LMFDB - Embedded newform 390.2.bh.c.71.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(11,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("390.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bh (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.7
Character	$\chi$	$=$	390.71
Dual form			390.2.bh.c.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.192053 + 1.72137i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(0.260015 + 1.71242i) q^{6} +(-0.213554 + 0.796995i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.92623 - 0.661187i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.192053 + 1.72137i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(0.260015 + 1.71242i) q^{6} +(-0.213554 + 0.796995i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.92623 - 0.661187i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.981698 + 3.66375i) q^{11} +(0.694363 + 1.58678i) q^{12} +(3.42697 + 1.12067i) q^{13} +0.825110i q^{14} +(-1.35299 + 1.08139i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.49980 - 2.59772i) q^{17} +(-2.99765 + 0.118707i) q^{18} +(1.17350 + 0.314438i) q^{19} +(0.965926 + 0.258819i) q^{20} +(-1.33091 - 0.520671i) q^{21} +(1.89649 + 3.28482i) q^{22} +(-1.76190 + 3.05169i) q^{23} +(1.08139 + 1.35299i) q^{24} +1.00000i q^{25} +(3.60025 + 0.195522i) q^{26} +(1.70014 - 4.91015i) q^{27} +(0.213554 + 0.796995i) q^{28} +(-6.48200 - 3.74239i) q^{29} +(-1.02701 + 1.39472i) q^{30} +(0.00278407 - 0.00278407i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-6.49520 + 0.986234i) q^{33} +(-2.12103 - 2.12103i) q^{34} +(-0.714566 + 0.412555i) q^{35} +(-2.86478 + 0.890511i) q^{36} +(10.9895 - 2.94462i) q^{37} +1.21489 q^{38} +(-2.58725 + 5.68385i) q^{39} +1.00000 q^{40} +(-4.61510 + 1.23661i) q^{41} +(-1.42032 - 0.158464i) q^{42} +(3.40698 - 1.96702i) q^{43} +(2.68205 + 2.68205i) q^{44} +(-1.60163 - 2.53669i) q^{45} +(-0.912024 + 3.40372i) q^{46} +(7.01463 - 7.01463i) q^{47} +(1.39472 + 1.02701i) q^{48} +(5.47258 + 3.15960i) q^{49} +(0.258819 + 0.965926i) q^{50} +(4.75968 - 2.08280i) q^{51} +(3.52818 - 0.742952i) q^{52} -4.90674i q^{53} +(0.371368 - 5.18286i) q^{54} +(-1.89649 + 3.28482i) q^{55} +(0.412555 + 0.714566i) q^{56} +(-0.766637 + 1.95964i) q^{57} +(-7.22973 - 1.93720i) q^{58} +(-4.67330 - 1.25221i) q^{59} +(-0.631032 + 1.61301i) q^{60} +(-6.87481 - 11.9075i) q^{61} +(0.00196864 - 0.00340978i) q^{62} +(1.15187 - 2.19099i) q^{63} -1.00000i q^{64} +(1.63080 + 3.21567i) q^{65} +(-6.01863 + 2.63371i) q^{66} +(-3.00389 - 11.2107i) q^{67} +(-2.59772 - 1.49980i) q^{68} +(-4.91472 - 3.61896i) q^{69} +(-0.583441 + 0.583441i) q^{70} +(-1.52747 + 5.70060i) q^{71} +(-2.53669 + 1.60163i) q^{72} +(-8.49044 - 8.49044i) q^{73} +(9.85289 - 5.68857i) q^{74} +(-1.72137 - 0.192053i) q^{75} +(1.17350 - 0.314438i) q^{76} -3.12963 q^{77} +(-1.02800 + 6.15981i) q^{78} +5.90955 q^{79} +(0.965926 - 0.258819i) q^{80} +(8.12566 + 3.86957i) q^{81} +(-4.13778 + 2.38895i) q^{82} +(5.36244 + 5.36244i) q^{83} +(-1.41294 + 0.214541i) q^{84} +(0.776351 - 2.89738i) q^{85} +(2.78179 - 2.78179i) q^{86} +(7.68692 - 10.4392i) q^{87} +(3.28482 + 1.89649i) q^{88} +(-1.85846 - 6.93588i) q^{89} +(-2.20360 - 2.03572i) q^{90} +(-1.62501 + 2.49195i) q^{91} +3.52379i q^{92} +(0.00425773 + 0.00532711i) q^{93} +(4.96009 - 8.59113i) q^{94} +(0.607447 + 1.05213i) q^{95} +(1.61301 + 0.631032i) q^{96} +(-7.65690 - 2.05166i) q^{97} +(6.10387 + 1.63553i) q^{98} +(-0.450254 - 11.3701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9	$ 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) $ 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9 + 8 * q^13 + 4 * q^15 + 20 * q^16 - 8 * q^18 - 16 * q^19 + 4 * q^21 - 8 * q^22 + 8 * q^24 - 48 * q^27 + 8 * q^28 + 36 * q^31 + 12 * q^33 + 16 * q^34 - 12 * q^36 - 64 * q^37 - 60 * q^39 + 40 * q^40 - 12 * q^42 + 8 * q^45 - 32 * q^46 + 48 * q^49 + 24 * q^52 - 28 * q^54 + 8 * q^55 - 76 * q^57 - 28 * q^58 + 4 * q^60 - 40 * q^61 + 80 * q^63 + 40 * q^66 - 28 * q^67 - 36 * q^69 + 16 * q^70 + 16 * q^72 + 8 * q^73 - 16 * q^76 - 28 * q^78 + 40 * q^79 + 12 * q^81 + 20 * q^84 + 44 * q^85 + 40 * q^87 + 12 * q^88 + 120 * q^91 - 8 * q^93 - 16 * q^94 + 4 * q^96 - 160 * q^97 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.192053	+	1.72137i	−0.110882	+	0.993834i
$3$	−0.192053	+	1.72137i	−0.110882	+	0.993834i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	0.260015	+	1.71242i	0.106151	+	0.699094i
$7$	−0.213554	+	0.796995i	−0.0807159	+	0.301236i	−0.994469	−	0.105035i	$-0.966504\pi$
$7$	−0.213554	+	0.796995i	−0.0807159	+	0.301236i	0.913753	+	0.406271i	$0.133171\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.92623	−	0.661187i	−0.975411	−	0.220396i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	0.981698	+	3.66375i	0.295993	+	1.10466i	0.940426	+	0.340000i	$0.110427\pi$
$11$	0.981698	+	3.66375i	0.295993	+	1.10466i	−0.644433	+	0.764661i	$0.722906\pi$
