LMFDB - Embedded newform 690.2.m.h.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	690.121
Dual form			690.2.m.h.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.588355 + 4.09210i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.588355 + 4.09210i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(1.71070 + 3.74591i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.950503 - 6.61089i) q^{13} +(-3.47789 - 2.23511i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.01785 + 1.17466i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(2.03851 + 2.35257i) q^{19} +(0.959493 + 0.281733i) q^{20} +(1.71740 - 3.76058i) q^{21} -4.11805 q^{22} +(-3.65046 - 3.11033i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(6.40833 + 1.88166i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(3.47789 - 2.23511i) q^{28} +(-2.33110 + 2.69023i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-6.73851 + 1.97861i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.586059 - 4.07613i) q^{33} +(-0.645678 - 1.41384i) q^{34} +(-1.71740 - 3.76058i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-9.03066 - 5.80365i) q^{37} +(-2.98680 + 0.877003i) q^{38} +(-0.950503 + 6.61089i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(-8.31888 + 5.34622i) q^{41} +(2.70731 + 3.12440i) q^{42} +(-3.96316 - 1.16369i) q^{43} +(1.71070 - 3.74591i) q^{44} -1.00000 q^{45} +(4.34571 - 2.02850i) q^{46} +1.01242 q^{47} +(0.415415 - 0.909632i) q^{48} +(-9.68265 - 2.84308i) q^{49} +(0.654861 + 0.755750i) q^{50} +(1.30756 - 0.840316i) q^{51} +(-4.37373 + 5.04756i) q^{52} +(-0.927860 + 6.45341i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-3.46432 - 2.22639i) q^{55} +(0.588355 + 4.09210i) q^{56} +(-1.29314 - 2.83159i) q^{57} +(-1.47875 - 3.23800i) q^{58} +(0.344016 + 2.39268i) q^{59} +(-0.841254 - 0.540641i) q^{60} +(8.74442 - 2.56759i) q^{61} +(0.999476 - 6.95151i) q^{62} +(-2.70731 + 3.12440i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.37373 + 5.04756i) q^{65} +(3.95124 + 1.16019i) q^{66} +(3.02680 - 6.62777i) q^{67} +1.55430 q^{68} +(2.62631 + 4.01279i) q^{69} +4.13418 q^{70} +(0.258490 - 0.566015i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-4.71259 - 5.43862i) q^{73} +(9.03066 - 5.80365i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.443011 - 3.08121i) q^{76} +(-16.3351 + 4.79643i) q^{77} +(-5.61863 - 3.61087i) q^{78} +(-1.65649 - 11.5212i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-1.40731 - 9.78802i) q^{82} +(12.6674 + 8.14081i) q^{83} +(-3.96671 + 1.16473i) q^{84} +(0.221199 - 1.53848i) q^{85} +(2.70488 - 3.12160i) q^{86} +(2.99460 - 1.92451i) q^{87} +(2.69675 + 3.11221i) q^{88} +(8.17130 + 2.39931i) q^{89} +(0.415415 - 0.909632i) q^{90} +27.6117 q^{91} +(0.0399113 + 4.79567i) q^{92} +7.02299 q^{93} +(-0.420574 + 0.920928i) q^{94} +(-2.98680 - 0.877003i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-1.31434 + 0.844676i) q^{97} +(6.60848 - 7.62659i) q^{98} +(-0.586059 + 4.07613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−0.588355	+	4.09210i	−0.222377	+	1.54667i	0.506631	+	0.862163i	$0.330891\pi$
$7$	−0.588355	+	4.09210i	−0.222377	+	1.54667i	−0.729008	+	0.684505i	$0.760018\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	1.71070	+	3.74591i	0.515795	+	1.12943i	0.971007	+	0.239051i	$0.0768363\pi$
$11$	1.71070	+	3.74591i	0.515795	+	1.12943i	−0.455212	+	0.890383i	$0.650436\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	−0.950503	−	6.61089i	−0.263622	−	1.83353i	−0.505022	−	0.863106i	$-0.668516\pi$
$13$	−0.950503	−	6.61089i	−0.263622	−	1.83353i	0.241400	−	0.970426i	$-0.422393\pi$
$14$	−3.47789	−	2.23511i	−0.929506	−	0.597357i
$15$	0.959493	−	0.281733i	0.247740	−	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−1.01785	+	1.17466i	−0.246864	+	0.284897i	−0.865636	−	0.500675i	$-0.833085\pi$
$17$	−1.01785	+	1.17466i	−0.246864	+	0.284897i	0.618771	+	0.785571i	$0.287631\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	2.03851	+	2.35257i	0.467667	+	0.539716i	0.939761	−	0.341832i	$-0.111047\pi$
$19$	2.03851	+	2.35257i	0.467667	+	0.539716i	−0.472095	+	0.881548i	$0.656502\pi$
$20$	0.959493	+	0.281733i	0.214549	+	0.0629973i
$21$	1.71740	−	3.76058i	0.374767	−	0.820626i
$22$	−4.11805			−0.877971
$23$	−3.65046	−	3.11033i	−0.761173	−	0.648549i
$23$	−3.65046	−	3.11033i	−0.761173	−	0.648549i
$24$	−1.00000			−0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	6.40833	+	1.88166i	1.25678	+	0.369023i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	3.47789	−	2.23511i	0.657260	−	0.422395i
$29$	−2.33110	+	2.69023i	−0.432874	+	0.499563i	−0.929716	−	0.368278i	$-0.879947\pi$
$29$	−2.33110	+	2.69023i	−0.432874	+	0.499563i	0.496842	+	0.867841i	$0.334493\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	−6.73851	+	1.97861i	−1.21027	+	0.355368i	−0.823772	−	0.566921i	$-0.808134\pi$
$31$	−6.73851	+	1.97861i	−1.21027	+	0.355368i	−0.386500	+	0.922289i	$0.626316\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.586059	−	4.07613i	−0.102020	−	0.709564i
$34$	−0.645678	−	1.41384i	−0.110733	−	0.242471i
$35$	−1.71740	−	3.76058i	−0.290294	−	0.635654i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−9.03066	−	5.80365i	−1.48463	−	0.954115i	−0.996695	−	0.0812358i	$-0.974113\pi$
$37$	−9.03066	−	5.80365i	−1.48463	−	0.954115i	−0.487937	−	0.872879i	$-0.662250\pi$
$38$	−2.98680	+	0.877003i	−0.484523	+	0.142269i
$39$	−0.950503	+	6.61089i	−0.152202	+	1.05859i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	−8.31888	+	5.34622i	−1.29919	+	0.834940i	−0.993124	−	0.117070i	$-0.962650\pi$
$41$	−8.31888	+	5.34622i	−1.29919	+	0.834940i	−0.306068	+	0.952010i	$0.599013\pi$
$42$	2.70731	+	3.12440i	0.417747	+	0.482106i
$43$	−3.96316	−	1.16369i	−0.604376	−	0.177461i	−0.0347927	−	0.999395i	$-0.511077\pi$
$43$	−3.96316	−	1.16369i	−0.604376	−	0.177461i	−0.569583	+	0.821934i	$0.692895\pi$
$44$	1.71070	−	3.74591i	0.257898	−	0.564717i
$45$	−1.00000			−0.149071
$46$	4.34571	−	2.02850i	0.640740	−	0.299085i
$47$	1.01242			0.147676			0.0738382	−	0.997270i	$-0.476475\pi$
$47$	1.01242			0.147676			0.0738382	+	0.997270i	$0.476475\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−9.68265	−	2.84308i	−1.38324	−	0.406155i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	1.30756	−	0.840316i	0.183095	−	0.117668i
$52$	−4.37373	+	5.04756i	−0.606528	+	0.699970i
$53$	−0.927860	+	6.45341i	−0.127451	+	0.886444i	0.821317	+	0.570472i	$0.193240\pi$
$53$	−0.927860	+	6.45341i	−0.127451	+	0.886444i	−0.948768	+	0.315972i	$0.897669\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	−3.46432	−	2.22639i	−0.467129	−	0.300206i
$56$	0.588355	+	4.09210i	0.0786222	+	0.546830i
$57$	−1.29314	−	2.83159i	−0.171281	−	0.375053i
$58$	−1.47875	−	3.23800i	−0.194169	−	0.425170i
$59$	0.344016	+	2.39268i	0.0447871	+	0.311501i	0.999884	+	0.0152085i	$0.00484120\pi$
$59$	0.344016	+	2.39268i	0.0447871	+	0.311501i	−0.955097	+	0.296292i	$0.904250\pi$
$60$	−0.841254	−	0.540641i	−0.108605	−	0.0697964i
$61$	8.74442	−	2.56759i	1.11961	−	0.328747i	0.330993	−	0.943633i	$-0.392616\pi$
$61$	8.74442	−	2.56759i	1.11961	−	0.328747i	0.788616	+	0.614887i	$0.210798\pi$
$62$	0.999476	−	6.95151i	0.126934	−	0.882842i
$63$	−2.70731	+	3.12440i	−0.341089	+	0.393638i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	4.37373	+	5.04756i	0.542495	+	0.626072i
$66$	3.95124	+	1.16019i	0.486364	+	0.142809i
$67$	3.02680	−	6.62777i	0.369783	−	0.809712i	−0.629677	−	0.776857i	$-0.716813\pi$
$67$	3.02680	−	6.62777i	0.369783	−	0.809712i	0.999460	−	0.0328547i	$-0.0104599\pi$
$68$	1.55430			0.188486
$69$	2.62631	+	4.01279i	0.316170	+	0.483083i
$70$	4.13418			0.494129
$71$	0.258490	−	0.566015i	0.0306772	−	0.0671736i	−0.893673	−	0.448719i	$-0.851881\pi$
$71$	0.258490	−	0.566015i	0.0306772	−	0.0671736i	0.924350	+	0.381545i	$0.124608\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	−4.71259	−	5.43862i	−0.551567	−	0.636542i	0.409681	−	0.912229i	$-0.365640\pi$
$73$	−4.71259	−	5.43862i	−0.551567	−	0.636542i	−0.961248	+	0.275687i	$0.911095\pi$
$74$	9.03066	−	5.80365i	1.04979	−	0.674661i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.443011	−	3.08121i	0.0508168	−	0.353439i
$77$	−16.3351	+	4.79643i	−1.86156	+	0.546603i
$78$	−5.61863	−	3.61087i	−0.636184	−	0.408851i
$79$	−1.65649	−	11.5212i	−0.186370	−	1.29623i	−0.841311	−	0.540551i	$-0.818216\pi$
$79$	−1.65649	−	11.5212i	−0.186370	−	1.29623i	0.654941	−	0.755680i	$-0.272693\pi$
$80$	−0.415415	−	0.909632i	−0.0464448	−	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−1.40731	−	9.78802i	−0.155411	−	1.08091i
$83$	12.6674	+	8.14081i	1.39042	+	0.893570i	0.999638	−	0.0269115i	$-0.00856724\pi$
$83$	12.6674	+	8.14081i	1.39042	+	0.893570i	0.390785	+	0.920482i	$0.372204\pi$
$84$	−3.96671	+	1.16473i	−0.432804	+	0.127083i
$85$	0.221199	−	1.53848i	0.0239924	−	0.166871i
$86$	2.70488	−	3.12160i	0.291675	−	0.336611i
$87$	2.99460	−	1.92451i	0.321054	−	0.206329i
$88$	2.69675	+	3.11221i	0.287474	+	0.331763i
