52495i	0.280254	−	0.180108i	0.673215	+	0.739447i	$0.264913\pi$
$942$	5.11522	+	5.90328i	0.166663	+	0.192339i
$943$	−3.41484	+	23.7507i	−0.111203	+	0.773431i
$944$	−1.52388	−	10.5988i	−0.0495980	−	0.344962i
$945$	0.272331	−	0.596322i	0.00885893	−	0.0193984i
$946$	−3.72022	+	1.09235i	−0.120955	+	0.0355155i
$947$	3.24026	−	7.09519i	0.105294	−	0.230563i	−0.849650	−	0.527347i	$-0.823187\pi$
$947$	3.24026	−	7.09519i	0.105294	−	0.230563i	0.954945	+	0.296784i	$0.0959142\pi$
$948$	2.39878	+	1.54160i	0.0779086	+	0.0500688i
$949$	−6.85636	+	47.6870i	−0.222567	+	1.54799i
$950$	5.82331	+	1.70988i	0.188933	+	0.0554757i
$951$	−0.785141	−	0.230538i	−0.0254599	−	0.00747571i
$952$	−0.664225	−	0.766557i	−0.0215277	−	0.0248443i
$953$	3.89134	+	8.52084i	0.126053	+	0.276017i	0.962128	−	0.272597i	$-0.0878827\pi$
$953$	3.89134	+	8.52084i	0.126053	+	0.276017i	−0.836075	+	0.548615i	$0.815155\pi$
$954$	−0.658503	+	4.57999i	−0.0213198	+	0.148283i
$955$	−0.484673	+	0.559342i	−0.0156836	+	0.0180999i
$956$	0.229772	+	0.265171i	0.00743135	+	0.00857624i
$957$	0.860998	+	1.88532i	0.0278321	+	0.0609438i
$958$	22.2596	−	14.3054i	0.719174	−	0.462185i
$959$	−0.111892	−	0.778229i	−0.00361319	−	0.0251303i
$960$	0.490330	+	0.315116i	0.0158253	+	0.0101703i
$961$	−19.5954	+	12.5932i	−0.632110	+	0.406233i
$962$	18.0775	−	20.8626i	0.582843	−	0.672637i
$963$	47.9133	+	14.0686i	1.54398	+	0.453355i
$964$	3.15660	−	3.64291i	0.101667	−	0.117330i
$965$	2.42212	+	16.8462i	0.0779710	+	0.542300i
$966$	−0.322409	+	0.0946679i	−0.0103733	+	0.00304589i
$967$	−44.2308			−1.42237			−0.711183	−	0.703007i	$-0.751840\pi$
$967$	−44.2308			−1.42237			−0.711183	+	0.703007i	$0.751840\pi$
$968$	10.6907			0.343612
$969$	−17.3253	+	5.08718i	−0.556570	+	0.163424i
$970$	0.311962	+	0.200486i	0.0100165	+	0.00643720i
$971$	4.09138	+	8.95887i	0.131299	+	0.287504i	0.963851	−	0.266443i	$-0.0858484\pi$
$971$	4.09138	+	8.95887i	0.131299	+	0.287504i	−0.832552	+	0.553947i	$0.813121\pi$
$972$	5.57831	+	12.2148i	0.178924	+	0.391790i
$973$	3.01136	+	1.93528i	0.0965397	+	0.0620423i
$974$	10.4766	−	3.07622i	0.335693	−	0.0985683i
$975$	1.66730			0.0533964
$976$	11.1772			0.357772
$977$	−9.69975	+	2.84810i	−0.310323	+	0.0911189i	−0.433186	−	0.901305i	$-0.642611\pi$
$977$	−9.69975	+	2.84810i	−0.310323	+	0.0911189i	0.122863	+	0.992424i	$0.460792\pi$
$978$	0.828285	+	5.76085i	0.0264856	+	0.184212i
$979$	3.16044	−	3.64735i	0.101008	−	0.116570i
$980$	6.67857	+	1.96100i	0.213339	+	0.0626420i
$981$	−28.5644	+	32.9651i	−0.911991	+	1.05249i
$982$	−28.2458	+	18.1525i	−0.901359	+	0.579268i
$983$	−13.9158	−	8.94311i	−0.443844	−	0.285241i	0.299568	−	0.954075i	$-0.403157\pi$
$983$	−13.9158	−	8.94311i	−0.443844	−	0.285241i	−0.743412	+	0.668834i	$0.766794\pi$
$984$	0.686031	+	4.77145i	0.0218699	+	0.152108i
$985$	−0.456194	+	0.293178i	−0.0145356	+	0.00934144i
$986$	13.5584	+	29.6887i	0.431787	+	0.945481i
$987$	−0.0393912	−	0.0454599i	−0.00125384	−	0.00144700i
$988$	−11.3692	+	13.1207i	−0.361702	+	0.417426i
$989$	−2.87860	+	20.0211i	−0.0915342	+	0.636634i
$990$	−0.614600	−	1.34579i	−0.0195333	−	0.0427719i
$991$	8.24172	+	9.51145i	0.261807	+	0.302141i	0.871400	−	0.490573i	$-0.163213\pi$
$991$	8.24172	+	9.51145i	0.261807	+	0.302141i	−0.609593	+	0.792714i	$0.708667\pi$
$992$	2.66367	+	0.782125i	0.0845717	+	0.0248325i
$993$	−2.48532	−	0.729756i	−0.0788692	−	0.0231581i
$994$	0.440136	−	3.06122i	0.0139603	−	0.0970959i
$995$	0.576003	+	0.370175i	0.0182605	+	0.0117353i
$996$	−2.38788	+	5.22872i	−0.0756628	+	0.165678i
$997$	−44.6326	+	13.1053i	−1.41353	+	0.415049i	−0.897307	−	0.441407i	$-0.854480\pi$
$997$	−44.6326	+	13.1053i	−1.41353	+	0.415049i	−0.516220	+	0.856456i	$0.672661\pi$