$12$	0.694363	+	1.58678i	0.200445	+	0.458063i
$13$	3.42697	+	1.12067i	0.950469	+	0.310819i
$13$	3.42697	+	1.12067i	0.950469	+	0.310819i
$14$			0.825110i			0.220520i
$15$	−1.35299	+	1.08139i	−0.349342	+	0.279214i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.49980	−	2.59772i	−0.363754	−	0.630040i	0.624822	−	0.780768i	$-0.285172\pi$
$17$	−1.49980	−	2.59772i	−0.363754	−	0.630040i	−0.988575	+	0.150727i	$0.951838\pi$
$18$	−2.99765	+	0.118707i	−0.706553	+	0.0279795i
$19$	1.17350	+	0.314438i	0.269219	+	0.0721370i	0.390903	−	0.920432i	$-0.372163\pi$
$19$	1.17350	+	0.314438i	0.269219	+	0.0721370i	−0.121684	+	0.992569i	$0.538829\pi$
$20$	0.965926	+	0.258819i	0.215988	+	0.0578737i
$21$	−1.33091	−	0.520671i	−0.290428	−	0.113620i
$22$	1.89649	+	3.28482i	0.404334	+	0.700327i
$23$	−1.76190	+	3.05169i	−0.367381	+	0.636322i	−0.989155	−	0.146874i	$-0.953079\pi$
$23$	−1.76190	+	3.05169i	−0.367381	+	0.636322i	0.621775	+	0.783196i	$0.286412\pi$
$24$	1.08139	+	1.35299i	0.220738	+	0.276179i
$25$			1.00000i			0.200000i
$26$	3.60025	+	0.195522i	0.706066	+	0.0383451i
$27$	1.70014	−	4.91015i	0.327192	−	0.944958i
$28$	0.213554	+	0.796995i	0.0403580	+	0.150618i
$29$	−6.48200	−	3.74239i	−1.20368	−	0.694943i	−0.242306	−	0.970200i	$-0.577904\pi$
$29$	−6.48200	−	3.74239i	−1.20368	−	0.694943i	−0.961371	+	0.275256i	$0.911237\pi$
$30$	−1.02701	+	1.39472i	−0.187505	+	0.254641i
$31$	0.00278407	−	0.00278407i	0.000500034	−	0.000500034i	−0.706857	−	0.707357i	$-0.749887\pi$
$31$	0.00278407	−	0.00278407i	0.000500034	−	0.000500034i	0.707357	+	0.706857i	$0.249887\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−6.49520	+	0.986234i	−1.13067	+	0.171681i
$34$	−2.12103	−	2.12103i	−0.363754	−	0.363754i
$35$	−0.714566	+	0.412555i	−0.120784	+	0.0697345i
$36$	−2.86478	+	0.890511i	−0.477464	+	0.148419i
$37$	10.9895	−	2.94462i	1.80666	−	0.484093i	0.811673	−	0.584112i	$-0.198557\pi$
$37$	10.9895	−	2.94462i	1.80666	−	0.484093i	0.994985	+	0.100020i	$0.0318906\pi$
$38$	1.21489			0.197082
$39$	−2.58725	+	5.68385i	−0.414291	+	0.910144i
$40$	1.00000			0.158114
$41$	−4.61510	+	1.23661i	−0.720757	+	0.193126i	−0.600509	−	0.799618i	$-0.705035\pi$
$41$	−4.61510	+	1.23661i	−0.720757	+	0.193126i	−0.120247	+	0.992744i	$0.538369\pi$
$42$	−1.42032	−	0.158464i	−0.219160	−	0.0244516i
$43$	3.40698	−	1.96702i	0.519560	−	0.299968i	−0.217195	−	0.976128i	$-0.569691\pi$
$43$	3.40698	−	1.96702i	0.519560	−	0.299968i	0.736755	+	0.676160i	$0.236357\pi$
$44$	2.68205	+	2.68205i	0.404334	+	0.404334i
$45$	−1.60163	−	2.53669i	−0.238757	−	0.378147i
$46$	−0.912024	+	3.40372i	−0.134471	+	0.501851i
$47$	7.01463	−	7.01463i	1.02319	−	1.02319i	0.0234640	−	0.999725i	$-0.492530\pi$
$47$	7.01463	−	7.01463i	1.02319	−	1.02319i	0.999725	−	0.0234640i	$-0.00746952\pi$
$48$	1.39472	+	1.02701i	0.201311	+	0.148236i
$49$	5.47258	+	3.15960i	0.781797	+	0.451371i
$50$	0.258819	+	0.965926i	0.0366025	+	0.136603i
$51$	4.75968	−	2.08280i	0.666489	−	0.291651i
$52$	3.52818	−	0.742952i	0.489270	−	0.103029i
$53$		−	4.90674i		−	0.673992i	−0.941506	−	0.336996i	$-0.890589\pi$
$53$		−	4.90674i		−	0.673992i	0.941506	−	0.336996i	$-0.109411\pi$
$54$	0.371368	−	5.18286i	0.0505367	−	0.705299i
$55$	−1.89649	+	3.28482i	−0.255723	+	0.442926i
$56$	0.412555	+	0.714566i	0.0551300	+	0.0954880i
$57$	−0.766637	+	1.95964i	−0.101544	+	0.259560i
$58$	−7.22973	−	1.93720i	−0.949310	−	0.254367i
$59$	−4.67330	−	1.25221i	−0.608412	−	0.163024i	−0.0585576	−	0.998284i	$-0.518650\pi$
$59$	−4.67330	−	1.25221i	−0.608412	−	0.163024i	−0.549854	+	0.835261i	$0.685317\pi$
$60$	−0.631032	+	1.61301i	−0.0814659	+	0.208239i
$61$	−6.87481	−	11.9075i	−0.880230	−	1.52460i	−0.851085	−	0.525027i	$-0.824055\pi$
$61$	−6.87481	−	11.9075i	−0.880230	−	1.52460i	−0.0291445	−	0.999575i	$-0.509278\pi$
$62$	0.00196864	−	0.00340978i	0.000250017	−	0.000433042i
$63$	1.15187	−	2.19099i	0.145122	−	0.276039i
$64$		−	1.00000i		−	0.125000i
$65$	1.63080	+	3.21567i	0.202275	+	0.398854i
$66$	−6.01863	+	2.63371i	−0.740842	+	0.324187i
$67$	−3.00389	−	11.2107i	−0.366984	−	1.36960i	−0.864711	−	0.502269i	$-0.832499\pi$
$67$	−3.00389	−	11.2107i	−0.366984	−	1.36960i	0.497727	−	0.867334i	$-0.334168\pi$
$68$	−2.59772	−	1.49980i	−0.315020	−	0.181877i
$69$	−4.91472	−	3.61896i	−0.591662	−	0.435672i
$70$	−0.583441	+	0.583441i	−0.0697345	+	0.0697345i
$71$	−1.52747	+	5.70060i	−0.181277	+	0.676537i	0.814119	+	0.580698i	$0.197220\pi$
$71$	−1.52747	+	5.70060i	−0.181277	+	0.676537i	−0.995397	+	0.0958392i	$0.969447\pi$
$72$	−2.53669	+	1.60163i	−0.298952	+	0.188754i
$73$	−8.49044	−	8.49044i	−0.993730	−	0.993730i	0.00625000	−	0.999980i	$-0.498011\pi$
$73$	−8.49044	−	8.49044i	−0.993730	−	0.993730i	−0.999980	+	0.00625000i	$0.998011\pi$
$74$	9.85289	−	5.68857i	1.14538	−	0.661283i
$75$	−1.72137	−	0.192053i	−0.198767	−	0.0221763i
$76$	1.17350	−	0.314438i	0.134609	−	0.0360685i
$77$	−3.12963			−0.356655
$78$	−1.02800	+	6.15981i	−0.116398	+	0.697461i
$79$	5.90955			0.664877			0.332438	−	0.943125i	$-0.392129\pi$