$89$	8.17130	+	2.39931i	0.866156	+	0.254326i	0.684480	−	0.729032i	$-0.260029\pi$
$89$	8.17130	+	2.39931i	0.866156	+	0.254326i	0.181677	+	0.983358i	$0.441848\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	27.6117			2.89449
$92$	0.0399113	+	4.79567i	0.00416104	+	0.499983i
$93$	7.02299			0.728250
$94$	−0.420574	+	0.920928i	−0.0433789	+	0.0949865i
$95$	−2.98680	−	0.877003i	−0.306439	−	0.0899786i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−1.31434	+	0.844676i	−0.133451	+	0.0857638i	−0.605663	−	0.795721i	$-0.707092\pi$
$97$	−1.31434	+	0.844676i	−0.133451	+	0.0857638i	0.472212	+	0.881485i	$0.343456\pi$
$98$	6.60848	−	7.62659i	0.667557	−	0.770402i
$99$	−0.586059	+	4.07613i	−0.0589012	+	0.409667i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	−3.52843	−	2.26759i	−0.351092	−	0.225633i	0.353193	−	0.935550i	$-0.385096\pi$
$101$	−3.52843	−	2.26759i	−0.351092	−	0.225633i	−0.704285	+	0.709917i	$0.748732\pi$
$102$	0.221199	+	1.53848i	0.0219020	+	0.152332i
$103$	−4.51783	−	9.89267i	−0.445155	−	0.974754i	−0.990623	−	0.136622i	$-0.956375\pi$
$103$	−4.51783	−	9.89267i	−0.445155	−	0.974754i	0.545468	−	0.838132i	$-0.316352\pi$
$104$	−2.77450	−	6.07532i	−0.272063	−	0.595734i
$105$	0.588355	+	4.09210i	0.0574176	+	0.399348i
$106$	−5.48478	−	3.52486i	−0.532729	−	0.342364i
$107$	−7.00637	+	2.05726i	−0.677332	+	0.198883i	−0.602265	−	0.798296i	$-0.705735\pi$
$107$	−7.00637	+	2.05726i	−0.677332	+	0.198883i	−0.0750664	+	0.997179i	$0.523917\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	−10.0668	+	11.6177i	−0.964225	+	1.11277i	0.0293468	+	0.999569i	$0.490657\pi$
$109$	−10.0668	+	11.6177i	−0.964225	+	1.11277i	−0.993572	+	0.113205i	$0.963888\pi$
$110$	3.46432	−	2.22639i	0.330310	−	0.212278i
$111$	7.02978	+	8.11280i	0.667237	+	0.770033i
$112$	−3.96671	−	1.16473i	−0.374819	−	0.110057i
$113$	−6.51649	+	14.2691i	−0.613020	+	1.34233i	0.307469	+	0.951558i	$0.400518\pi$
$113$	−6.51649	+	14.2691i	−0.613020	+	1.34233i	−0.920489	+	0.390768i	$0.872209\pi$
$114$	3.11289			0.291549
$115$	4.75253	+	0.642989i	0.443176	+	0.0599591i
$116$	3.55968			0.330508
$117$	2.77450	−	6.07532i	0.256503	−	0.561663i
$118$	−2.31937	−	0.681029i	−0.213515	−	0.0626938i
$119$	−4.20796	−	4.85625i	−0.385743	−	0.445171i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	−3.90188	+	4.50300i	−0.354716	+	0.409364i
$122$	−1.29700	+	9.02082i	−0.117425	+	0.816707i
$123$	9.48811	−	2.78596i	0.855514	−	0.251202i
$124$	5.90812	+	3.79692i	0.530565	+	0.340973i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	−1.71740	−	3.76058i	−0.152998	−	0.335019i
$127$	8.38913	+	18.3696i	0.744414	+	1.63004i	0.776153	+	0.630544i	$0.217168\pi$
$127$	8.38913	+	18.3696i	0.744414	+	1.63004i	−0.0317389	+	0.999496i	$0.510104\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	3.47477	+	2.23310i	0.305937	+	0.196614i
$130$	−6.40833	+	1.88166i	−0.562048	+	0.165032i
$131$	1.51297	−	10.5229i	0.132189	−	0.919392i	−0.810505	−	0.585732i	$-0.800807\pi$
$131$	1.51297	−	10.5229i	0.132189	−	0.919392i	0.942693	−	0.333660i	$-0.108284\pi$
$132$	−2.69675	+	3.11221i	−0.234722	+	0.270883i
$133$	−10.8263	+	6.95764i	−0.938760	+	0.603304i
$134$	4.77146	+	5.50655i	0.412191	+	0.475694i
$135$	0.959493	+	0.281733i	0.0825800	+	0.0242477i
$136$	−0.645678	+	1.41384i	−0.0553664	+	0.121236i
$137$	1.36262			0.116416			0.0582082	−	0.998304i	$-0.481461\pi$
$137$	1.36262			0.116416			0.0582082	+	0.998304i	$0.481461\pi$
$138$	−4.74117	+	0.721999i	−0.403595	+	0.0614607i
$139$	7.97454			0.676392			0.338196	−	0.941076i	$-0.390183\pi$
$139$	7.97454			0.676392			0.338196	+	0.941076i	$0.390183\pi$
$140$	−1.71740	+	3.76058i	−0.145147	+	0.317827i
$141$	−0.971409	−	0.285231i	−0.0818074	−	0.0240208i
$142$	0.407484	+	0.470262i	0.0341953	+	0.0394635i
$143$	23.1378	−	14.8697i	1.93488	−	1.24347i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	0.506596	−	3.52345i	0.0420705	−	0.292607i
$146$	6.90482	−	2.02744i	0.571447	−	0.167792i
$147$	8.48945	+	5.45584i	0.700198	+	0.449990i
$148$	1.52772	+	10.6255i	0.125578	+	0.873411i
$149$	0.0294510	+	0.0644886i	0.00241272	+	0.00528311i	0.910835	−	0.412772i	$-0.135439\pi$
$149$	0.0294510	+	0.0644886i	0.00241272	+	0.00528311i	−0.908422	+	0.418055i	$0.862712\pi$
$150$	−0.415415	−	0.909632i	−0.0339185	−	0.0742711i
$151$	−0.995787	−	6.92585i	−0.0810360	−	0.563618i	−0.989375	−	0.145384i	$-0.953558\pi$
$151$	−0.995787	−	6.92585i	−0.0810360	−	0.563618i	0.908339	−	0.418234i	$-0.137351\pi$
$152$	2.61873	+	1.68296i	0.212407	+	0.136506i
$153$	−1.49134	+	0.437896i	−0.120567	+	0.0354018i
$154$	2.42287	−	16.8515i	0.195241	−	1.35793i
$155$	4.59908	−	5.30762i	0.369407	−	0.426319i
$156$	5.61863	−	3.61087i	0.449850	−	0.289101i
$157$	3.63654	+	4.19679i	0.290228	+	0.334941i	0.882075	−	0.471110i	$-0.156146\pi$
$157$	3.63654	+	4.19679i	0.290228	+	0.334941i	−0.591847	+	0.806050i	$0.701601\pi$
$158$	11.1681	+	3.27926i	0.888490	+	0.260884i
$159$	2.70841	−	5.93059i	0.214791	−	0.470327i
$160$	1.00000			0.0790569
$161$	14.8755	−	13.1081i	1.17236	−	1.03306i
$162$	−1.00000			−0.0785674
$163$	−10.0381	+	21.9804i	−0.786246	+	1.72164i	−0.0991509	+	0.995072i	$0.531613\pi$
$163$	−10.0381	+	21.9804i	−0.786246	+	1.72164i	−0.687095	+	0.726567i	$0.741115\pi$
$164$	9.48811	+	2.78596i	0.740897	+	0.217547i
$165$	2.69675	+	3.11221i	0.209942	+	0.242286i
$166$	−12.6674	+	8.14081i	−0.983177	+	0.631850i
$167$	−5.23177	+	6.03778i	−0.404847	+	0.467218i	−0.921161	−	0.389181i	$-0.872758\pi$
$167$	−5.23177	+	6.03778i	−0.404847	+	0.467218i	0.516315	+	0.856399i	$0.327303\pi$
$168$	0.588355	−	4.09210i	0.0453926	−	0.315712i
$169$	−30.3270	+	8.90482i	−2.33285	+	0.684987i
$170$	1.30756	+	0.840316i	0.100285	+	0.0644493i
$171$	0.443011	+	3.08121i	0.0338779	+	0.235626i
$172$	1.71586	+	3.75721i	0.130833	+	0.286484i
$173$	−1.04105	−	2.27959i	−0.0791497	−	0.173314i	0.865920	−	0.500183i	$-0.166734\pi$
$173$	−1.04105	−	2.27959i	−0.0791497	−	0.173314i	−0.945070	+	0.326869i	$0.894006\pi$
$174$	0.506596	+	3.52345i	0.0384049	+	0.267112i
$175$	3.47789	+	2.23511i	0.262904	+	0.168958i
$176$	−3.95124	+	1.16019i	−0.297836	+	0.0874525i
$177$	0.344016	−	2.39268i	0.0258578	−	0.179845i
$178$	−5.57697	+	6.43617i	−0.418012	+	0.482411i
$179$	−16.1333	+	10.3683i	−1.20586	+	0.774961i	−0.979961	−	0.199189i	$-0.936169\pi$
$179$	−16.1333	+	10.3683i	−1.20586	+	0.774961i	−0.225901	+	0.974150i	$0.572533\pi$
$180$	0.654861	+	0.755750i	0.0488104	+	0.0563302i
$181$	15.7806	+	4.63360i	1.17296	+	0.344413i	0.809457	−	0.587180i	$-0.199762\pi$
$181$	15.7806	+	4.63360i	1.17296	+	0.344413i	0.363505	+	0.931592i	$0.381580\pi$
$182$	−11.4703	+	25.1164i	−0.850235	+	1.86175i
$183$	−9.11358			−0.673696
$184$	−4.37887	−	1.95589i	−0.322815	−	0.144190i
$185$	10.7348			0.789236
$186$	−2.91746	+	6.38834i	−0.213918	+	0.468416i
$187$	−6.14140	−	1.80328i	−0.449103	−	0.131869i
$188$	−0.662993	−	0.765135i	−0.0483538	−	0.0558032i
$189$	3.47789	−	2.23511i	0.252979	−	0.162580i
$190$	2.03851	−	2.35257i	0.147889	−	0.170673i
$191$	0.944967	−	6.57239i	0.0683754	−	0.475561i	−0.926649	−	0.375928i	$-0.877324\pi$
$191$	0.944967	−	6.57239i	0.0683754	−	0.475561i	0.995024	−	0.0996332i	$-0.0317669\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	1.15563	+	0.742677i	0.0831839	+	0.0534591i	0.581572	−	0.813495i	$-0.302438\pi$
$193$	1.15563	+	0.742677i	0.0831839	+	0.0534591i	−0.498388	+	0.866954i	$0.666074\pi$
$194$	−0.222347	−	1.54646i	−0.0159636	−	0.111029i
$195$	−2.77450	−	6.07532i	−0.198686	−	0.435063i
$196$	4.19213	+	9.17949i	0.299438	+	0.655678i
$197$	−0.286779	−	1.99460i	−0.0204322	−	0.142109i	0.977052	−	0.213002i	$-0.0683241\pi$
$197$	−0.286779	−	1.99460i	−0.0204322	−	0.142109i	−0.997484	+	0.0708932i	$0.977415\pi$
$198$	−3.46432	−	2.22639i	−0.246199	−	0.158222i
$199$	−10.0722	+	2.95746i	−0.713998	+	0.209649i	−0.618505	−	0.785781i	$-0.712261\pi$
$199$	−10.0722	+	2.95746i	−0.713998	+	0.209649i	−0.0954939	+	0.995430i	$0.530443\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	−4.77146	+	5.50655i	−0.336553	+	0.388402i
$202$	3.52843	−	2.26759i	0.248260	−	0.159547i
$203$	−9.63717	−	11.1219i	−0.676396	−	0.780603i
$204$	−1.49134	−	0.437896i	−0.104414	−	0.0306588i
$205$	4.10790	−	8.99506i	0.286908	−	0.628242i
$206$	10.8755			0.757730
$207$	−1.38939	−	4.59016i	−0.0965693	−	0.319038i
$208$	6.67887			0.463097
$209$	−5.32522	+	11.6606i	−0.368353	+	0.806581i
$210$	−3.96671	−	1.16473i	−0.273729	−	0.0803742i
$211$	10.6711	+	12.3151i	0.734630	+	0.847808i	0.992985	−	0.118242i	$-0.0377258\pi$
$211$	10.6711	+	12.3151i	0.734630	+	0.847808i	−0.258355	+	0.966050i	$0.583180\pi$
$212$	5.48478	−	3.52486i	0.376696	−	0.242088i
$213$	−0.407484	+	0.470262i	−0.0279204	+	0.0322218i
$214$	1.03921	−	7.22784i	0.0710387	−	0.494085i
$215$	3.96316	−	1.16369i	0.270285	−	0.0793628i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−4.13201	−	28.7388i	−0.280499	−	1.95092i
$218$	−6.38594	−	13.9833i	−0.432510	−	0.947066i
$219$	2.98946	+	6.54601i	0.202009	+	0.442338i