$998$	−13.7218	+	30.0465i	−0.434356	+	0.951107i
$999$	4.53093	+	31.5133i	0.143352	+	0.997037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.c.91.4	yes	50
67.14	even	11	inner	670.2.k.c.81.4	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.c.81.4	✓	50	67.14	even	11	inner
670.2.k.c.91.4	yes	50	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.490330 - 0.315116i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.0829491 + 0.576924i) q^{6} +(-0.0825464 + 0.180751i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-1.10512 + 2.41987i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.490330 - 0.315116i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.0829491 + 0.576924i) q^{6} +(-0.0825464 + 0.180751i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-1.10512 + 2.41987i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.0791468 - 0.550478i) q^{11} +(-0.559247 - 0.164210i) q^{12} +(-2.74470 - 0.805915i) q^{13} +(-0.130126 - 0.150174i) q^{14} +(0.242127 + 0.530185i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.34272 + 3.85770i) q^{17} +(-1.74211 - 2.01050i) q^{18} +(2.52122 + 5.52069i) q^{19} +(0.841254 - 0.540641i) q^{20} +(0.0164827 + 0.114639i) q^{21} +(0.467854 + 0.300672i) q^{22} +(2.44070 - 1.56855i) q^{23} +(0.381690 - 0.440493i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(1.87327 - 2.16187i) q^{26} +(0.469515 + 3.26555i) q^{27} +(0.190659 - 0.0559826i) q^{28} -6.39403 q^{29} -0.582856 q^{30} +(-2.66367 + 0.782125i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.134656 - 0.294857i) q^{33} +(-2.12047 - 4.64319i) q^{34} +(-0.167164 - 0.107430i) q^{35} +(2.55252 - 0.749487i) q^{36} +9.65024 q^{37} -6.06915 q^{38} +(-1.59976 + 0.469733i) q^{39} +(0.142315 + 0.989821i) q^{40} +(-5.41603 + 6.25043i) q^{41} +(-0.111127 - 0.0326298i) q^{42} +(-4.56554 + 5.26891i) q^{43} +(-0.467854 + 0.300672i) q^{44} +(-2.23797 - 1.43826i) q^{45} +(0.412894 + 2.87174i) q^{46} +(-0.436918 + 0.280790i) q^{47} +(0.242127 + 0.530185i) q^{48} +(4.55817 + 5.26041i) q^{49} +(0.654861 - 0.755750i) q^{50} +(-0.423411 + 2.94489i) q^{51} +(1.18832 + 2.60206i) q^{52} +(-1.13902 - 1.31449i) q^{53} +(-3.16549 - 0.929472i) q^{54} +(0.533612 + 0.156682i) q^{55} +(-0.0282791 + 0.196686i) q^{56} +(2.97589 + 1.91249i) q^{57} +(2.65618 - 5.81622i) q^{58} +(-10.2741 + 3.01674i) q^{59} +(0.242127 - 0.530185i) q^{60} +(-1.59068 - 11.0634i) q^{61} +(0.395084 - 2.74787i) q^{62} +(-0.346172 - 0.399504i) q^{63} +(0.841254 - 0.540641i) q^{64} +(1.18832 - 2.60206i) q^{65} +0.324149 q^{66} +(1.52035 + 8.04292i) q^{67} +5.10447 q^{68} +(0.702477 - 1.53821i) q^{69} +(0.167164 - 0.107430i) q^{70} +(10.1923 + 11.7625i) q^{71} +(-0.378597 + 2.63320i) q^{72} +(-2.39685 - 16.6705i) q^{73} +(-4.00885 + 8.77816i) q^{74} +(-0.559247 + 0.164210i) q^{75} +(2.52122 - 5.52069i) q^{76} +(0.0929664 + 0.0597459i) q^{77} +(0.237282 - 1.65033i) q^{78} +(-4.69400 - 1.37828i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-3.96709 - 4.57827i) q^{81} +(-3.43569 - 7.52312i) q^{82} +(1.40352 - 9.76169i) q^{83} +(0.0758449 - 0.0875297i) q^{84} +(-3.34272 - 3.85770i) q^{85} +(-2.89618 - 6.34174i) q^{86} +(-3.13519 + 2.01486i) q^{87} +(-0.0791468 - 0.550478i) q^{88} +(7.30033 + 4.69164i) q^{89} +(2.23797 - 1.43826i) q^{90} +(0.372235 - 0.429582i) q^{91} +(-2.78375 - 0.817382i) q^{92} +(-1.05962 + 1.22287i) q^{93} +(-0.0739134 - 0.514079i) q^{94} +(-5.82331 + 1.70988i) q^{95} -0.582856 q^{96} -0.370829 q^{97} +(-6.67857 + 1.96100i) q^{98} +(1.24462 + 0.799870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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