$79$	5.90955			0.664877			0.332438	+	0.943125i	$0.392129\pi$
$80$	0.965926	−	0.258819i	0.107994	−	0.0289368i
$81$	8.12566	+	3.86957i	0.902852	+	0.429953i
$82$	−4.13778	+	2.38895i	−0.456942	+	0.263815i
$83$	5.36244	+	5.36244i	0.588605	+	0.588605i	0.937253	−	0.348649i	$-0.113359\pi$
$83$	5.36244	+	5.36244i	0.588605	+	0.588605i	−0.348649	+	0.937253i	$0.613359\pi$
$84$	−1.41294	+	0.214541i	−0.154164	+	0.0234083i
$85$	0.776351	−	2.89738i	0.0842071	−	0.314265i
$86$	2.78179	−	2.78179i	0.299968	−	0.299968i
$87$	7.68692	−	10.4392i	0.824124	−	1.11920i
$88$	3.28482	+	1.89649i	0.350163	+	0.202167i
$89$	−1.85846	−	6.93588i	−0.196997	−	0.735202i	−0.991741	−	0.128257i	$-0.959062\pi$
$89$	−1.85846	−	6.93588i	−0.196997	−	0.735202i	0.794744	−	0.606945i	$-0.207605\pi$
$90$	−2.20360	−	2.03572i	−0.232280	−	0.214584i
$91$	−1.62501	+	2.49195i	−0.170348	+	0.261227i
$92$			3.52379i			0.367381i
$93$	0.00425773	+	0.00532711i	0.000441506	+	0.000552395i
$94$	4.96009	−	8.59113i	0.511594	−	0.886107i
$95$	0.607447	+	1.05213i	0.0623228	+	0.107946i
$96$	1.61301	+	0.631032i	0.164627	+	0.0644044i
$97$	−7.65690	−	2.05166i	−0.777440	−	0.208314i	−0.151784	−	0.988414i	$-0.548502\pi$
$97$	−7.65690	−	2.05166i	−0.777440	−	0.208314i	−0.625656	+	0.780099i	$0.715169\pi$
$98$	6.10387	+	1.63553i	0.616584	+	0.165213i
$99$	−0.450254	−	11.3701i	−0.0452522	−	1.14273i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−7.69191	+	13.3228i	−0.765374	+	1.32567i	0.174675	+	0.984626i	$0.444113\pi$
$101$	−7.69191	+	13.3228i	−0.765374	+	1.32567i	−0.940049	+	0.341041i	$0.889221\pi$
$102$	4.05843	−	3.24373i	0.401844	−	0.321177i
$103$			16.3952i			1.61547i	0.589548	+	0.807733i	$0.299306\pi$
$103$			16.3952i			1.61547i	−0.589548	+	0.807733i	$0.700694\pi$
$104$	3.21567	−	1.63080i	0.315322	−	0.159913i
$105$	−0.572926	−	1.30927i	−0.0559118	−	0.127771i
$106$	−1.26996	−	4.73954i	−0.123349	−	0.460345i
$107$	0.677545	+	0.391181i	0.0655008	+	0.0378169i	0.532393	−	0.846497i	$-0.321293\pi$
$107$	0.677545	+	0.391181i	0.0655008	+	0.0378169i	−0.466892	+	0.884314i	$0.654626\pi$
$108$	−0.982710	−	5.10238i	−0.0945614	−	0.490977i
$109$	−0.503685	+	0.503685i	−0.0482443	+	0.0482443i	−0.730817	−	0.682573i	$-0.760861\pi$
$109$	−0.503685	+	0.503685i	−0.0482443	+	0.0482443i	0.682573	+	0.730817i	$0.260861\pi$
$110$	−0.981698	+	3.66375i	−0.0936012	+	0.349324i
$111$	2.95823	+	19.4825i	0.280782	+	1.84919i
$112$	0.583441	+	0.583441i	0.0551300	+	0.0551300i
$113$	5.41625	−	3.12708i	0.509518	−	0.294170i	−0.223117	−	0.974792i	$-0.571623\pi$
$113$	5.41625	−	3.12708i	0.509518	−	0.294170i	0.732636	+	0.680621i	$0.238290\pi$
$114$	−0.233324	+	2.09128i	−0.0218528	+	0.195867i
$115$	−3.40372	+	0.912024i	−0.317399	+	0.0850467i
$116$	−7.48477			−0.694943
$117$	−9.28712	−	5.54521i	−0.858595	−	0.512655i
$118$	−4.83816			−0.445389
$119$	2.39066	−	0.640575i	0.219151	−	0.0587215i
$120$	−0.192053	+	1.72137i	−0.0175319	+	0.157139i
$121$	−2.93302	+	1.69338i	−0.266638	+	0.153944i
$122$	−9.72246	−	9.72246i	−0.880230	−	0.880230i
$123$	−1.24233	−	8.18178i	−0.112017	−	0.737727i
$124$	0.00101904	−	0.00380311i	9.15126e−5	−	0.000341530i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	0.545552	−	2.41446i	0.0486016	−	0.215098i
$127$	0.683797	+	0.394790i	0.0606771	+	0.0350320i	0.530032	−	0.847978i	$-0.322180\pi$
$127$	0.683797	+	0.394790i	0.0606771	+	0.0350320i	−0.469355	+	0.883010i	$0.655513\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	2.73165	+	6.24245i	0.240509	+	0.549617i
$130$	2.40750	+	2.68401i	0.211152	+	0.235404i
$131$		−	0.615603i		−	0.0537854i	−0.999638	−	0.0268927i	$-0.991439\pi$
$131$		−	0.615603i		−	0.0537854i	0.999638	−	0.0268927i	$-0.00856125\pi$
$132$	−5.13189	+	4.10170i	−0.446674	+	0.357007i
$133$	−0.501211	+	0.868123i	−0.0434605	+	0.0752758i
$134$	−5.80308	−	10.0512i	−0.501309	−	0.868293i
$135$	4.67418	−	2.26982i	0.402289	−	0.195355i
$136$	−2.89738	−	0.776351i	−0.248448	−	0.0665716i
$137$	−10.3607	−	2.77613i	−0.885172	−	0.237181i	−0.212534	−	0.977154i	$-0.568172\pi$
$137$	−10.3607	−	2.77613i	−0.885172	−	0.237181i	−0.672637	+	0.739973i	$0.734838\pi$
$138$	−5.68391	−	2.22362i	−0.483846	−	0.189287i
$139$	11.5899	+	20.0743i	0.983042	+	1.70268i	0.650331	+	0.759651i	$0.274630\pi$
$139$	11.5899	+	20.0743i	0.983042	+	1.70268i	0.332711	+	0.943029i	$0.392037\pi$
$140$	−0.412555	+	0.714566i	−0.0348673	+	0.0603919i
$141$	10.7276	+	13.4220i	0.903427	+	1.13033i
$142$			5.90170i			0.495259i
$143$	−0.741614	+	13.6557i	−0.0620168	+	1.14195i
$144$	−2.03572	+	2.20360i	−0.169643	+	0.183633i
$145$	−1.93720	−	7.22973i	−0.160876	−	0.600397i
$146$	−10.3986	−	6.00365i	−0.860596	−	0.496865i
$147$	−6.48986	+	8.81353i	−0.535275	+	0.726928i
$148$	8.04485	−	8.04485i	0.661283	−	0.661283i
$149$	−1.19718	+	4.46795i	−0.0980772	+	0.366029i	−0.997468	−	0.0711164i	$-0.977344\pi$
$149$	−1.19718	+	4.46795i	−0.0980772	+	0.366029i	0.899391	+	0.437145i	$0.144010\pi$
$150$	−1.71242	+	0.260015i	−0.139819	+	0.0212301i