$220$	0.586059	+	4.07613i	0.0395121	+	0.274813i
$221$	8.73301	+	5.61236i	0.587446	+	0.377528i
$222$	−10.2999	+	3.02433i	−0.691286	+	0.202980i
$223$	−1.77710	+	12.3600i	−0.119003	+	0.827685i	0.839654	+	0.543122i	$0.182758\pi$
$223$	−1.77710	+	12.3600i	−0.119003	+	0.827685i	−0.958657	+	0.284563i	$0.908151\pi$
$224$	2.70731	−	3.12440i	0.180890	−	0.208758i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	−10.2726	−	11.8552i	−0.683323	−	0.788597i
$227$	6.01000	+	1.76470i	0.398898	+	0.117127i	0.475028	−	0.879971i	$-0.342438\pi$
$227$	6.01000	+	1.76470i	0.398898	+	0.117127i	−0.0761296	+	0.997098i	$0.524256\pi$
$228$	−1.29314	+	2.83159i	−0.0856404	+	0.187526i
$229$	24.2957			1.60550			0.802751	−	0.596314i	$-0.203369\pi$
$229$	24.2957			1.60550			0.802751	+	0.596314i	$0.203369\pi$
$230$	−2.55916	+	4.05595i	−0.168746	+	0.267441i
$231$	17.0247			1.12015
$232$	−1.47875	+	3.23800i	−0.0970844	+	0.212585i
$233$	−0.144385	−	0.0423954i	−0.00945900	−	0.00277741i	0.277000	−	0.960870i	$-0.410660\pi$
$233$	−0.144385	−	0.0423954i	−0.00945900	−	0.00277741i	−0.286459	+	0.958093i	$0.592478\pi$
$234$	4.37373	+	5.04756i	0.285920	+	0.329969i
$235$	−0.851701	+	0.547355i	−0.0555588	+	0.0357055i
$236$	1.58299	−	1.82686i	0.103044	−	0.118919i
$237$	−1.65649	+	11.5212i	−0.107601	+	0.748379i
$238$	6.16545	−	1.81034i	0.399647	−	0.117347i
$239$	14.9118	+	9.58325i	0.964566	+	0.619889i	0.925258	−	0.379338i	$-0.123848\pi$
$239$	14.9118	+	9.58325i	0.964566	+	0.619889i	0.0393078	+	0.999227i	$0.487485\pi$
$240$	0.142315	+	0.989821i	0.00918638	+	0.0638927i
$241$	−0.481717	−	1.05481i	−0.0310301	−	0.0679465i	0.893482	−	0.449098i	$-0.148255\pi$
$241$	−0.481717	−	1.05481i	−0.0310301	−	0.0679465i	−0.924512	+	0.381152i	$0.875527\pi$
$242$	−2.47518	−	5.41989i	−0.159111	−	0.348403i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	−7.66684	−	4.92718i	−0.490819	−	0.315430i
$245$	9.68265	−	2.84308i	0.618602	−	0.181638i
$246$	−1.40731	+	9.78802i	−0.0897265	+	0.624062i
$247$	13.6150	−	15.7125i	0.866299	−	0.999763i
$248$	−5.90812	+	3.79692i	−0.375166	+	0.241104i
$249$	−9.86071	−	11.3799i	−0.624897	−	0.721169i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	−10.1422	+	22.2083i	−0.640170	+	1.40178i	0.259730	+	0.965681i	$0.416366\pi$
$251$	−10.1422	+	22.2083i	−0.640170	+	1.40178i	−0.899900	+	0.436096i	$0.856361\pi$
$252$	4.13418			0.260429
$253$	5.40618	−	18.9951i	0.339883	−	1.19421i
$254$	−20.1946			−1.26712
$255$	−0.645678	+	1.41384i	−0.0404339	+	0.0885379i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−17.5814	−	20.2900i	−1.09670	−	1.26565i	−0.961491	−	0.274836i	$-0.911376\pi$
$257$	−17.5814	−	20.2900i	−1.09670	−	1.26565i	−0.135204	−	0.990818i	$-0.543169\pi$
$258$	−3.47477	+	2.23310i	−0.216330	+	0.139027i
$259$	29.0624	−	33.5397i	1.80585	−	2.08406i
$260$	0.950503	−	6.61089i	0.0589477	−	0.409990i
$261$	−3.41549	+	1.00288i	−0.211414	+	0.0620766i
$262$	8.94348	+	5.74763i	0.552530	+	0.355089i
$263$	1.74630	+	12.1458i	0.107682	+	0.748943i	0.970093	+	0.242734i	$0.0780443\pi$
$263$	1.74630	+	12.1458i	0.107682	+	0.748943i	−0.862411	+	0.506209i	$0.831047\pi$
$264$	−1.71070	−	3.74591i	−0.105286	−	0.230545i
$265$	−2.70841	−	5.93059i	−0.166376	−	0.364313i
$266$	−1.83149	−	12.7383i	−0.112296	−	0.781033i
$267$	−7.16434	−	4.60424i	−0.438451	−	0.281775i
$268$	−6.99107	+	2.05276i	−0.427048	+	0.125393i
$269$	1.93518	−	13.4594i	0.117990	−	0.820637i	−0.841774	−	0.539830i	$-0.818489\pi$
$269$	1.93518	−	13.4594i	0.117990	−	0.820637i	0.959764	−	0.280807i	$-0.0906022\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	16.2613	−	10.4505i	0.987802	−	0.634822i	0.0562452	−	0.998417i	$-0.482087\pi$
$271$	16.2613	−	10.4505i	0.987802	−	0.634822i	0.931557	+	0.363595i	$0.118451\pi$
$272$	−1.01785	−	1.17466i	−0.0617161	−	0.0712241i
$273$	−26.4932	−	7.77910i	−1.60344	−	0.470813i
$274$	−0.566052	+	1.23948i	−0.0341965	+	0.0748798i
$275$	4.11805			0.248328
$276$	1.31280	−	4.61265i	0.0790213	−	0.277649i
$277$	−7.06148			−0.424283			−0.212142	−	0.977239i	$-0.568044\pi$
$277$	−7.06148			−0.424283			−0.212142	+	0.977239i	$0.568044\pi$
$278$	−3.31274	+	7.25390i	−0.198685	+	0.435060i
$279$	−6.73851	−	1.97861i	−0.403424	−	0.118456i
$280$	−2.70731	−	3.12440i	−0.161793	−	0.186719i
$281$	−26.7908	+	17.2174i	−1.59820	+	1.02710i	−0.630113	+	0.776503i	$0.716992\pi$
$281$	−26.7908	+	17.2174i	−1.59820	+	1.02710i	−0.968091	+	0.250600i	$0.919372\pi$
$282$	0.662993	−	0.765135i	0.0394807	−	0.0455631i
$283$	−4.44778	+	30.9350i	−0.264393	+	1.83890i	0.234357	+	0.972151i	$0.424702\pi$
$283$	−4.44778	+	30.9350i	−0.264393	+	1.83890i	−0.498750	+	0.866746i	$0.666208\pi$
$284$	−0.597041	+	0.175307i	−0.0354278	+	0.0104026i
$285$	2.61873	+	1.68296i	0.155120	+	0.0996898i
$286$	3.91422	+	27.2240i	0.231453	+	1.60979i
$287$	−16.9828	−	37.1872i	−1.00246	−	2.19509i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	2.07554	+	14.4357i	0.122091	+	0.849160i
$290$	2.99460	+	1.92451i	0.175849	+	0.113011i
$291$	1.49907	−	0.440168i	0.0878773	−	0.0258031i
$292$	−1.02414	+	7.12308i	−0.0599335	+	0.416847i
$293$	10.5111	−	12.1305i	0.614066	−	0.708669i	−0.360503	−	0.932758i	$-0.617395\pi$
$293$	10.5111	−	12.1305i	0.614066	−	0.708669i	0.974569	+	0.224089i	$0.0719405\pi$
$294$	−8.48945	+	5.45584i	−0.495115	+	0.318191i
$295$	−1.58299	−	1.82686i	−0.0921651	−	0.106364i
$296$	−10.2999	−	3.02433i	−0.598672	−	0.175786i
$297$	1.71070	−	3.74591i	0.0992648	−	0.217360i
$298$	−0.0708953			−0.00410685
$299$	−17.0923	+	27.0892i	−0.988473	+	1.56661i
$300$	1.00000			0.0577350
$301$	7.09367	−	15.5330i	0.408872	−	0.895305i
$302$	6.71364	+	1.97130i	0.386326	+	0.113436i
$303$	2.74665	+	3.16981i	0.157791	+	0.182101i
$304$	−2.61873	+	1.68296i	−0.150195	+	0.0965242i
$305$	−5.96813	+	6.88759i	−0.341734	+	0.394382i
$306$	0.221199	−	1.53848i	0.0126451	−	0.0879488i
$307$	16.5158	−	4.84948i	0.942608	−	0.276775i	0.225902	−	0.974150i	$-0.427467\pi$
$307$	16.5158	−	4.84948i	0.942608	−	0.276775i	0.716706	+	0.697375i	$0.245649\pi$
$308$	14.3221	+	9.20427i	0.816079	+	0.524462i
$309$	1.54774	+	10.7648i	0.0880479	+	0.612386i
$310$	2.91746	+	6.38834i	0.165700	+	0.362833i
$311$	1.15249	+	2.52360i	0.0653518	+	0.143101i	0.939490	−	0.342578i	$-0.111300\pi$
$311$	1.15249	+	2.52360i	0.0653518	+	0.143101i	−0.874138	+	0.485678i	$0.838573\pi$
$312$	0.950503	+	6.61089i	0.0538116	+	0.374268i
$313$	−14.4709	−	9.29991i	−0.817946	−	0.525662i	0.0634804	−	0.997983i	$-0.479780\pi$
$313$	−14.4709	−	9.29991i	−0.817946	−	0.525662i	−0.881427	+	0.472321i	$0.843416\pi$
$314$	−5.32821	+	1.56450i	−0.300688	+	0.0882901i
$315$	0.588355	−	4.09210i	0.0331500	−	0.230564i
$316$	−7.62234	+	8.79664i	−0.428790	+	0.494850i
$317$	2.32519	−	1.49431i	0.130596	−	0.0839288i	−0.473712	−	0.880680i	$-0.657086\pi$
$317$	2.32519	−	1.49431i	0.130596	−	0.0839288i	0.604308	+	0.796751i	$0.293450\pi$
$318$	4.26954	+	4.92732i	0.239424	+	0.276310i
$319$	−14.0652	−	4.12990i	−0.787497	−	0.231230i
$320$	−0.415415	+	0.909632i	−0.0232224	+	0.0508500i
$321$	7.30216			0.407567
$322$	5.74398	+	18.9766i	0.320100	+	1.05752i
$323$	−4.83836			−0.269213
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−6.40833	−	1.88166i	−0.355470	−	0.104376i
$326$	−15.8241	−	18.2620i	−0.876416	−	1.01144i
$327$	12.9321	−	8.31096i	0.715147	−	0.459597i
$328$	−6.47571	+	7.47336i	−0.357561	+	0.412647i
$329$	−0.595661	+	4.14292i	−0.0328399	+	0.228406i
$330$	−3.95124	+	1.16019i	−0.217509	+	0.0638663i
$331$	12.0186	+	7.72386i	0.660599	+	0.424541i	0.827526	−	0.561428i	$-0.189748\pi$
$331$	12.0186	+	7.72386i	0.660599	+	0.424541i	−0.166926	+	0.985969i	$0.553384\pi$
$332$	−2.14294	−	14.9044i	−0.117609	−	0.817988i
$333$	−4.45938	−	9.76469i	−0.244373	−	0.535102i
$334$	−3.31881	−	7.26717i	−0.181597	−	0.397642i
$335$	1.03694	+	7.21205i	0.0566539	+	0.394036i
$336$	3.47789	+	2.23511i	0.189735	+	0.121935i
$337$	−5.31951	+	1.56195i	−0.289772	+	0.0850849i	−0.423388	−	0.905948i	$-0.639159\pi$
$337$	−5.31951	+	1.56195i	−0.289772	+	0.0850849i	0.133616	+	0.991033i	$0.457341\pi$
$338$	4.49820	−	31.2857i	0.244670	−	1.70172i
$339$	10.2726	−	11.8552i	0.557931	−	0.643887i
$340$	−1.30756	+	0.840316i	−0.0709122	+	0.0455725i
$341$	−18.9392	−	21.8571i	−1.02562	−	1.18363i
$342$	−2.98680	−	0.877003i	−0.161508	−	0.0474229i
$343$	5.30922	−	11.6256i	0.286671	−	0.627722i
$344$	−4.13047			−0.222700
$345$	−4.37887	−	1.95589i	−0.235750	−	0.105301i
$346$	2.50605			0.134726
$347$	2.13797	−	4.68151i	0.114772	−	0.251317i	−0.843525	−	0.537091i	$-0.819523\pi$
$347$	2.13797	−	4.68151i	0.114772	−	0.251317i	0.958297	+	0.285774i	$0.0922506\pi$
$348$	−3.41549	−	1.00288i	−0.183089	−	0.0537599i
$349$	5.49002	+	6.33582i	0.293874	+	0.339149i	0.883416	−	0.468589i	$-0.155237\pi$
$349$	5.49002	+	6.33582i	0.293874	+	0.339149i	−0.589542	+	0.807737i	$0.700692\pi$
$350$	−3.47789	+	2.23511i	−0.185901	+	0.119471i
$351$	−4.37373	+	5.04756i	−0.233453	+	0.269419i
$352$	0.586059	−	4.07613i	0.0312371	−	0.217259i
$353$	30.5074	−	8.95779i	1.62375	−	0.476775i	0.661724	−	0.749747i	$-0.269825\pi$