$151$	−5.26555	−	5.26555i	−0.428504	−	0.428504i	0.459614	−	0.888119i	$-0.347988\pi$
$151$	−5.26555	−	5.26555i	−0.428504	−	0.428504i	−0.888119	+	0.459614i	$0.847988\pi$
$152$	1.05213	−	0.607447i	0.0853390	−	0.0492705i
$153$	2.67117	+	8.59318i	0.215951	+	0.694718i
$154$	−3.02299	+	0.810009i	−0.243600	+	0.0652724i
$155$	0.00393727			0.000316249
$156$	0.601301	+	6.21598i	0.0481426	+	0.497677i
$157$	4.36770			0.348580			0.174290	−	0.984694i	$-0.444237\pi$
$157$	4.36770			0.348580			0.174290	+	0.984694i	$0.444237\pi$
$158$	5.70819	−	1.52950i	0.454119	−	0.121681i
$159$	8.44631	+	0.942351i	0.669836	+	0.0747333i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−2.05592	−	2.05592i	−0.162030	−	0.162030i
$162$	8.85031	+	1.63464i	0.695346	+	0.128430i
$163$	1.31903	−	4.92267i	0.103314	−	0.385574i	−0.894834	−	0.446398i	$-0.852706\pi$
$163$	1.31903	−	4.92267i	0.103314	−	0.385574i	0.998148	+	0.0608248i	$0.0193731\pi$
$164$	−3.37848	+	3.37848i	−0.263815	+	0.263815i
$165$	−5.29017	−	3.89543i	−0.411839	−	0.303259i
$166$	6.56762	+	3.79182i	0.509747	+	0.294302i
$167$	−2.38628	−	8.90571i	−0.184656	−	0.689144i	−0.994704	−	0.102781i	$-0.967226\pi$
$167$	−2.38628	−	8.90571i	−0.184656	−	0.689144i	0.810048	−	0.586363i	$-0.199441\pi$
$168$	−1.30927	+	0.572926i	−0.101012	+	0.0442022i
$169$	10.4882	+	7.68101i	0.806784	+	0.590847i
$170$		−	2.99959i		−	0.230058i
$171$	−3.22603	−	1.69602i	−0.246700	−	0.129698i
$172$	1.96702	−	3.40698i	0.149984	−	0.259780i
$173$	2.74926	+	4.76186i	0.209023	+	0.362038i	0.951407	−	0.307937i	$-0.0996384\pi$
$173$	2.74926	+	4.76186i	0.209023	+	0.362038i	−0.742384	+	0.669974i	$0.766305\pi$
$174$	4.72313	−	12.0730i	0.358059	−	0.915252i
$175$	−0.796995	−	0.213554i	−0.0602472	−	0.0161432i
$176$	3.66375	+	0.981698i	0.276165	+	0.0739982i
$177$	3.05303	−	7.80399i	0.229480	−	0.586584i
$178$	−3.59028	−	6.21854i	−0.269103	−	0.466100i
$179$	2.40507	−	4.16571i	0.179764	−	0.311360i	−0.762036	−	0.647535i	$-0.775800\pi$
$179$	2.40507	−	4.16571i	0.179764	−	0.311360i	0.941800	+	0.336175i	$0.109133\pi$
$180$	−2.65539	−	1.39602i	−0.197921	−	0.104053i
$181$			9.68726i			0.720048i	0.932943	+	0.360024i	$0.117232\pi$
$181$			9.68726i			0.720048i	−0.932943	+	0.360024i	$0.882768\pi$
$182$	−0.924678	+	2.82762i	−0.0685417	+	0.209597i
$183$	21.8176	−	9.54723i	1.61280	−	0.705752i
$184$	0.912024	+	3.40372i	0.0672353	+	0.250926i
$185$	9.85289	+	5.68857i	0.724399	+	0.418232i
$186$	0.00549141	+	0.00404361i	0.000402650	+	0.000296492i
$187$	8.04505	−	8.04505i	0.588312	−	0.588312i
$188$	2.56753	−	9.58216i	0.187257	−	0.698851i
$189$	3.55029	+	2.40358i	0.258246	+	0.174835i
$190$	0.859060	+	0.859060i	0.0623228	+	0.0623228i
$191$	−4.55237	+	2.62831i	−0.329398	+	0.190178i	−0.655574	−	0.755131i	$-0.727573\pi$
$191$	−4.55237	+	2.62831i	−0.329398	+	0.190178i	0.326176	+	0.945309i	$0.394240\pi$
$192$	1.72137	+	0.192053i	0.124229	+	0.0138602i
$193$	−0.170227	+	0.0456122i	−0.0122532	+	0.00328324i	−0.264940	−	0.964265i	$-0.585352\pi$
$193$	−0.170227	+	0.0456122i	−0.0122532	+	0.00328324i	0.252687	+	0.967548i	$0.418686\pi$
$194$	−7.92700			−0.569126
$195$	−5.84855	+	2.18963i	−0.418823	+	0.156802i
$196$	6.31919			0.451371
$197$	−7.06564	+	1.89323i	−0.503406	+	0.134887i	−0.501580	−	0.865111i	$-0.667248\pi$
$197$	−7.06564	+	1.89323i	−0.503406	+	0.134887i	−0.00182570	+	0.999998i	$0.500581\pi$
$198$	−3.37770	−	10.8661i	−0.240043	−	0.772220i
$199$	−16.9120	+	9.76412i	−1.19886	+	0.692160i	−0.960300	−	0.278969i	$-0.910007\pi$
$199$	−16.9120	+	9.76412i	−1.19886	+	0.692160i	−0.238556	+	0.971129i	$0.576674\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	19.8746	−	3.01777i	1.40185	−	0.212857i
$202$	−3.98163	+	14.8596i	−0.280146	+	1.04552i
$203$	4.36692	−	4.36692i	0.306498	−	0.306498i
$204$	3.08060	−	4.18360i	0.215685	−	0.292911i
$205$	−4.13778	−	2.38895i	−0.288995	−	0.166851i
$206$	4.24339	+	15.8365i	0.295651	+	1.10338i
$207$	7.17345	−	7.76502i	0.498589	−	0.539706i
$208$	2.68401	−	2.40750i	0.186103	−	0.166930i
$209$			4.60808i			0.318748i
$210$	−0.892267	−	1.11637i	−0.0615723	−	0.0770368i
$211$	−3.04589	+	5.27563i	−0.209688	+	0.363189i	−0.951616	−	0.307289i	$-0.900578\pi$
$211$	−3.04589	+	5.27563i	−0.209688	+	0.363189i	0.741929	+	0.670479i	$0.233911\pi$
$212$	−2.45337	−	4.24936i	−0.168498	−	0.291847i
$213$	−9.51949	−	3.72416i	−0.652265	−	0.255175i
$214$	0.755704	+	0.202490i	0.0516588	+	0.0138419i
$215$	3.79999	+	1.01821i	0.259157	+	0.0694410i
$216$	−2.26982	−	4.67418i	−0.154442	−	0.318037i
$217$	0.00162434	+	0.00281344i	0.000110267	+	0.000190989i
$218$	−0.356159	+	0.616886i	−0.0241221	+	0.0417808i
$219$	16.2458	−	12.9846i	1.09779	−	0.877416i
$220$			3.79299i			0.255723i
$221$	−2.22855	−	10.5831i	−0.149909	−	0.711895i
$222$	7.89986	+	18.0530i	0.530204	+	1.21164i
$223$	−2.15128	−	8.02867i	−0.144060	−	0.537640i	−0.999795	−	0.0202258i	$-0.993561\pi$
$223$	−2.15128	−	8.02867i	−0.144060	−	0.537640i	0.855735	−	0.517414i	$-0.173105\pi$
$224$	0.714566	+	0.412555i	0.0477440	+	0.0275650i
$225$	0.661187	−	2.92623i	0.0440791	−	0.195082i
$226$	4.42235	−	4.42235i	0.294170	−	0.294170i
$227$	−5.28248	+	19.7145i	−0.350611	+	1.30850i	0.535309	+	0.844657i	$0.320195\pi$
$227$	−5.28248	+	19.7145i	−0.350611	+	1.30850i	−0.885919	+	0.463840i	$0.846471\pi$
$228$	0.315891	+	2.08041i	0.0209204	+	0.137779i
$229$	−0.725435	−	0.725435i	−0.0479381	−	0.0479381i	0.682731	−	0.730669i	$-0.260792\pi$
$229$	−0.725435	−	0.725435i	−0.0479381	−	0.0479381i	−0.730669	+	0.682731i	$0.760792\pi$
$230$	−3.05169	+	1.76190i	−0.201223	+	0.116176i
$231$	0.601054	−	5.38726i	0.0395465	−	0.354456i
$232$	−7.22973	+	1.93720i	−0.474655	+	0.127183i
$233$	11.6818			0.765300			0.382650	−	0.923893i	$-0.375012\pi$
$233$	11.6818			0.765300			0.382650	+	0.923893i	$0.375012\pi$
$234$	−10.4059	−	2.95258i	−0.680253	−	0.193016i
$235$	9.92018			0.647121
$236$	−4.67330	+	1.25221i	−0.304206	+	0.0815118i
$237$	−1.13494	+	10.1725i	−0.0737226	+	0.660777i
$238$	2.14341	−	1.23750i	0.138936	−	0.0802150i
$239$	14.3879	+	14.3879i	0.930674	+	0.930674i	0.997748	−	0.0670742i	$-0.0213664\pi$
$239$	14.3879	+	14.3879i	0.930674	+	0.930674i	−0.0670742	+	0.997748i	$0.521366\pi$
$240$	0.260015	+	1.71242i	0.0167839	+	0.110536i
$241$	−4.66870	+	17.4238i	−0.300738	+	1.12237i	0.635815	+	0.771841i	$0.280664\pi$
$241$	−4.66870	+	17.4238i	−0.300738	+	1.12237i	−0.936553	+	0.350527i	$0.886003\pi$
$242$	−2.39480	+	2.39480i	−0.153944	+	0.153944i
$243$	−8.22152	+	13.2441i	−0.527411	+	0.849610i
$244$	−11.9075	−	6.87481i	−0.762301	−	0.440115i
$245$	1.63553	+	6.10387i	0.104490	+	0.389962i
$246$	−3.31760	−	7.58146i	−0.211522	−	0.483376i
$247$	3.66916	+	2.39267i	0.233463	+	0.152242i
$248$		−	0.00393727i		−	0.000250017i
$249$	−10.2606	+	8.20088i	−0.650240	+	0.519710i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−14.7378	−	25.5266i	−0.930242	−	1.61123i	−0.782906	−	0.622139i	$-0.786264\pi$
$251$	−14.7378	−	25.5266i	−0.930242	−	1.61123i	−0.147335	−	0.989087i	$-0.547070\pi$
$252$	−0.0979463	−	2.47339i	−0.00617004	−	0.155809i
$253$	−12.9103	−	3.45930i	−0.811662	−	0.217484i
$254$	0.762676	+	0.204358i	0.0478546	+	0.0128226i
$255$	4.83837	+	1.89284i	0.302990	+	0.118534i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.45733	−	11.1844i	0.402797	−	0.697665i	−0.591265	−	0.806477i	$-0.701371\pi$
$257$	6.45733	−	11.1844i	0.402797	−	0.697665i	0.994062	+	0.108812i	$0.0347047\pi$
$258$	4.25424	+	5.32274i	0.264857	+	0.331379i
$259$			9.38739i			0.583304i
$260$	3.02014	+	1.96945i	0.187301	+	0.122140i
$261$	16.4934	+	15.2369i	1.02092	+	0.943140i
$262$	−0.159330	−	0.594626i	−0.00984342	−	0.0367361i
$263$	23.8997	+	13.7985i	1.47372	+	0.850850i	0.999562	−	0.0295919i	$-0.00942077\pi$
$263$	23.8997	+	13.7985i	1.47372	+	0.850850i	0.474154	+	0.880442i	$0.342754\pi$
$264$	−3.89543	+	5.29017i	−0.239747	+	0.325588i
$265$	3.46959	−	3.46959i	0.213135	−	0.213135i
$266$	−0.259446	+	0.968265i	−0.0159077	+	0.0593682i
$267$	12.2961	−	1.86705i	0.752512	−	0.114262i
$268$	−8.20679	−	8.20679i	−0.501309	−	0.501309i
$269$	−18.1139	+	10.4581i	−1.10442	+	0.637639i	−0.937379	−	0.348310i	$-0.886756\pi$
$269$	−18.1139	+	10.4581i	−1.10442	+	0.637639i	−0.167044	+	0.985949i	$0.553422\pi$
$270$	3.92744	−	3.40224i	0.239016	−	0.207054i
$271$	−15.0716	+	4.03842i	−0.915534	+	0.245316i	−0.685675	−	0.727908i	$-0.740493\pi$
$271$	−15.0716	+	4.03842i	−0.915534	+	0.245316i	−0.229858	+	0.973224i	$0.573826\pi$
$272$	−2.99959			−0.181877
$273$	−3.97748	−	3.27584i	−0.240728	−	0.198263i
$274$	−10.7262			−0.647991
$275$	−3.66375	+	0.981698i	−0.220932	+	0.0591986i
$276$	−6.06575	−	0.676753i	−0.365115	−	0.0407357i
$277$	−21.0524	+	12.1546i	−1.26492	+	0.730301i	−0.974022	−	0.226453i	$-0.927287\pi$
$277$	−21.0524	+	12.1546i	−1.26492	+	0.730301i	−0.290897	+	0.956754i	$0.593954\pi$
$278$	16.3906	+	16.3906i	0.983042	+	0.983042i
$279$	−0.00998763	+	0.00630605i	−0.000597944	+	0.000377533i
$280$	−0.213554	+	0.796995i	−0.0127623	+	0.0476296i
$281$	16.7143	−	16.7143i	0.997090	−	0.997090i	−0.00290627	−	0.999996i	$-0.500925\pi$
$281$	16.7143	−	16.7143i	0.997090	−	0.997090i	0.999996	+	0.00290627i	$0.000925096\pi$
$282$	13.8359	+	10.1881i	0.823917	+	0.606693i
$283$	19.5493	+	11.2868i	1.16208	+	0.670930i	0.951803	−	0.306711i	$-0.0992285\pi$
$283$	19.5493	+	11.2868i	1.16208	+	0.670930i	0.210282	+	0.977641i	$0.432562\pi$
$284$	1.52747	+	5.70060i	0.0906387	+	0.338268i
$285$	−1.92777	+	0.843578i	−0.114191	+	0.0499692i
$286$	2.81801	+	13.3823i	0.166632	+	0.791314i
$287$		−	3.94229i		−	0.232706i
$288$	−1.39602	+	2.65539i	−0.0822614	+	0.156471i
$289$	4.00123	−	6.93033i	0.235366	−	0.407666i
$290$	−3.74239	−	6.48200i	−0.219760	−	0.380636i
$291$	5.00219	−	12.7863i	0.293234	−	0.749548i
$292$	−11.5982	−	3.10772i	−0.678731	−	0.181865i
$293$	−27.9435	−	7.48743i	−1.63247	−	0.437420i	−0.677843	−	0.735207i	$-0.737085\pi$
$293$	−27.9435	−	7.48743i	−1.63247	−	0.437420i	−0.954632	+	0.297787i	$0.903752\pi$
$294$	−3.98761	+	10.1929i	−0.232562	+	0.594463i