$353$	30.5074	−	8.95779i	1.62375	−	0.476775i	0.962022	+	0.272972i	$0.0880067\pi$
$354$	2.03355	+	1.30688i	0.108082	+	0.0694601i
$355$	0.0885548	+	0.615912i	0.00470000	+	0.0326892i
$356$	−3.53779	−	7.74667i	−0.187502	−	0.410573i
$357$	2.66935	+	5.84506i	0.141277	+	0.309353i
$358$	−2.72928	−	18.9825i	−0.144247	−	1.00326i
$359$	−22.2744	−	14.3149i	−1.17560	−	0.755512i	−0.201028	−	0.979586i	$-0.564428\pi$
$359$	−22.2744	−	14.3149i	−1.17560	−	0.755512i	−0.974572	+	0.224073i	$0.928064\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	1.32494	−	9.21514i	0.0697335	−	0.485007i
$362$	−10.7704	+	12.4297i	−0.566078	+	0.653288i
$363$	5.01246	−	3.22132i	0.263086	−	0.169075i
$364$	−18.0818	−	20.8675i	−0.947743	−	1.09375i
$365$	6.90482	+	2.02744i	0.361415	+	0.106121i
$366$	3.78592	−	8.29001i	0.197893	−	0.433326i
$367$	−17.5654			−0.916908			−0.458454	−	0.888718i	$-0.651597\pi$
$367$	−17.5654			−0.916908			−0.458454	+	0.888718i	$0.651597\pi$
$368$	3.59819	−	3.17066i	0.187568	−	0.165282i
$369$	−9.88868			−0.514784
$370$	−4.45938	+	9.76469i	−0.231832	+	0.507642i
$371$	−25.8621	−	7.59379i	−1.34269	−	0.394250i
$372$	−4.59908	−	5.30762i	−0.238451	−	0.275187i
$373$	−1.03916	+	0.667825i	−0.0538054	+	0.0345787i	−0.567267	−	0.823534i	$-0.691999\pi$
$373$	−1.03916	+	0.667825i	−0.0538054	+	0.0345787i	0.513462	+	0.858113i	$0.328363\pi$
$374$	4.19155	−	4.83730i	0.216740	−	0.250131i
$375$	0.142315	−	0.989821i	0.00734911	−	0.0511142i
$376$	0.971409	−	0.285231i	0.0500966	−	0.0147097i
$377$	20.0005	+	12.8536i	1.03008	+	0.661992i
$378$	0.588355	+	4.09210i	0.0302617	+	0.210475i
$379$	−4.24855	−	9.30303i	−0.218233	−	0.477864i	0.768575	−	0.639760i	$-0.220966\pi$
$379$	−4.24855	−	9.30303i	−0.218233	−	0.477864i	−0.986808	+	0.161896i	$0.948239\pi$
$380$	1.29314	+	2.83159i	0.0663368	+	0.145257i
$381$	−2.87399	−	19.9890i	−0.147239	−	1.02407i
$382$	5.58590	+	3.58984i	0.285800	+	0.183672i
$383$	34.8626	−	10.2366i	1.78139	−	0.523064i	0.785940	−	0.618303i	$-0.212180\pi$
$383$	34.8626	−	10.2366i	1.78139	−	0.523064i	0.995454	+	0.0952388i	$0.0303615\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	11.1488	−	12.8664i	0.568197	−	0.655735i
$386$	−1.15563	+	0.742677i	−0.0588199	+	0.0378013i
$387$	−2.70488	−	3.12160i	−0.137497	−	0.158680i
$388$	1.49907	+	0.440168i	0.0761039	+	0.0223461i
$389$	−9.61441	+	21.0526i	−0.487470	+	1.06741i	0.492871	+	0.870102i	$0.335947\pi$
$389$	−9.61441	+	21.0526i	−0.487470	+	1.06741i	−0.980341	+	0.197308i	$0.936780\pi$
$390$	6.67887			0.338198
$391$	7.36919	−	1.12220i	0.372676	−	0.0567521i
$392$	−10.0914			−0.509694
$393$	−4.41633	+	9.67042i	−0.222775	+	0.487808i
$394$	1.93348	+	0.567721i	0.0974073	+	0.0286014i
$395$	7.62234	+	8.79664i	0.383521	+	0.442607i
$396$	3.46432	−	2.22639i	0.174089	−	0.111880i
$397$	−19.2154	+	22.1757i	−0.964392	+	1.11297i	0.0291586	+	0.999575i	$0.490717\pi$
$397$	−19.2154	+	22.1757i	−0.964392	+	1.11297i	−0.993550	+	0.113393i	$0.963828\pi$
$398$	1.49394	−	10.3906i	0.0748843	−	0.520832i
$399$	12.3480	−	3.62569i	0.618171	−	0.181511i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−2.86416	−	19.9207i	−0.143029	−	0.994791i	−0.927286	−	0.374354i	$-0.877864\pi$
$401$	−2.86416	−	19.9207i	−0.143029	−	0.994791i	0.784256	−	0.620437i	$-0.213045\pi$
$402$	−3.02680	−	6.62777i	−0.150963	−	0.330563i
$403$	19.4853	+	42.6669i	0.970633	+	2.12539i
$404$	0.596905	+	4.15156i	0.0296971	+	0.206548i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	14.1202	−	4.14608i	0.700776	−	0.205766i
$407$	6.29121	−	43.7563i	0.311844	−	2.16892i
$408$	1.01785	−	1.17466i	0.0503910	−	0.0581543i
$409$	0.0555562	−	0.0357038i	0.00274708	−	0.00176544i	−0.539267	−	0.842135i	$-0.681298\pi$
$409$	0.0555562	−	0.0357038i	0.00274708	−	0.00176544i	0.542014	+	0.840370i	$0.317662\pi$
$410$	6.47571	+	7.47336i	0.319812	+	0.369083i
$411$	−1.30742	−	0.383894i	−0.0644904	−	0.0189361i
$412$	−4.51783	+	9.89267i	−0.222578	+	0.487377i
$413$	−9.99350			−0.491748
$414$	4.75253	+	0.642989i	0.233574	+	0.0316012i
$415$	−15.0577			−0.739154
$416$	−2.77450	+	6.07532i	−0.136031	+	0.297867i
$417$	−7.65152	−	2.24669i	−0.374696	−	0.110021i
$418$	−8.39469	−	9.68799i	−0.410598	−	0.473855i
$419$	0.313354	−	0.201380i	0.0153083	−	0.00983808i	−0.532964	−	0.846138i	$-0.678922\pi$
$419$	0.313354	−	0.201380i	0.0153083	−	0.00983808i	0.548273	+	0.836300i	$0.315286\pi$
$420$	2.70731	−	3.12440i	0.132103	−	0.152455i
$421$	3.27394	−	22.7707i	0.159562	−	1.10978i	−0.739881	−	0.672738i	$-0.765118\pi$
$421$	3.27394	−	22.7707i	0.159562	−	1.10978i	0.899443	−	0.437039i	$-0.143973\pi$
$422$	−15.6352	+	4.59090i	−0.761109	+	0.223482i
$423$	0.851701	+	0.547355i	0.0414111	+	0.0266133i
$424$	0.927860	+	6.45341i	0.0450609	+	0.313405i
$425$	0.645678	+	1.41384i	0.0313200	+	0.0685812i
$426$	−0.258490	−	0.566015i	−0.0125239	−	0.0274235i
$427$	5.36202	+	37.2937i	0.259486	+	1.80477i
$428$	6.14297	+	3.94785i	0.296932	+	0.190826i
$429$	−26.3898	+	7.74875i	−1.27411	+	0.374113i
$430$	−0.587827	+	4.08843i	−0.0283475	+	0.197161i
$431$	4.09594	−	4.72696i	0.197294	−	0.227690i	−0.648478	−	0.761233i	$-0.724594\pi$
$431$	4.09594	−	4.72696i	0.197294	−	0.227690i	0.845773	+	0.533543i	$0.179140\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	24.7910	+	28.6103i	1.19138	+	1.37492i	0.909622	+	0.415436i	$0.136371\pi$
$433$	24.7910	+	28.6103i	1.19138	+	1.37492i	0.281755	+	0.959486i	$0.409083\pi$
$434$	27.8582	+	8.17991i	1.33724	+	0.392648i
$435$	−1.47875	+	3.23800i	−0.0709004	+	0.155250i
$436$	15.3724			0.736206
$437$	−0.124240	−	14.9284i	−0.00594319	−	0.714122i
$438$	−7.19632			−0.343854
$439$	−1.39784	+	3.06084i	−0.0667152	+	0.146086i	−0.940052	−	0.341031i	$-0.889224\pi$
$439$	−1.39784	+	3.06084i	−0.0667152	+	0.146086i	0.873337	+	0.487117i	$0.161951\pi$
$440$	−3.95124	−	1.16019i	−0.188368	−	0.0553098i
$441$	−6.60848	−	7.62659i	−0.314690	−	0.363171i
$442$	−8.73301	+	5.61236i	−0.415387	+	0.266953i
$443$	−19.4716	+	22.4714i	−0.925122	+	1.06765i	0.0724058	+	0.997375i	$0.476932\pi$
$443$	−19.4716	+	22.4714i	−0.925122	+	1.06765i	−0.997528	+	0.0702725i	$0.977613\pi$
$444$	1.52772	−	10.6255i	0.0725022	−	0.504264i
$445$	−8.17130	+	2.39931i	−0.387357	+	0.113738i
$446$	−10.5048	−	6.75102i	−0.497416	−	0.319670i
$447$	−0.0100895	−	0.0701737i	−0.000477215	−	0.00331910i
$448$	1.71740	+	3.76058i	0.0811395	+	0.177671i
$449$	−15.2745	−	33.4465i	−0.720848	−	1.57844i	−0.812712	−	0.582666i	$-0.802010\pi$
$449$	−15.2745	−	33.4465i	−0.720848	−	1.57844i	0.0918638	−	0.995772i	$-0.470718\pi$
$450$	0.142315	+	0.989821i	0.00670879	+	0.0466606i
$451$	−34.2576	−	22.0160i	−1.61313	−	1.03669i
$452$	15.0513	−	4.41945i	0.707953	−	0.207874i
$453$	−0.995787	+	6.92585i	−0.0467861	+	0.325405i
$454$	−4.10187	+	4.73381i	−0.192510	+	0.222169i
$455$	−23.2284	+	14.9280i	−1.08896	+	0.699835i
$456$	−2.03851	−	2.35257i	−0.0954620	−	0.110169i
$457$	−5.99798	−	1.76117i	−0.280574	−	0.0823839i	0.138418	−	0.990374i	$-0.455798\pi$
$457$	−5.99798	−	1.76117i	−0.280574	−	0.0823839i	−0.418992	+	0.907990i	$0.637616\pi$
$458$	−10.0928	+	22.1001i	−0.471605	+	1.03267i
$459$	1.55430			0.0725483
$460$	−2.62631	−	4.01279i	−0.122452	−	0.187097i
$461$	13.7881			0.642177			0.321089	−	0.947049i	$-0.395951\pi$
$461$	13.7881			0.642177			0.321089	+	0.947049i	$0.395951\pi$
$462$	−7.07234	+	15.4863i	−0.329035	+	0.720486i
$463$	−2.63688	−	0.774257i	−0.122546	−	0.0359828i	0.219884	−	0.975526i	$-0.429432\pi$
$463$	−2.63688	−	0.774257i	−0.122546	−	0.0359828i	−0.342431	+	0.939543i	$0.611250\pi$
$464$	−2.33110	−	2.69023i	−0.108218	−	0.124891i
$465$	−5.90812	+	3.79692i	−0.273982	+	0.176078i
$466$	0.0985440	−	0.113726i	0.00456496	−	0.00526825i
$467$	−2.54852	+	17.7254i	−0.117932	+	0.820232i	0.841896	+	0.539640i	$0.181440\pi$
$467$	−2.54852	+	17.7254i	−0.117932	+	0.820232i	−0.959827	+	0.280592i	$0.909469\pi$
$468$	−6.40833	+	1.88166i	−0.296225	+	0.0869796i
$469$	25.3407	+	16.2855i	1.17012	+	0.751993i
$470$	−0.144082	−	1.00211i	−0.00664602	−	0.0462241i
$471$	−2.30686	−	5.05133i	−0.106295	−	0.232753i
$472$	1.00418	+	2.19884i	0.0462210	+	0.101210i
$473$	−2.42070	−	16.8363i	−0.111304	−	0.774136i
$474$	−9.79188	−	6.29286i	−0.449756	−	0.289041i
$475$	2.98680	−	0.877003i	0.137044	−	0.0402397i
$476$	−0.914478	+	6.36033i	−0.0419150	+	0.291525i
$477$	−4.26954	+	4.92732i	−0.195489	+	0.225606i
$478$	−14.9118	+	9.58325i	−0.682051	+	0.438328i
$479$	25.9018	+	29.8922i	1.18348	+	1.36581i	0.915466	+	0.402396i	$0.131822\pi$
$479$	25.9018	+	29.8922i	1.18348	+	1.36581i	0.268016	+	0.963415i	$0.413632\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	−29.7837	+	65.2171i	−1.35802	+	2.97365i
$482$	1.15960			0.0528186
$483$	−17.9659	+	8.38616i	−0.817479	+	0.381584i
$484$	5.95833			0.270833
$485$	0.649028	−	1.42117i	0.0294708	−	0.0645321i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	−0.298755	−	0.344781i	−0.0135379	−	0.0156235i	0.748940	−	0.662638i	$-0.230563\pi$
$487$	−0.298755	−	0.344781i	−0.0135379	−	0.0156235i	−0.762478	+	0.647014i	$0.776018\pi$