$295$	−2.41908	−	4.18997i	−0.140844	−	0.243949i
$296$	5.68857	−	9.85289i	0.330641	−	0.572688i
$297$	19.6585	+	1.40859i	1.14070	+	0.0817349i
$298$			4.62556i			0.267952i
$299$	−9.45790	+	8.48354i	−0.546965	+	0.490616i
$300$	−1.58678	+	0.694363i	−0.0916126	+	0.0400891i
$301$	0.840132	+	3.13541i	0.0484244	+	0.180722i
$302$	−6.44895	−	3.72330i	−0.371095	−	0.214252i
$303$	−21.4562	−	15.7993i	−1.23263	−	0.907647i
$304$	0.859060	−	0.859060i	0.0492705	−	0.0492705i
$305$	3.55867	−	13.2811i	0.203769	−	0.760475i
$306$	4.80423	+	7.60903i	0.274640	+	0.434979i
$307$	−5.27808	−	5.27808i	−0.301236	−	0.301236i	0.540261	−	0.841497i	$-0.318325\pi$
$307$	−5.27808	−	5.27808i	−0.301236	−	0.301236i	−0.841497	+	0.540261i	$0.818325\pi$
$308$	−2.71034	+	1.56482i	−0.154436	+	0.0891637i
$309$	−28.2222	−	3.14874i	−1.60550	−	0.179125i
$310$	0.00380311	−	0.00101904i	0.000216002	−	5.78776e-5i
$311$	−17.2916			−0.980516			−0.490258	−	0.871577i	$-0.663097\pi$
$311$	−17.2916			−0.980516			−0.490258	+	0.871577i	$0.663097\pi$
$312$	2.18963	+	5.84855i	0.123963	+	0.331109i
$313$	−3.71423			−0.209941			−0.104970	−	0.994475i	$-0.533475\pi$
$313$	−3.71423			−0.209941			−0.104970	+	0.994475i	$0.533475\pi$
$314$	4.21887	−	1.13044i	0.238085	−	0.0637946i
$315$	2.36376	−	0.734770i	0.133183	−	0.0413996i
$316$	5.11782	−	2.95478i	0.287900	−	0.166219i
$317$	11.8820	+	11.8820i	0.667358	+	0.667358i	0.957104	−	0.289746i	$-0.0935708\pi$
$317$	11.8820	+	11.8820i	0.667358	+	0.667358i	−0.289746	+	0.957104i	$0.593571\pi$
$318$	8.40241	−	1.27582i	0.471184	−	0.0715447i
$319$	7.34778	−	27.4223i	0.411397	−	1.53535i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$	−0.803492	+	1.09118i	−0.0448465	+	0.0609037i
$322$	−2.51798	−	1.45376i	−0.140322	−	0.0810148i
$323$	−0.943185	−	3.52001i	−0.0524802	−	0.195859i
$324$	8.97182	−	0.711684i	0.498434	−	0.0395380i
$325$	−1.12067	+	3.42697i	−0.0621637	+	0.190094i
$326$		−	5.09633i		−	0.282259i
$327$	−0.770294	−	0.963762i	−0.0425974	−	0.0532962i
$328$	−2.38895	+	4.13778i	−0.131908	+	0.228471i
$329$	4.09262	+	7.08863i	0.225634	+	0.390809i
$330$	−6.11813	−	2.39350i	−0.336792	−	0.131758i
$331$	−18.7857	−	5.03361i	−1.03256	−	0.276672i	−0.297531	−	0.954712i	$-0.596163\pi$
$331$	−18.7857	−	5.03361i	−1.03256	−	0.276672i	−0.735025	+	0.678040i	$0.762830\pi$
$332$	7.32523	+	1.96279i	0.402024	+	0.107722i
$333$	−34.1047	+	1.35055i	−1.86893	+	0.0740094i
$334$	−4.60993	−	7.98464i	−0.252244	−	0.436900i
$335$	5.80308	−	10.0512i	0.317056	−	0.549157i
$336$	−1.11637	+	0.892267i	−0.0609029	+	0.0486771i
$337$			29.4143i			1.60230i	0.598465	+	0.801149i	$0.295777\pi$
$337$			29.4143i			1.60230i	−0.598465	+	0.801149i	$0.704223\pi$
$338$	12.1188	+	4.70474i	0.659176	+	0.255904i
$339$	4.34265	+	9.92394i	0.235860	+	0.538994i
$340$	−0.776351	−	2.89738i	−0.0421036	−	0.157133i
$341$	0.0129332	+	0.00746701i	0.000700375	+	0.000404361i
$342$	−3.55506	−	0.803273i	−0.192236	−	0.0434360i
$343$	−7.77096	+	7.77096i	−0.419593	+	0.419593i
$344$	1.01821	−	3.79999i	0.0548980	−	0.204882i
$345$	−0.916238	−	6.03422i	−0.0493286	−	0.324871i
$346$	3.88804	+	3.88804i	0.209023	+	0.209023i
$347$	18.3677	−	10.6046i	0.986030	−	0.569285i	0.0819448	−	0.996637i	$-0.473887\pi$
$347$	18.3677	−	10.6046i	0.986030	−	0.569285i	0.904085	+	0.427352i	$0.140554\pi$
$348$	1.43747	−	12.8841i	0.0770564	−	0.690658i
$349$	−15.5273	+	4.16053i	−0.831157	+	0.222708i	−0.649218	−	0.760602i	$-0.724904\pi$
$349$	−15.5273	+	4.16053i	−0.831157	+	0.222708i	−0.181939	+	0.983310i	$0.558237\pi$
$350$	−0.825110			−0.0441040
$351$	11.3290	−	14.9216i	0.604696	−	0.796456i
$352$	3.79299			0.202167
$353$	31.5613	−	8.45683i	1.67984	−	0.450112i	0.712103	−	0.702075i	$-0.247743\pi$
$353$	31.5613	−	8.45683i	1.67984	−	0.450112i	0.967737	+	0.251963i	$0.0810762\pi$
$354$	0.929180	−	8.32826i	0.0493854	−	0.442642i
$355$	−5.11102	+	2.95085i	−0.271265	+	0.156615i
$356$	−5.07742	−	5.07742i	−0.269103	−	0.269103i
$357$	0.643535	+	4.23824i	0.0340595	+	0.224311i
$358$	1.24496	−	4.64624i	0.0657980	−	0.245562i
$359$	4.78448	−	4.78448i	0.252515	−	0.252515i	−0.569486	−	0.822001i	$-0.692858\pi$
$359$	4.78448	−	4.78448i	0.252515	−	0.252515i	0.822001	+	0.569486i	$0.192858\pi$
$360$	−2.92623	−	0.661187i	−0.154226	−	0.0348476i
$361$	−15.1763	−	8.76202i	−0.798750	−	0.461159i
$362$	2.50725	+	9.35718i	0.131778	+	0.491802i
$363$	−2.35164	−	5.37404i	−0.123429	−	0.282064i
$364$	−0.161327	+	2.97060i	−0.00845585	+	0.155702i
$365$		−	12.0073i		−	0.628490i
$366$	18.6032	−	14.8687i	0.972403	−	0.777201i
$367$	6.73485	−	11.6651i	0.351556	−	0.608913i	−0.634966	−	0.772540i	$-0.718986\pi$
$367$	6.73485	−	11.6651i	0.351556	−	0.608913i	0.986522	+	0.163627i	$0.0523192\pi$
$368$	1.76190	+	3.05169i	0.0918451	+	0.159080i
$369$	14.3225	−	0.567170i	0.745598	−	0.0295257i
$370$	10.9895	+	2.94462i	0.571315	+	0.153084i
$371$	3.91065	+	1.04785i	0.203031	+	0.0544019i
$372$	0.00635086	+	0.00248454i	0.000329277	+	0.000128818i
$373$	−17.0360	−	29.5072i	−0.882089	−	1.52782i	−0.849014	−	0.528370i	$-0.822804\pi$
$373$	−17.0360	−	29.5072i	−0.882089	−	1.52782i	−0.0330743	−	0.999453i	$-0.510530\pi$
$374$	5.68871	−	9.85313i	0.294156	−	0.509493i
$375$	−1.08139	−	1.35299i	−0.0558428	−	0.0698683i
$376$		−	9.92018i		−	0.511594i
$377$	−18.0196	−	20.0892i	−0.928057	−	1.03465i
$378$	4.05141	+	1.40280i	0.208382	+	0.0721523i
$379$	−6.18511	−	23.0832i	−0.317708	−	1.18570i	−0.921442	−	0.388516i	$-0.872988\pi$
$379$	−6.18511	−	23.0832i	−0.317708	−	1.18570i	0.603734	−	0.797186i	$-0.293679\pi$
$380$	1.05213	+	0.607447i	0.0539731	+	0.0311614i
$381$	−0.810905	+	1.10125i	−0.0415439	+	0.0564186i
$382$	−3.71699	+	3.71699i	−0.190178	+	0.190178i
$383$	−5.87449	+	21.9239i	−0.300172	+	1.12026i	0.636850	+	0.770988i	$0.280237\pi$
$383$	−5.87449	+	21.9239i	−0.300172	+	1.12026i	−0.937022	+	0.349270i	$0.886430\pi$
$384$	1.71242	−	0.260015i	0.0873867	−	0.0132688i
$385$	−2.21299	−	2.21299i	−0.112784	−	0.112784i
$386$	−0.152621	+	0.0881160i	−0.00776822	+	0.00448499i
$387$	−11.2702	+	3.50331i	−0.572896	+	0.178083i
$388$	−7.65690	+	2.05166i	−0.388720	+	0.104157i
$389$	9.80108			0.496934			0.248467	−	0.968640i	$-0.420073\pi$
$389$	9.80108			0.496934			0.248467	+	0.968640i	$0.420073\pi$
$390$	−5.08255	+	3.62873i	−0.257365	+	0.183748i
$391$	10.5699			0.534544
$392$	6.10387	−	1.63553i	0.308292	−	0.0826066i
$393$	1.05968	+	0.118228i	0.0534538	+	0.00596381i
$394$	−6.33488	+	3.65744i	−0.319147	+	0.184259i
$395$	4.17869	+	4.17869i	0.210252	+	0.210252i
$396$	−6.07496	−	9.62163i	−0.305278	−	0.483505i
$397$	6.48832	−	24.2147i	0.325640	−	1.21530i	−0.588028	−	0.808841i	$-0.700095\pi$
$397$	6.48832	−	24.2147i	0.325640	−	1.21530i	0.913667	−	0.406463i	$-0.133238\pi$
$398$	−13.8085	+	13.8085i	−0.692160	+	0.692160i
$399$	−1.39810	−	1.02950i	−0.0699927	−	0.0515392i
$400$	0.866025	+	0.500000i	0.0433013	+	0.0250000i
$401$	−8.23082	−	30.7179i	−0.411028	−	1.53398i	−0.792661	−	0.609663i	$-0.791305\pi$
$401$	−8.23082	−	30.7179i	−0.411028	−	1.53398i	0.381633	−	0.924314i	$-0.375362\pi$
$402$	18.4164	−	8.05888i	0.918525	−	0.401940i
$403$	0.0126609	−	0.00642089i	0.000630687	−	0.000319847i
$404$			15.3838i			0.765374i
$405$	3.00951	+	8.48191i	0.149544	+	0.421470i
$406$	3.08788	−	5.34837i	0.153249	−	0.265435i
$407$	21.5767	+	37.3719i	1.06952	+	1.85246i
$408$	1.89284	−	4.83837i	0.0937094	−	0.239535i
$409$	21.7307	+	5.82273i	1.07451	+	0.287915i	0.752347	−	0.658767i	$-0.228922\pi$
$409$	21.7307	+	5.82273i	1.07451	+	0.287915i	0.322168	+	0.946683i	$0.395588\pi$
$410$	−4.61510	−	1.23661i	−0.227923	−	0.0610719i
$411$	6.76854	−	17.3014i	0.333868	−	0.853414i
$412$	8.19760	+	14.1987i	0.403867	+	0.699518i
$413$	1.99601	−	3.45719i	0.0982171	−	0.170117i
$414$	4.91929	−	9.35706i	0.241770	−	0.459874i
$415$			7.58364i			0.372266i
$416$	1.96945	−	3.02014i	0.0965602	−	0.148075i
$417$	−36.7812	+	16.0952i	−1.80118	+	0.788185i
$418$	1.19266	+	4.45107i	0.0583349	+	0.217709i
$419$	−16.2904	−	9.40527i	−0.795838	−	0.459477i	0.0461757	−	0.998933i	$-0.485297\pi$
$419$	−16.2904	−	9.40527i	−0.795838	−	0.459477i	−0.842014	+	0.539456i	$0.818630\pi$
$420$	−1.15080	−	0.847394i	−0.0561533	−	0.0413486i
$421$	22.9593	−	22.9593i	1.11897	−	1.11897i	0.127075	−	0.991893i	$-0.459441\pi$
$421$	22.9593	−	22.9593i	1.11897	−	1.11897i	0.991893	−	0.127075i	$-0.0405590\pi$
$422$	−1.57667	+	5.88420i	−0.0767510	+	0.286439i
$423$	−25.1644	+	15.8884i	−1.22354	+	0.772523i
$424$	−3.46959	−	3.46959i	−0.168498	−	0.168498i
$425$	2.59772	−	1.49980i	0.126008	−	0.0727508i
$426$	−10.1590	−	1.13344i	−0.492205	−	0.0549151i
$427$	10.9584	−	2.93629i	0.530314	−	0.142097i
$428$	0.782362			0.0378169
$429$	−23.3641	−	3.89920i	−1.12803	−	0.188255i
$430$	3.93404			0.189716
$431$	−21.1395	+	5.66432i	−1.01825	+	0.272840i	−0.729075	−	0.684434i	$-0.760049\pi$
$431$	−21.1395	+	5.66432i	−1.01825	+	0.272840i	−0.289180	+	0.957275i	$0.593383\pi$
$432$	−3.40224	−	3.92744i	−0.163690	−	0.188959i
$433$	−5.85090	+	3.37802i	−0.281176	+	0.162337i	−0.633956	−	0.773369i	$-0.718570\pi$
$433$	−5.85090	+	3.37802i	−0.281176	+	0.162337i	0.352779	+	0.935707i	$0.385237\pi$
$434$	0.00229717	+	0.00229717i	0.000110267	+	0.000110267i
$435$	12.8171	−	1.94615i	0.614533	−	0.0933109i
$436$	−0.184361	+	0.688046i	−0.00882931	+	0.0329515i
$437$	−3.02715	+	3.02715i	−0.144808	+	0.144808i
$438$	12.3316	−	16.7469i	0.589226	−	0.800196i
$439$	−23.5242	−	13.5817i	−1.12275	−	0.648219i	−0.180648	−	0.983548i	$-0.557819\pi$
$439$	−23.5242	−	13.5817i	−1.12275	−	0.648219i	−0.942101	+	0.335329i	$0.891153\pi$
$440$	0.981698	+	3.66375i	0.0468006	+	0.174662i
$441$	−13.9250	−	12.8641i	−0.663093	−	0.612577i
$442$	−4.89172	−	9.64568i	−0.232675	−	0.458798i
$443$		−	30.5438i		−	1.45118i	−0.688126	−	0.725591i	$-0.741566\pi$
$443$		−	30.5438i		−	1.45118i	0.688126	−	0.725591i	$-0.258434\pi$
$444$	12.3031	+	15.3932i	0.583881	+	0.730529i
$445$	3.59028	−	6.21854i	0.170195	−	0.294787i
$446$	−4.15595	−	7.19831i	−0.196790	−	0.340850i
$447$	−7.46108	−	2.91888i	−0.352897	−	0.138058i