$488$	7.66684	−	4.92718i	0.347061	−	0.223043i
$489$	15.8241	−	18.2620i	0.715591	−	0.825836i
$490$	−1.43616	+	9.98871i	−0.0648791	+	0.451244i
$491$	−21.9761	+	6.45277i	−0.991769	+	0.291210i	−0.737074	−	0.675812i	$-0.763793\pi$
$491$	−21.9761	+	6.45277i	−0.991769	+	0.291210i	−0.254695	+	0.967022i	$0.581975\pi$
$492$	−8.31888	−	5.34622i	−0.375044	−	0.241026i
$493$	−0.787399	−	5.47648i	−0.0354627	−	0.246648i
$494$	8.63674	+	18.9118i	0.388585	+	0.850883i
$495$	−1.71070	−	3.74591i	−0.0768902	−	0.168366i
$496$	−0.999476	−	6.95151i	−0.0448778	−	0.312132i
$497$	2.16410	+	1.39079i	0.0970733	+	0.0623852i
$498$	14.4478	−	4.24225i	0.647420	−	0.190100i
$499$	−0.765534	+	5.32440i	−0.0342700	+	0.238353i	−0.999756	−	0.0221030i	$-0.992964\pi$
$499$	−0.765534	+	5.32440i	−0.0342700	+	0.238353i	0.965486	+	0.260456i	$0.0838729\pi$
$500$	0.654861	−	0.755750i	0.0292863	−	0.0337981i
$501$	6.72089	−	4.31925i	0.300267	−	0.192970i
$502$	−15.9882	−	18.4513i	−0.713587	−	0.823524i
$503$	−39.6936	−	11.6551i	−1.76985	−	0.519675i	−0.776033	−	0.630692i	$-0.782771\pi$
$503$	−39.6936	−	11.6551i	−1.76985	−	0.519675i	−0.993819	+	0.111017i	$0.964589\pi$
$504$	−1.71740	+	3.76058i	−0.0764991	+	0.167510i
$505$	4.19425			0.186642
$506$	15.0328	+	12.8085i	0.668288	+	0.569407i
$507$	31.6074			1.40373
$508$	8.38913	−	18.3696i	0.372207	−	0.815020i
$509$	−17.3856	−	5.10487i	−0.770603	−	0.226269i	−0.127283	−	0.991866i	$-0.540626\pi$
$509$	−17.3856	−	5.10487i	−0.770603	−	0.226269i	−0.643320	+	0.765597i	$0.722444\pi$
$510$	−1.01785	−	1.17466i	−0.0450710	−	0.0520148i
$511$	25.0280	−	16.0845i	1.10718	−	0.711538i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.443011	−	3.08121i	0.0195594	−	0.136039i
$514$	25.7600	−	7.56381i	1.13622	−	0.333625i
$515$	9.14902	+	5.87972i	0.403154	+	0.259091i
$516$	−0.587827	−	4.08843i	−0.0258776	−	0.179983i
$517$	1.73194	+	3.79243i	0.0761708	+	0.166791i
$518$	18.4359	+	40.3690i	0.810026	+	1.77371i
$519$	0.356649	+	2.48055i	0.0156551	+	0.108884i
$520$	5.61863	+	3.61087i	0.246393	+	0.158347i
$521$	−17.4114	+	5.11244i	−0.762805	+	0.223980i	−0.639921	−	0.768441i	$-0.721033\pi$
$521$	−17.4114	+	5.11244i	−0.762805	+	0.223980i	−0.122885	+	0.992421i	$0.539215\pi$
$522$	0.506596	−	3.52345i	0.0221731	−	0.154217i
$523$	1.35109	−	1.55924i	0.0590790	−	0.0681808i	−0.725441	−	0.688285i	$-0.758364\pi$
$523$	1.35109	−	1.55924i	0.0590790	−	0.0681808i	0.784520	+	0.620104i	$0.212910\pi$
$524$	−8.94348	+	5.74763i	−0.390698	+	0.251086i
$525$	−2.70731	−	3.12440i	−0.118157	−	0.136360i
$526$	−11.7737	−	3.45706i	−0.513356	−	0.150735i
$527$	4.53459	−	9.92937i	0.197530	−	0.432530i
$528$	4.11805			0.179215
$529$	3.65169	+	22.7083i	0.158769	+	0.987316i
$530$	6.51977			0.283201
$531$	−1.00418	+	2.19884i	−0.0435776	+	0.0954216i
$532$	12.3480	+	3.62569i	0.535352	+	0.157193i
$533$	43.2504	+	49.9137i	1.87338	+	2.16200i
$534$	7.16434	−	4.60424i	0.310032	−	0.199245i
$535$	4.78190	−	5.51861i	0.206740	−	0.238590i
$536$	1.03694	−	7.21205i	0.0447888	−	0.311513i
$537$	18.4009	−	5.40299i	0.794058	−	0.233156i
$538$	11.4392	+	7.35156i	0.493181	+	0.316948i
$539$	−5.91418	−	41.1340i	−0.254742	−	1.77177i
$540$	−0.415415	−	0.909632i	−0.0178766	−	0.0391443i
$541$	−5.44020	−	11.9124i	−0.233892	−	0.512153i	0.755897	−	0.654690i	$-0.227201\pi$
$541$	−5.44020	−	11.9124i	−0.233892	−	0.512153i	−0.989789	+	0.142538i	$0.954474\pi$
$542$	2.75092	+	19.1331i	0.118162	+	0.821836i
$543$	−13.8359	−	8.89181i	−0.593756	−	0.381584i
$544$	1.49134	−	0.437896i	0.0639405	−	0.0187746i
$545$	2.18773	−	15.2160i	0.0937119	−	0.651780i
$546$	18.0818	−	20.8675i	0.773829	−	0.893047i
$547$	26.7602	−	17.1977i	1.14418	−	0.735321i	0.175710	−	0.984442i	$-0.443778\pi$
$547$	26.7602	−	17.1977i	1.14418	−	0.735321i	0.968472	+	0.249121i	$0.0801416\pi$
$548$	−0.892325	−	1.02980i	−0.0381182	−	0.0439908i
$549$	8.74442	+	2.56759i	0.373203	+	0.109582i
$550$	−1.71070	+	3.74591i	−0.0729445	+	0.159726i
$551$	−11.0809			−0.472063
$552$	3.65046	+	3.11033i	0.155374	+	0.132384i
$553$	48.1203			2.04628
$554$	2.93344	−	6.42335i	0.124630	−	0.272902i
$555$	−10.2999	−	3.02433i	−0.437208	−	0.128376i
$556$	−5.22221	−	6.02676i	−0.221471	−	0.255591i
$557$	−1.80566	+	1.16043i	−0.0765083	+	0.0491689i	−0.578336	−	0.815799i	$-0.696298\pi$
$557$	−1.80566	+	1.16043i	−0.0765083	+	0.0491689i	0.501827	+	0.864968i	$0.332661\pi$
$558$	4.59908	−	5.30762i	0.194695	−	0.224690i
$559$	−3.92602	+	27.3061i	−0.166053	+	1.15492i
$560$	3.96671	−	1.16473i	0.167624	−	0.0492189i
$561$	5.38458	+	3.46046i	0.227337	+	0.146101i
$562$	−4.53220	−	31.5221i	−0.191179	−	1.32968i
$563$	4.27396	+	9.35866i	0.180126	+	0.394420i	0.978060	−	0.208324i	$-0.0668010\pi$
$563$	4.27396	+	9.35866i	0.180126	+	0.394420i	−0.797934	+	0.602745i	$0.794074\pi$
$564$	0.420574	+	0.920928i	0.0177094	+	0.0387781i
$565$	−2.23245	−	15.5270i	−0.0939199	−	0.653227i
$566$	−26.2918	−	16.8967i	−1.10513	−	0.710222i
$567$	−3.96671	+	1.16473i	−0.166586	+	0.0489142i
$568$	0.0885548	−	0.615912i	0.00371568	−	0.0258431i
$569$	3.15835	−	3.64493i	0.132405	−	0.152804i	−0.685675	−	0.727908i	$-0.740493\pi$
$569$	3.15835	−	3.64493i	0.132405	−	0.152804i	0.818080	+	0.575104i	$0.195038\pi$
$570$	−2.61873	+	1.68296i	−0.109687	+	0.0704913i
$571$	4.71324	+	5.43937i	0.197243	+	0.227631i	0.845752	−	0.533577i	$-0.179152\pi$
$571$	4.71324	+	5.43937i	0.197243	+	0.227631i	−0.648509	+	0.761207i	$0.724607\pi$
$572$	−26.3898	−	7.74875i	−1.10341	−	0.323992i
$573$	−2.75834	+	6.03993i	−0.115231	+	0.252322i
$574$	40.8815			1.70636
$575$	−4.34571	+	2.02850i	−0.181229	+	0.0845941i
$576$	1.00000			0.0416667
$577$	15.3677	−	33.6505i	0.639764	−	1.40089i	−0.260470	−	0.965482i	$-0.583877\pi$
$577$	15.3677	−	33.6505i	0.639764	−	1.40089i	0.900234	−	0.435406i	$-0.143395\pi$
$578$	−13.9934	−	4.10883i	−0.582049	−	0.170905i
$579$	−0.899580	−	1.03817i	−0.0373853	−	0.0431449i
$580$	−2.99460	+	1.92451i	−0.124344	+	0.0799109i
$581$	−40.7659	+	47.0464i	−1.69125	+	1.95181i
$582$	−0.222347	+	1.54646i	−0.00921658	+	0.0641027i
$583$	−25.7612	+	7.56416i	−1.06692	+	0.313276i
$584$	−6.05393	−	3.89063i	−0.250514	−	0.160995i
$585$	0.950503	+	6.61089i	0.0392985	+	0.273327i
$586$	6.66779	+	14.6004i	0.275444	+	0.603138i
$587$	−3.71825	−	8.14182i	−0.153468	−	0.336049i	0.817245	−	0.576291i	$-0.195500\pi$
$587$	−3.71825	−	8.14182i	−0.153468	−	0.336049i	−0.970713	+	0.240242i	$0.922773\pi$
$588$	−1.43616	−	9.98871i	−0.0592262	−	0.411928i
$589$	−18.3913	−	11.8194i	−0.757802	−	0.487010i
$590$	2.31937	−	0.681029i	0.0954870	−	0.0280375i
$591$	−0.286779	+	1.99460i	−0.0117965	+	0.0820467i
$592$	7.02978	−	8.11280i	0.288922	−	0.333434i
$593$	8.64769	−	5.55753i	0.355118	−	0.228220i	−0.350902	−	0.936412i	$-0.614125\pi$
$593$	8.64769	−	5.55753i	0.355118	−	0.228220i	0.706020	+	0.708192i	$0.250489\pi$
$594$	2.69675	+	3.11221i	0.110649	+	0.127696i
$595$	6.16545	+	1.81034i	0.252759	+	0.0742167i
$596$	0.0294510	−	0.0644886i	0.00120636	−	0.00264156i
$597$	10.4974			0.429630
$598$	−17.5408	−	26.8009i	−0.717296	−	1.09597i
$599$	41.3573			1.68981			0.844907	−	0.534913i	$-0.179656\pi$
$599$	41.3573			1.68981			0.844907	+	0.534913i	$0.179656\pi$
$600$	−0.415415	+	0.909632i	−0.0169592	+	0.0371356i
$601$	−34.2011	−	10.0424i	−1.39509	−	0.409637i	−0.504097	−	0.863647i	$-0.668175\pi$
$601$	−34.2011	−	10.0424i	−1.39509	−	0.409637i	−0.890996	+	0.454010i	$0.849993\pi$
$602$	11.1825	+	12.9053i	0.455763	+	0.525979i
$603$	6.12955	−	3.93923i	0.249615	−	0.160418i
$604$	−4.58211	+	5.28803i	−0.186443	+	0.215167i
$605$	0.847959	−	5.89768i	0.0344744	−	0.239775i
$606$	−4.02436	+	1.18166i	−0.163478	+	0.0480016i
$607$	25.1692	+	16.1753i	1.02159	+	0.656535i	0.940367	−	0.340161i	$-0.110482\pi$
$607$	25.1692	+	16.1753i	1.02159	+	0.656535i	0.0812211	+	0.996696i	$0.474118\pi$
$608$	−0.443011	−	3.08121i	−0.0179665	−	0.124959i
$609$	6.11340	+	13.3865i	0.247727	+	0.542447i
$610$	−3.78592	−	8.29001i	−0.153287	−	0.335653i
$611$	−0.962307	−	6.69299i	−0.0389308	−	0.270769i
$612$	1.30756	+	0.840316i	0.0528549	+	0.0339678i
$613$	22.6122	−	6.63954i	0.913298	−	0.268168i	0.208870	−	0.977944i	$-0.433022\pi$
$613$	22.6122	−	6.63954i	0.913298	−	0.268168i	0.704428	+	0.709775i	$0.251203\pi$
$614$	−2.44968	+	17.0379i	−0.0988609	+	0.687593i
$615$	−6.47571	+	7.47336i	−0.261126	+	0.301355i
$616$	−14.3221	+	9.20427i	−0.577055	+	0.370851i
$617$	25.4519	+	29.3730i	1.02465	+	1.18251i	0.983042	+	0.183379i	$0.0587037\pi$
$617$	25.4519	+	29.3730i	1.02465	+	1.18251i	0.0416114	+	0.999134i	$0.486751\pi$
$618$	−10.4349	−	3.06397i	−0.419755	−	0.123251i
$619$	4.22932	−	9.26092i	0.169991	−	0.372228i	−0.805393	−	0.592741i	$-0.798046\pi$
$619$	4.22932	−	9.26092i	0.169991	−	0.372228i	0.975384	+	0.220513i	$0.0707732\pi$
$620$	−7.02299			−0.282050
$621$	0.0399113	+	4.79567i	0.00160159	+	0.192443i
$622$	−2.77431			−0.111240
$623$	−14.6258	+	32.0261i	−0.585972	+	1.28310i
$624$	−6.40833	−	1.88166i	−0.256539	−	0.0753265i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	14.4709	−	9.29991i	0.578375	−	0.371699i
$627$	8.39469	−	9.68799i	0.335252	−	0.386901i
$628$	0.790296	−	5.49663i	0.0315363	−	0.219339i
$629$	16.0091	−	4.70071i	0.638326	−	0.187430i
$630$	3.47789	+	2.23511i	0.138563	+	0.0890487i
$631$	0.819206	+	5.69770i	0.0326121	+	0.226822i	0.999609	−	0.0279667i	$-0.00890323\pi$
$631$	0.819206	+	5.69770i	0.0326121	+	0.226822i	−0.966997	+	0.254789i	$0.917994\pi$
$632$	−4.83528	−	10.5878i	−0.192337	−	0.421159i
$633$	−6.76929	−	14.8227i	−0.269055	−	0.589149i
$634$	0.393353	+	2.73583i	0.0156220	+	0.108654i
$635$	−16.9887	−	10.9180i	−0.674178	−	0.433268i
$636$	−6.25568	+	1.83683i	−0.248054	+	0.0728351i
$637$	−9.59193	+	66.7134i	−0.380046	+	2.64328i
$638$	9.59957	−	11.0785i	0.380051	−	0.438602i
$639$	0.523467	−	0.336412i	0.0207080	−	0.0133082i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	−1.68187	−	0.493842i	−0.0664299	−	0.0195056i	0.248349	−	0.968671i	$-0.420112\pi$
$641$	−1.68187	−	0.493842i	−0.0664299	−	0.0195056i	−0.314779	+	0.949165i	$0.601930\pi$
$642$	−3.03343	+	6.64228i	−0.119720	+	0.262150i
$643$	−5.79881			−0.228683			−0.114341	−	0.993442i	$-0.536476\pi$
$643$	−5.79881			−0.228683			−0.114341	+	0.993442i	$0.536476\pi$
$644$	−19.6478	−	2.65823i	−0.774232	−	0.104749i
$645$	−4.13047			−0.162637
$646$	2.00993	−	4.40112i	0.0790795	−	0.173160i
$647$	2.80155	+	0.822609i	0.110140	+	0.0323401i	0.336338	−	0.941741i	$-0.390811\pi$
$647$	2.80155	+	0.822609i	0.110140	+	0.0323401i	−0.226198	+	0.974081i	$0.572630\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−8.37427	+	5.38182i	−0.328719	+	0.211255i
$650$	4.37373	−	5.04756i	0.171552	−	0.197981i
$651$	−4.13201	+	28.7388i	−0.161946	+	1.12636i
$652$	23.1853	−	6.80781i	0.908005	−	0.266614i
$653$	12.3088	+	7.91039i	0.481681	+	0.309557i	0.758852	−	0.651263i	$-0.225761\pi$
$653$	12.3088	+	7.91039i	0.481681	+	0.309557i	−0.277171	+	0.960821i	$0.589397\pi$
$654$	2.18773	+	15.2160i	0.0855468	+	0.594991i
$655$	4.41633	+	9.67042i	0.172560	+	0.377855i
$656$	−4.10790	−	8.99506i	−0.160387	−	0.351198i
$657$	−1.02414	−	7.12308i	−0.0399557	−	0.277898i
$658$	−3.52108	−	2.26286i	−0.137266	−	0.0882156i
$659$	5.08161	−	1.49209i	0.197951	−	0.0581238i	−0.181254	−	0.983436i	$-0.558016\pi$
$659$	5.08161	−	1.49209i	0.197951	−	0.0581238i	0.379205	+	0.925313i	$0.376197\pi$
$660$	0.586059	−	4.07613i	0.0228123	−	0.158663i
$661$	−8.20829	+	9.47287i	−0.319265	+	0.368452i	−0.892584	−	0.450880i	$-0.851110\pi$
$661$	−8.20829	+	9.47287i	−0.319265	+	0.368452i	0.573319	+	0.819332i	$0.305656\pi$
$662$	−12.0186	+	7.72386i	−0.467114	+	0.300196i
$663$	−6.79808	−	7.84540i	−0.264015	−	0.304690i
$664$	14.4478	+	4.24225i	0.560682	+	0.164631i
$665$	5.34608	−	11.7063i	0.207312	−	0.453950i
$666$	10.7348			0.415964
$667$	16.8771	−	2.57009i	0.653483	−	0.0995142i
$668$	7.98913			0.309109
$669$	5.18732	−	11.3586i	0.200553	−	0.439150i
$670$	−6.99107	−	2.05276i	−0.270089	−	0.0793052i
$671$	24.5770	+	28.3634i	0.948786	+	1.09496i
$672$	−3.47789	+	2.23511i	−0.134163	+	0.0862211i
$673$	−2.53897	+	2.93012i	−0.0978700	+	0.112948i	−0.802572	−	0.596556i	$-0.796535\pi$
$673$	−2.53897	+	2.93012i	−0.0978700	+	0.112948i	0.704702	+	0.709504i	$0.251081\pi$
$674$	0.789006	−	5.48766i	0.0303914	−	0.211377i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	26.5898	+	17.0882i	1.02269	+	0.657240i
$677$	3.21789	+	22.3809i	0.123673	+	0.860167i	0.953338	+	0.301905i	$0.0976226\pi$
$677$	3.21789	+	22.3809i	0.123673	+	0.860167i	−0.829665	+	0.558262i	$0.811468\pi$
$678$	6.51649	+	14.2691i	0.250264	+	0.548002i
$679$	−2.68320	−	5.87538i	−0.102972	−	0.225476i
$680$	−0.221199	−	1.53848i	−0.00848261	−	0.0589978i
$681$	−5.26938	−	3.38643i	−0.201923	−	0.129768i
$682$	27.7495	−	8.14799i	1.06258	−	0.312003i
$683$	−2.33450	+	16.2368i	−0.0893270	+	0.621283i	0.895149	+	0.445766i	$0.147069\pi$
$683$	−2.33450	+	16.2368i	−0.0893270	+	0.621283i	−0.984476	+	0.175517i	$0.943840\pi$
$684$	2.03851	−	2.35257i	0.0779444	−	0.0899527i
$685$	−1.14631	+	0.736687i	−0.0437982	+	0.0281474i
$686$	8.36946	+	9.65887i	0.319547	+	0.368777i
$687$	−23.3115	−	6.84488i	−0.889390	−	0.261148i
$688$	1.71586	−	3.75721i	0.0654165	−	0.143242i
$689$	43.5447			1.65892
$690$	3.59819	−	3.17066i	0.136981	−	0.120705i
$691$	3.67109			0.139655			0.0698274	−	0.997559i	$-0.477755\pi$
$691$	3.67109			0.139655			0.0698274	+	0.997559i	$0.477755\pi$
$692$	−1.04105	+	2.27959i	−0.0395749	+	0.0866569i
$693$	−16.3351	−	4.79643i	−0.620520	−	0.182201i
$694$	3.37031	+	3.88954i	0.127935	+	0.147645i
$695$	−6.70861	+	4.31136i	−0.254472	+	0.163539i
$696$	2.33110	−	2.69023i	0.0883600	−	0.101973i
$697$	2.18737	−	15.2135i	0.0828525	−	0.576252i
$698$	−8.04390	+	2.36190i	−0.304466	+	0.0893994i
$699$	0.126593	+	0.0813561i	0.00478817	+	0.00307717i
$700$	−0.588355	−	4.09210i	−0.0222377	−	0.154667i
$701$	−4.85377	−	10.6283i	−0.183324	−	0.401424i	0.795550	−	0.605888i	$-0.207182\pi$
$701$	−4.85377	−	10.6283i	−0.183324	−	0.401424i	−0.978874	+	0.204464i	$0.934455\pi$
$702$	−2.77450	−	6.07532i	−0.104717	−	0.229298i
$703$	−4.75562	−	33.0761i	−0.179362	−	1.24749i
$704$	3.46432	+	2.22639i	0.130567	+	0.0839101i
$705$	0.971409	−	0.285231i	0.0365854	−	0.0107424i
$706$	−4.52495	+	31.4717i	−0.170299	+	1.18445i
$707$	11.3552	−	13.1045i	0.427054	−	0.492847i
$708$	−2.03355	+	1.30688i	−0.0764256	+	0.0491157i
$709$	2.74995	+	3.17362i	0.103277	+	0.119188i	0.805035	−	0.593228i	$-0.202147\pi$
$709$	2.74995	+	3.17362i	0.103277	+	0.119188i	−0.701758	+	0.712415i	$0.747601\pi$
$710$	−0.597041	−	0.175307i	−0.0224065	−	0.00657915i
$711$	4.83528	−	10.5878i	0.181337	−	0.397073i
$712$	8.51627			0.319161
$713$	30.7528	+	13.7362i	1.15170	+	0.514424i
$714$	−6.42574			−0.240477
$715$	−11.4255	+	25.0185i	−0.427291	+	0.935637i
$716$	18.4009	+	5.40299i	0.687674	+	0.201919i
$717$	−11.6079	−	13.3962i	−0.433504	−	0.500290i
$718$	22.2744	−	14.3149i	0.831275	−	0.534228i
$719$	−29.1285	+	33.6161i	−1.08631	+	1.25367i	−0.120977	+	0.992655i	$0.538603\pi$
$719$	−29.1285	+	33.6161i	−1.08631	+	1.25367i	−0.965335	+	0.261015i	$0.915943\pi$
$720$	0.142315	−	0.989821i	0.00530376	−	0.0368885i
$721$	43.1399	−	12.6670i	1.60661	−	0.471744i
$722$	7.83199	+	5.03331i	0.291476	+	0.187320i
$723$	0.165029	+	1.14780i	0.00613749	+	0.0426872i
$724$	−6.83225	−	14.9605i	−0.253918	−	0.556004i
$725$	1.47875	+	3.23800i	0.0549192	+	0.120256i
$726$	0.847959	+	5.89768i	0.0314707	+	0.218883i
$727$	−5.85473	−	3.76261i	−0.217140	−	0.139547i	0.427550	−	0.903992i	$-0.359377\pi$
$727$	−5.85473	−	3.76261i	−0.217140	−	0.139547i	−0.644689	+	0.764445i	$0.723013\pi$
$728$	26.4932	−	7.77910i	0.981903	−	0.288313i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−4.71259	+	5.43862i	−0.174421	+	0.201292i
$731$	5.40082	−	3.47090i	0.199757	−	0.128376i
$732$	5.96813	+	6.88759i	0.220588	+	0.254573i
$733$	−7.49462	−	2.20062i	−0.276820	−	0.0812817i	0.140376	−	0.990098i	$-0.455169\pi$
$733$	−7.49462	−	2.20062i	−0.276820	−	0.0812817i	−0.417196	+	0.908817i	$0.636987\pi$
$734$	7.29695	−	15.9781i	0.269335	−	0.589762i
$735$	−10.0914			−0.372228
$736$	1.38939	+	4.59016i	0.0512136	+	0.169196i
$737$	30.0050			1.10525
$738$	4.10790	−	8.99506i	0.151214	−	0.331113i
$739$	36.3039	+	10.6598i	1.33546	+	0.392127i	0.870048	−	0.492967i	$-0.164088\pi$
$739$	36.3039	+	10.6598i	1.33546	+	0.392127i	0.465413	+	0.885094i	$0.345906\pi$
$740$	−7.02978	−	8.11280i	−0.258420	−	0.298232i
$741$	−17.4902	+	11.2403i	−0.642518	+	0.412921i
$742$	17.6511	−	20.3704i	0.647990	−	0.747821i
$743$	5.45157	−	37.9165i	0.199999	−	1.39102i	−0.604281	−	0.796772i	$-0.706539\pi$
$743$	5.45157	−	37.9165i	0.199999	−	1.39102i	0.804279	−	0.594251i	$-0.202552\pi$
$744$	6.73851	−	1.97861i	0.247046	−	0.0725392i
$745$	−0.0596409	−	0.0383289i	−0.00218507	−	0.00140426i
$746$	−0.175794	−	1.22267i	−0.00643627	−	0.0447653i
$747$	6.25520	+	13.6970i	0.228866	+	0.501146i
$748$	2.65893	+	5.82225i	0.0972202	+	0.212883i
$749$	−4.29626	−	29.8812i	−0.156982	−	1.09183i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	−3.67194	+	1.07818i	−0.133991	+	0.0393433i	−0.348041	−	0.937479i	$-0.613153\pi$
$751$	−3.67194	+	1.07818i	−0.133991	+	0.0393433i	0.214049	+	0.976823i	$0.431335\pi$
$752$	−0.144082	+	1.00211i	−0.00525414	+	0.0365433i
$753$	15.9882	−	18.4513i	0.582642	−	0.672404i
$754$	−20.0005	+	12.8536i	−0.728376	+	0.468099i
$755$	4.58211	+	5.28803i	0.166760	+	0.192451i
$756$	−3.96671	−	1.16473i	−0.144268	−	0.0423609i
$757$	−20.2901	+	44.4292i	−0.737457	+	1.61480i	0.0502366	+	0.998737i	$0.484002\pi$
$757$	−20.2901	+	44.4292i	−0.737457	+	1.61480i	−0.787693	+	0.616068i	$0.788725\pi$
$758$	10.2272			0.371470
$759$	−10.5387	+	16.7026i	−0.382532	+	0.606266i
$760$	−3.11289			−0.112916
$761$	−13.8019	+	30.2220i	−0.500319	+	1.09555i	0.476046	+	0.879420i	$0.342069\pi$
$761$	−13.8019	+	30.2220i	−0.500319	+	1.09555i	−0.976366	+	0.216126i	$0.930658\pi$
$762$	19.3765	+	5.68947i	0.701938	+	0.206108i
$763$	−41.6180	−	48.0297i	−1.50667	−	1.73879i
$764$	−5.58590	+	3.58984i	−0.202091	+	0.129876i
$765$	1.01785	−	1.17466i	0.0368004	−	0.0424699i
$766$	−5.17092	+	35.9645i	−0.186833	+	1.29945i
$767$	15.4908	−	4.54851i	0.559340	−	0.164237i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	−6.70228	−	46.6154i	−0.241690	−	1.68099i	−0.643638	−	0.765330i	$-0.722576\pi$
$769$	−6.70228	−	46.6154i	−0.241690	−	1.68099i	0.401947	−	0.915663i	$-0.368334\pi$
$770$	7.07234	+	15.4863i	0.254869	+	0.558086i
$771$	11.1528	+	24.4213i	0.401660	+	0.879513i
$772$	−0.195498	−	1.35972i	−0.00703611	−	0.0489372i
$773$	6.76800	+	4.34953i	0.243428	+	0.156442i	0.656666	−	0.754181i	$-0.271966\pi$
$773$	6.76800	+	4.34953i	0.243428	+	0.156442i	−0.413238	+	0.910623i	$0.635602\pi$
$774$	3.96316	−	1.16369i	0.142453	−	0.0418279i
$775$	−0.999476	+	6.95151i	−0.0359022	+	0.249706i
$776$	−1.02313	+	1.18075i	−0.0367282	+	0.0423866i
$777$	−37.3344	+	23.9933i	−1.33936	+	0.860756i
$778$	−15.1562	−	17.4912i	−0.543375	−	0.627088i
$779$	−29.5355	−	8.67240i	−1.05822	−	0.310721i
$780$	−2.77450	+	6.07532i	−0.0993432	+	0.217531i
$781$	2.56244			0.0916913
$782$	−2.04048	+	7.16943i	−0.0729674	+	0.256378i
$783$	3.55968			0.127213
$784$	4.19213	−	9.17949i	0.149719	−	0.327839i
$785$	−5.32821	−	1.56450i	−0.190172	−	0.0558396i
$786$	−6.96191	−	8.03448i	−0.248323	−	0.286580i
$787$	31.8470	−	20.4668i	1.13522	−	0.729564i	0.168579	−	0.985688i	$-0.446082\pi$
$787$	31.8470	−	20.4668i	1.13522	−	0.729564i	0.966644	+	0.256125i	$0.0824457\pi$
$788$	−1.31961	+	1.52292i	−0.0470093	+	0.0542516i
$789$	1.74630	−	12.1458i	0.0621701	−	0.432402i
$790$	−11.1681	+	3.27926i	−0.397345	+	0.116671i
$791$	−54.5566	−	35.0614i	−1.93981	−	1.24664i
$792$	0.586059	+	4.07613i	0.0208247	+	0.144839i
$793$	−25.2857	−	55.3679i	−0.897921	−	1.96617i
$794$	−12.1894	−	26.6910i	−0.432585	−	0.947230i
$795$	0.927860	+	6.45341i	0.0329078	+	0.228879i
$796$	8.83098	+	5.67533i	0.313006	+	0.201157i
$797$	−17.4035	+	5.11014i	−0.616465	+	0.181010i	−0.575032	−	0.818131i	$-0.695010\pi$
$797$	−17.4035	+	5.11014i	−0.616465	+	0.181010i	−0.0414327	+	0.999141i	$0.513192\pi$
$798$	−1.83149	+	12.7383i	−0.0648339	+	0.450930i
$799$	−1.03049	+	1.18925i	−0.0364560	+	0.0420725i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	5.57697	+	6.43617i	0.197053	+	0.227411i
$802$	19.3103	+	5.67001i	0.681870	+	0.200215i
$803$	12.3107	−	26.9568i	0.434437	−	0.951284i
$804$	7.28622			0.256965
$805$	−5.42735	+	19.0695i	−0.191289	+	0.672112i
$806$	−46.9057			−1.65218
$807$	−5.64875	+	12.3690i	−0.198846	+	0.435411i
$808$	−4.02436	−	1.18166i	−0.141576	−	0.0415706i
$809$	19.8491	+	22.9070i	0.697856	+	0.805368i	0.988461	−	0.151475i	$-0.0484022\pi$
$809$	19.8491	+	22.9070i	0.697856	+	0.805368i	−0.290605	+	0.956843i	$0.593857\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	−4.16188	+	4.80306i	−0.146143	+	0.168658i	−0.824102	−	0.566442i	$-0.808320\pi$
$811$	−4.16188	+	4.80306i	−0.146143	+	0.168658i	0.677958	+	0.735100i	$0.262865\pi$
$812$	−2.09436	+	14.5666i	−0.0734975	+	0.511186i
$813$	−18.5468	+	5.44584i	−0.650466	+	0.190994i
$814$	37.1887	+	23.8997i	1.30346	+	0.837685i
$815$	−3.43891	−	23.9181i	−0.120460	−	0.837815i
$816$	0.645678	+	1.41384i	0.0226032	+	0.0494942i
$817$	−5.34128	−	11.6958i	−0.186868	−	0.409184i
$818$	0.00939845	+	0.0653676i	0.000328609	+	0.00228553i
$819$	23.2284	+	14.9280i	0.811666	+	0.521626i
$820$	−9.48811	+	2.78596i	−0.331339	+	0.0972900i
$821$	7.24898	−	50.4178i	0.252991	−	1.75959i	−0.327052	−	0.945006i	$-0.606055\pi$
$821$	7.24898	−	50.4178i	0.252991	−	1.75959i	0.580043	−	0.814586i	$-0.303036\pi$
$822$	0.892325	−	1.02980i	0.0311234	−	0.0359183i
$823$	−38.1387	+	24.5103i	−1.32943	+	0.854374i	−0.996082	−	0.0884296i	$-0.971815\pi$
$823$	−38.1387	+	24.5103i	−1.32943	+	0.854374i	−0.333349	+	0.942803i	$0.608179\pi$
$824$	−7.12192	−	8.21913i	−0.248104	−	0.286327i
$825$	−3.95124	−	1.16019i	−0.137564	−	0.0403926i
$826$	4.15145	−	9.09041i	0.144447	−	0.316296i
$827$	3.05456			0.106217			0.0531087	−	0.998589i	$-0.483087\pi$
$827$	3.05456			0.106217			0.0531087	+	0.998589i	$0.483087\pi$
$828$	−2.55916	+	4.05595i	−0.0889369	+	0.140954i
$829$	14.6415			0.508522			0.254261	−	0.967136i	$-0.418168\pi$
$829$	14.6415			0.508522			0.254261	+	0.967136i	$0.418168\pi$
$830$	6.25520	−	13.6970i	0.217121	−	0.475429i
$831$	6.77544	+	1.98945i	0.235037	+	0.0690132i
$832$	−4.37373	−	5.04756i	−0.151632	−	0.174993i
$833$	13.1951	−	8.47999i	0.457184	−	0.293814i
$834$	5.22221	−	6.02676i	0.180830	−	0.208689i
$835$	1.13697	−	7.90782i	0.0393465	−	0.273661i
$836$	12.2998	−	3.61154i	0.425397	−	0.124908i
$837$	5.90812	+	3.79692i	0.204214	+	0.131241i
$838$	0.0530101	+	0.368693i	0.00183120	+	0.0127363i
$839$	−3.36849	−	7.37596i	−0.116293	−	0.254646i	0.842531	−	0.538649i	$-0.181065\pi$
$839$	−3.36849	−	7.37596i	−0.116293	−	0.254646i	−0.958824	+	0.284002i	$0.908338\pi$
$840$	1.71740	+	3.76058i	0.0592559	+	0.129752i
$841$	2.32381	+	16.1625i	0.0801314	+	0.557326i
$842$	19.3529	+	12.4374i	0.666946	+	0.428620i
$843$	30.5563	−	8.97213i	1.05241	−	0.309017i
$844$	2.31906	−	16.1294i	0.0798252	−	0.555196i
$845$	20.6984	−	23.8873i	0.712047	−	0.821747i
$846$	−0.851701	+	0.547355i	−0.0292821	+	0.0188184i
$847$	−16.1310	−	18.6162i	−0.554269	−	0.639661i
$848$	−6.25568	−	1.83683i	−0.214821	−	0.0630771i
$849$	12.9830	−	28.4289i	0.445576	−	0.975676i
$850$	−1.55430			−0.0533119
$851$	14.9148	+	49.2743i	0.511272	+	1.68910i
$852$	0.622246			0.0213178
$853$	−2.39235	+	5.23851i	−0.0819124	+	0.179363i	−0.946156	−	0.323710i	$-0.895070\pi$
$853$	−2.39235	+	5.23851i	−0.0819124	+	0.179363i	0.864244	+	0.503073i	$0.167797\pi$
$854$	−36.1510	−	10.6149i	−1.23706	−	0.363234i
$855$	−2.03851	−	2.35257i	−0.0697156	−	0.0804561i
$856$	−6.14297	+	3.94785i	−0.209962	+	0.134935i
$857$	−32.8099	+	37.8646i	−1.12076	+	1.29343i	−0.169337	+	0.985558i	$0.554163\pi$
$857$	−32.8099	+	37.8646i	−1.12076	+	1.29343i	−0.951427	+	0.307873i	$0.900383\pi$
$858$	3.91422	−	27.2240i	0.133629	−	0.929411i
$859$	26.1057	−	7.66533i	0.890715	−	0.261538i	0.195813	−	0.980641i	$-0.437266\pi$
$859$	26.1057	−	7.66533i	0.890715	−	0.261538i	0.694903	+	0.719104i	$0.255447\pi$
$860$	−3.47477	−	2.23310i	−0.118489	−	0.0761481i
$861$	5.81805	+	40.4654i	0.198279	+	1.37906i
$862$	2.59828	+	5.68945i	0.0884979	+	0.193783i
$863$	−2.77893	−	6.08500i	−0.0945958	−	0.207136i	0.856419	−	0.516282i	$-0.172684\pi$
$863$	−2.77893	−	6.08500i	−0.0945958	−	0.207136i	−0.951015	+	0.309146i	$0.899957\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	2.10823	+	1.35487i	0.0716819	+	0.0460671i
$866$	−36.3234	+	10.6655i	−1.23432	+	0.362429i
$867$	2.07554	−	14.4357i	0.0704891	−	0.490263i
$868$	−19.0134	+	21.9427i	−0.645358	+	0.744782i
$869$	40.3234	−	25.9143i	1.36788	−	0.879082i
$870$	−2.33110	−	2.69023i	−0.0790316	−	0.0912073i
$871$	−46.6925	−	13.7102i	−1.58211	−	0.464551i
$872$	−6.38594	+	13.9833i	−0.216255	+	0.473533i
$873$	−1.56236			−0.0528779
$874$	13.6310	+	6.08847i	0.461074	+	0.205945i
$875$	−4.13418			−0.139761
$876$	2.98946	−	6.54601i	0.101005	−	0.221169i
$877$	−26.4829	−	7.77608i	−0.894264	−	0.262580i	−0.197861	−	0.980230i	$-0.563399\pi$
$877$	−26.4829	−	7.77608i	−0.894264	−	0.262580i	−0.696404	+	0.717650i	$0.745218\pi$
$878$	−2.20355	−	2.54304i	−0.0743664	−	0.0858234i
$879$	−13.5029	+	8.67778i	−0.455441	+	0.292694i
$880$	2.69675	−	3.11221i	0.0909074	−	0.104913i
$881$	−3.52577	+	24.5223i	−0.118786	+	0.826177i	0.840109	+	0.542417i	$0.182491\pi$
$881$	−3.52577	+	24.5223i	−0.118786	+	0.826177i	−0.958895	+	0.283760i	$0.908418\pi$
$882$	9.68265	−	2.84308i	0.326032	−	0.0957316i
$883$	−40.7987	−	26.2197i	−1.37298	−	0.882363i	−0.374000	−	0.927429i	$-0.622014\pi$
$883$	−40.7987	−	26.2197i	−1.37298	−	0.882363i	−0.998984	+	0.0450651i	$0.985650\pi$
$884$	−1.47736	−	10.2753i	−0.0496891	−	0.345595i
$885$	1.00418	+	2.19884i	0.0337551	+	0.0739133i
$886$	−12.3519	−	27.0469i	−0.414971	−	0.908659i
$887$	−7.53993	−	52.4414i	−0.253166	−	1.76081i	−0.578949	−	0.815364i	$-0.696537\pi$
$887$	−7.53993	−	52.4414i	−0.253166	−	1.76081i	0.325783	−	0.945445i	$-0.394372\pi$
$888$	9.03066	+	5.80365i	0.303049	+	0.194758i
$889$	−80.1061	+	23.5213i	−2.68667	+	0.788878i
$890$	1.21199	−	8.42959i	0.0406261	−	0.282560i
$891$	−2.69675	+	3.11221i	−0.0903445	+	0.104263i
$892$	10.5048	−	6.75102i	0.351727	−	0.226041i
$893$	2.06383	+	2.38178i	0.0690633	+	0.0797033i
$894$	0.0680235	+	0.0199735i	0.00227505	+	0.000668014i
$895$	7.96672	−	17.4447i	0.266298	−	0.583111i
$896$	−4.13418			−0.138113
$897$	24.0318	−	21.1764i	0.802400	−	0.707060i
$898$	36.7692			1.22701
$899$	10.3852	−	22.7405i	0.346366	−	0.758437i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	−6.63613	−	7.65851i	−0.221082	−	0.255142i
$902$	34.2576	−	22.0160i	1.14065	−	0.733053i
$903$	−11.1825	+	12.9053i	−0.372129	+	0.429460i
$904$	−2.23245	+	15.5270i	−0.0742502	+	0.516421i
$905$	−15.7806	+	4.63360i	−0.524564	+	0.154026i
$906$	−5.88631	−	3.78290i	−0.195559	−	0.125678i
$907$	7.02536	+	48.8625i	0.233273	+	1.62245i	0.683787	+	0.729682i	$0.260332\pi$
$907$	7.02536	+	48.8625i	0.233273	+	1.62245i	−0.450513	+	0.892770i	$0.648759\pi$
$908$	−2.60205	−	5.69769i	−0.0863519	−	0.189084i
$909$	−1.74236	−	3.81523i	−0.0577903	−	0.126543i
$910$	−3.92955	−	27.3306i	−0.130263	−	0.906001i
$911$	−0.962930	−	0.618838i	−0.0319033	−	0.0205030i	0.524592	−	0.851354i	$-0.324218\pi$
$911$	−0.962930	−	0.618838i	−0.0319033	−	0.0205030i	−0.556495	+	0.830851i	$0.687854\pi$
$912$	2.98680	−	0.877003i	0.0989028	−	0.0290405i
$913$	−8.82472	+	61.3772i	−0.292055	+	2.03129i
$914$	4.09367	−	4.72434i	0.135406	−	0.156267i
$915$	7.66684	−	4.92718i	0.253458	−	0.162887i
$916$	−15.9103	−	18.3614i	−0.525690	−	0.606679i
$917$	42.1707	+	12.3824i	1.39260	+	0.408904i
$918$	−0.645678	+	1.41384i	−0.0213105	+	0.0466636i
$919$	19.5963			0.646421			0.323211	−	0.946327i	$-0.395238\pi$
$919$	19.5963			0.646421			0.323211	+	0.946327i	$0.395238\pi$
$920$	4.74117	−	0.721999i	0.156312	−	0.0238036i
$921$	−17.2131			−0.567190
$922$	−5.72779	+	12.5421i	−0.188635	+	0.413053i
$923$	−3.98756	−	1.17085i	−0.131252	−	0.0385391i
$924$	−11.1488	−	12.8664i	−0.366770	−	0.423275i
$925$	−9.03066	+	5.80365i	−0.296926	+	0.190823i
$926$	1.79969	−	2.07695i	0.0591414	−	0.0682528i
$927$	1.54774	−	10.7648i	0.0508345	−	0.353561i
$928$	3.41549	−	1.00288i	0.112119	−	0.0329211i
$929$	−23.4456	−	15.0676i	−0.769224	−	0.494351i	0.0962171	−	0.995360i	$-0.469326\pi$
$929$	−23.4456	−	15.0676i	−0.769224	−	0.494351i	−0.865442	+	0.501010i	$0.832962\pi$
$930$	−0.999476	−	6.95151i	−0.0327741	−	0.227949i
$931$	−13.0497	−	28.5748i	−0.427685	−	0.936500i
$932$	0.0625120	+	0.136882i	0.00204765	+	0.00448373i
$933$	−0.394826	−	2.74608i	−0.0129260	−	0.0899025i
$934$	−15.0649	−	9.68160i	−0.492937	−	0.316792i
$935$	6.14140	−	1.80328i	0.200845	−	0.0589734i
$936$	0.950503	−	6.61089i	0.0310682	−	0.216084i
$937$	35.3420	−	40.7869i	1.15457	−	1.33245i	0.220492	−	0.975389i	$-0.429234\pi$
$937$	35.3420	−	40.7869i	1.15457	−	1.33245i	0.934082	−	0.357060i	$-0.116221\pi$
$938$	−25.3407	+	16.2855i	−0.827402	+	0.531739i
$939$	11.2647	+	13.0001i	0.367609	+	0.424243i
$940$	0.971409	+	0.285231i	0.0316839	+	0.00930322i
$941$	3.41139	−	7.46991i	0.111208	−	0.243512i	−0.845842	−	0.533433i	$-0.820902\pi$
$941$	3.41139	−	7.46991i	0.111208	−	0.243512i	0.957051	+	0.289921i	$0.0936290\pi$
$942$	5.55315			0.180932
$943$	46.9963	+	6.35831i	1.53041	+	0.207055i
$944$	−2.41729			−0.0786760
$945$	−1.71740	+	3.76058i	−0.0558670	+	0.122332i
$946$	16.3205	+	4.79212i	0.530624	+	0.155805i
$947$	18.4497	+	21.2920i	0.599533	+	0.691898i	0.971687	−	0.236273i	$-0.0759259\pi$
$947$	18.4497	+	21.2920i	0.599533	+	0.691898i	−0.372153	+	0.928171i	$0.621380\pi$
$948$	9.79188	−	6.29286i	0.318025	−	0.204383i
$949$	−31.4748	+	36.3239i	−1.02172	+	1.17912i
$950$	−0.443011	+	3.08121i	−0.0143732	+	0.0999676i
$951$	−2.65200	+	0.778698i	−0.0859970	+	0.0252510i
$952$	−5.40567	−	3.47402i	−0.175199	−	0.112593i
$953$	−2.36522	−	16.4504i	−0.0766169	−	0.532882i	−0.991595	−	0.129379i	$-0.958702\pi$
$953$	−2.36522	−	16.4504i	−0.0766169	−	0.532882i	0.914978	−	0.403503i	$-0.132208\pi$
$954$	−2.70841	−	5.93059i	−0.0876881	−	0.192010i
$955$	2.75834	+	6.03993i	0.0892579	+	0.195448i
$956$	−2.52263	−	17.5453i	−0.0815878	−	0.567455i
$957$	12.3319	+	7.92522i	0.398633	+	0.256186i
$958$	−37.9509	+	11.1434i	−1.22614	+	0.360027i
$959$	−0.801703	+	5.57597i	−0.0258883	+	0.180057i
$960$	0.654861	−	0.755750i	0.0211355	−	0.0243917i
$961$	15.4138	−	9.90585i	0.497219	−	0.319544i
$962$	−46.9510	−	54.1844i	−1.51376	−	1.74697i
$963$	−7.00637	−	2.05726i	−0.225777	−	0.0662942i
$964$	−0.481717	+	1.05481i	−0.0155151	+	0.0339733i
$965$	−1.37370			−0.0442209
$966$	−0.165000	−	19.8261i	−0.00530880	−	0.637895i
$967$	−54.5421			−1.75396			−0.876979	−	0.480530i	$-0.840444\pi$
$967$	−54.5421			−1.75396			−0.876979	+	0.480530i	$0.840444\pi$
$968$	−2.47518	+	5.41989i	−0.0795553	+	0.174202i
$969$	4.64237	+	1.36312i	0.149134	+	0.0437898i
$970$	1.02313	+	1.18075i	0.0328507	+	0.0379117i
$971$	42.8776	−	27.5558i	1.37601	−	0.884307i	0.376888	−	0.926259i	$-0.376994\pi$
$971$	42.8776	−	27.5558i	1.37601	−	0.884307i	0.999120	+	0.0419521i	$0.0133577\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−4.69186	+	32.6326i	−0.150414	+	1.04615i
$974$	0.437731	−	0.128530i	0.0140258	−	0.00411835i
$975$	5.61863	+	3.61087i	0.179940	+	0.115640i
$976$	1.29700	+	9.02082i	0.0415159	+	0.288749i
$977$	−12.3382	−	27.0168i	−0.394733	−	0.864345i	−0.997777	−	0.0666370i	$-0.978773\pi$
$977$	−12.3382	−	27.0168i	−0.394733	−	0.864345i	0.603044	−	0.797708i	$-0.293954\pi$
$978$	10.0381	+	21.9804i	0.320984	+	0.702856i
$979$	4.99104	+	34.7135i	0.159514	+	1.10945i
$980$	−8.48945	−	5.45584i	−0.271186	−	0.174280i
$981$	−14.7497	+	4.33091i	−0.470923	+	0.138275i
$982$	3.25956	−	22.6708i	0.104017	−	0.723453i
$983$	−31.9696	+	36.8949i	−1.01967	+	1.17676i	−0.0355318	+	0.999369i	$0.511313\pi$
$983$	−31.9696	+	36.8949i	−1.01967	+	1.17676i	−0.984140	+	0.177395i	$0.943233\pi$
$984$	8.31888	−	5.34622i	0.265196	−	0.170431i
$985$	1.31961	+	1.52292i	0.0420464	+	0.0485241i
$986$	5.30868	+	1.55877i	0.169063	+	0.0496413i
$987$	1.73873	−	3.80728i	0.0553443	−	0.121187i
$988$	−20.7906			−0.661438
$989$	10.8479	+	16.5747i	0.344943	+	0.527045i
$990$	4.11805			0.130880
$991$	12.4391	−	27.2377i	0.395139	−	0.865235i	−0.602601	−	0.798043i	$-0.705869\pi$
$991$	12.4391	−	27.2377i	0.395139	−	0.865235i	0.997740	−	0.0671918i	$-0.0214039\pi$
$992$	6.73851	+	1.97861i	0.213948	+	0.0628208i
$993$	−9.35566	−	10.7970i	−0.296893	−	0.342633i
$994$	−2.16410	+	1.39079i	−0.0686412	+	0.0441130i
$995$	6.87434	−	7.93341i	0.217931	−	0.251506i
$996$	−2.14294	+	14.9044i	−0.0679015	+	0.472265i
$997$	−16.3811	+	4.80993i	−0.518795	+	0.152332i	−0.530639	−	0.847598i	$-0.678048\pi$
$997$	−16.3811	+	4.80993i	−0.518795	+	0.152332i	0.0118441	+	0.999930i	$0.496230\pi$
$998$	−4.52523	−	2.90819i	−0.143244	−	0.0920572i
$999$	1.52772	+	10.6255i	0.0483348	+	0.336176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.121.1	✓	30
23.4	even	11	inner	690.2.m.h.211.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.121.1	✓	30	1.1	even	1	trivial
690.2.m.h.211.1	yes	30	23.4	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.588355 + 4.09210i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.588355 + 4.09210i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(1.71070 + 3.74591i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.950503 - 6.61089i) q^{13} +(-3.47789 - 2.23511i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.01785 + 1.17466i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(2.03851 + 2.35257i) q^{19} +(0.959493 + 0.281733i) q^{20} +(1.71740 - 3.76058i) q^{21} -4.11805 q^{22} +(-3.65046 - 3.11033i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(6.40833 + 1.88166i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(3.47789 - 2.23511i) q^{28} +(-2.33110 + 2.69023i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-6.73851 + 1.97861i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.586059 - 4.07613i) q^{33} +(-0.645678 - 1.41384i) q^{34} +(-1.71740 - 3.76058i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-9.03066 - 5.80365i) q^{37} +(-2.98680 + 0.877003i) q^{38} +(-0.950503 + 6.61089i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(-8.31888 + 5.34622i) q^{41} +(2.70731 + 3.12440i) q^{42} +(-3.96316 - 1.16369i) q^{43} +(1.71070 - 3.74591i) q^{44} -1.00000 q^{45} +(4.34571 - 2.02850i) q^{46} +1.01242 q^{47} +(0.415415 - 0.909632i) q^{48} +(-9.68265 - 2.84308i) q^{49} +(0.654861 + 0.755750i) q^{50} +(1.30756 - 0.840316i) q^{51} +(-4.37373 + 5.04756i) q^{52} +(-0.927860 + 6.45341i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-3.46432 - 2.22639i) q^{55} +(0.588355 + 4.09210i) q^{56} +(-1.29314 - 2.83159i) q^{57} +(-1.47875 - 3.23800i) q^{58} +(0.344016 + 2.39268i) q^{59} +(-0.841254 - 0.540641i) q^{60} +(8.74442 - 2.56759i) q^{61} +(0.999476 - 6.95151i) q^{62} +(-2.70731 + 3.12440i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.37373 + 5.04756i) q^{65} +(3.95124 + 1.16019i) q^{66} +(3.02680 - 6.62777i) q^{67} +1.55430 q^{68} +(2.62631 + 4.01279i) q^{69} +4.13418 q^{70} +(0.258490 - 0.566015i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-4.71259 - 5.43862i) q^{73} +(9.03066 - 5.80365i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.443011 - 3.08121i) q^{76} +(-16.3351 + 4.79643i) q^{77} +(-5.61863 - 3.61087i) q^{78} +(-1.65649 - 11.5212i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-1.40731 - 9.78802i) q^{82} +(12.6674 + 8.14081i) q^{83} +(-3.96671 + 1.16473i) q^{84} +(0.221199 - 1.53848i) q^{85} +(2.70488 - 3.12160i) q^{86} +(2.99460 - 1.92451i) q^{87} +(2.69675 + 3.11221i) q^{88} +(8.17130 + 2.39931i) q^{89} +(0.415415 - 0.909632i) q^{90} +27.6117 q^{91} +(0.0399113 + 4.79567i) q^{92} +7.02299 q^{93} +(-0.420574 + 0.920928i) q^{94} +(-2.98680 - 0.877003i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-1.31434 + 0.844676i) q^{97} +(6.60848 - 7.62659i) q^{98} +(-0.586059 + 4.07613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more