$448$	0.796995	+	0.213554i	0.0376545	+	0.0100895i
$449$	14.7387	+	3.94923i	0.695563	+	0.186376i	0.589242	−	0.807956i	$-0.299426\pi$
$449$	14.7387	+	3.94923i	0.695563	+	0.186376i	0.106321	+	0.994332i	$0.466093\pi$
$450$	−0.118707	−	2.99765i	−0.00559590	−	0.141311i
$451$	−9.06126	−	15.6946i	−0.426678	−	0.739028i
$452$	3.12708	−	5.41625i	0.147085	−	0.254759i
$453$	10.0752	−	8.05269i	0.473375	−	0.378349i
$454$			20.4099i			0.957886i
$455$	−2.91113	+	0.613018i	−0.136476	+	0.0287387i
$456$	0.843578	+	1.92777i	0.0395041	+	0.0902759i
$457$	0.951818	+	3.55223i	0.0445242	+	0.166167i	0.984608	−	0.174777i	$-0.0559203\pi$
$457$	0.951818	+	3.55223i	0.0445242	+	0.166167i	−0.940084	+	0.340943i	$0.889254\pi$
$458$	−0.888473	−	0.512960i	−0.0415156	−	0.0239690i
$459$	−15.3051	+	2.94773i	−0.714379	+	0.137588i
$460$	−2.49170	+	2.49170i	−0.116176	+	0.116176i
$461$	4.95099	−	18.4773i	0.230591	−	0.860576i	−0.749497	−	0.662008i	$-0.769704\pi$
$461$	4.95099	−	18.4773i	0.230591	−	0.860576i	0.980087	−	0.198568i	$-0.0636290\pi$
$462$	−0.813752	−	5.35926i	−0.0378591	−	0.249335i
$463$	28.1621	+	28.1621i	1.30880	+	1.30880i	0.922280	+	0.386523i	$0.126324\pi$
$463$	28.1621	+	28.1621i	1.30880	+	1.30880i	0.386523	+	0.922280i	$0.373676\pi$
$464$	−6.48200	+	3.74239i	−0.300919	+	0.173736i
$465$	−0.000756163		0.00677750i	−3.50662e−5		0.000314299i
$466$	11.2837	−	3.02347i	0.522709	−	0.140060i
$467$	−31.6851			−1.46621			−0.733105	−	0.680116i	$-0.761930\pi$
$467$	−31.6851			−1.46621			−0.733105	+	0.680116i	$0.761930\pi$
$468$	−10.8155	−	0.158733i	−0.499946	−	0.00733745i
$469$	9.57635			0.442195
$470$	9.58216	−	2.56753i	0.441992	−	0.118431i
$471$	−0.838827	+	7.51842i	−0.0386511	+	0.346431i
$472$	−4.18997	+	2.41908i	−0.192859	+	0.111347i
$473$	10.5513	+	10.5513i	0.485149	+	0.485149i
$474$	1.53657	+	10.1197i	0.0705771	+	0.464811i
$475$	−0.314438	+	1.17350i	−0.0144274	+	0.0538438i
$476$	1.75008	−	1.75008i	0.0802150	−	0.0802150i
$477$	−3.24427	+	14.3582i	−0.148545	+	0.657419i
$478$	17.6215	+	10.1738i	0.805987	+	0.465337i
$479$	−6.64561	−	24.8018i	−0.303646	−	1.13322i	−0.934105	−	0.356999i	$-0.883800\pi$
$479$	−6.64561	−	24.8018i	−0.303646	−	1.13322i	0.630459	−	0.776222i	$-0.282867\pi$
$480$	0.694363	+	1.58678i	0.0316932	+	0.0724261i
$481$	40.9605	+	2.22448i	1.86764	+	0.101428i
$482$			18.0385i			0.821631i
$483$	3.93385	−	3.14416i	0.178996	−	0.143064i
$484$	−1.69338	+	2.93302i	−0.0769719	+	0.133319i
$485$	−3.96350	−	6.86499i	−0.179973	−	0.311723i
$486$	−4.51355	+	14.9207i	−0.204739	+	0.676818i
$487$	−23.2525	−	6.23048i	−1.05367	−	0.282330i	−0.309903	−	0.950768i	$-0.600297\pi$
$487$	−23.2525	−	6.23048i	−1.05367	−	0.282330i	−0.743768	+	0.668438i	$0.766963\pi$
$488$	−13.2811	−	3.55867i	−0.601208	−	0.161093i
$489$	8.22042	+	3.21594i	0.371740	+	0.145430i
$490$	3.15960	+	5.47258i	0.142736	+	0.247226i
$491$	−5.01301	+	8.68279i	−0.226234	+	0.391849i	−0.956689	−	0.291112i	$-0.905975\pi$
$491$	−5.01301	+	8.68279i	−0.226234	+	0.391849i	0.730455	+	0.682961i	$0.239308\pi$
$492$	−5.16678	−	6.46447i	−0.232936	−	0.291441i
$493$			22.4512i			1.01115i
$494$	4.16340	+	1.36150i	0.187320	+	0.0612567i
$495$	7.72146	−	8.35822i	0.347054	−	0.375674i
$496$	−0.00101904	−	0.00380311i	−4.57563e−5	−	0.000170765i
$497$	−4.21715	−	2.43477i	−0.189165	−	0.109215i
$498$	−7.78846	+	10.5771i	−0.349009	+	0.473971i
$499$	−15.2170	+	15.2170i	−0.681206	+	0.681206i	−0.960272	−	0.279066i	$-0.909975\pi$
$499$	−15.2170	+	15.2170i	−0.681206	+	0.681206i	0.279066	+	0.960272i	$0.409975\pi$
$500$	−0.258819	+	0.965926i	−0.0115747	+	0.0431975i
$501$	15.7883	−	2.39730i	0.705370	−	0.107104i
$502$	−20.8424	−	20.8424i	−0.930242	−	0.930242i
$503$	−30.8229	+	17.7956i	−1.37433	+	0.793467i	−0.991469	−	0.130341i	$-0.958393\pi$
$503$	−30.8229	+	17.7956i	−1.37433	+	0.793467i	−0.382856	+	0.923808i	$0.625060\pi$
$504$	−0.734770	−	2.36376i	−0.0327292	−	0.105290i
$505$	−14.8596	+	3.98163i	−0.661245	+	0.177180i
$506$	−13.3657			−0.594178
$507$	−15.2361	+	16.5789i	−0.676661	+	0.736295i
$508$	0.789580			0.0350320
$509$	25.7113	−	6.88933i	1.13963	−	0.305364i	0.360830	−	0.932632i	$-0.382493\pi$
$509$	25.7113	−	6.88933i	1.13963	−	0.305364i	0.778804	+	0.627267i	$0.215827\pi$
$510$	5.16341	+	0.576079i	0.228640	+	0.0255092i
$511$	8.58001	−	4.95367i	0.379557	−	0.219137i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.53904	−	5.22746i	0.156253	−	0.230798i
$514$	3.34256	−	12.4746i	0.147434	−	0.550231i
$515$	−11.5932	+	11.5932i	−0.510855	+	0.510855i
$516$	5.48691	+	4.04029i	0.241548	+	0.177864i
$517$	32.5861	+	18.8136i	1.43313	+	0.827420i
$518$	2.42964	+	9.06753i	0.106752	+	0.398404i
$519$	−8.72493	+	3.81797i	−0.382982	+	0.167590i
$520$	3.42697	+	1.12067i	0.150282	+	0.0491447i
$521$			13.4752i			0.590358i	0.955442	+	0.295179i	$0.0953793\pi$
$521$			13.4752i			0.590358i	−0.955442	+	0.295179i	$0.904621\pi$
$522$	19.8750	+	10.4489i	0.869906	+	0.457336i
$523$	2.98474	−	5.16972i	0.130514	−	0.226056i	−0.793361	−	0.608751i	$-0.791671\pi$
$523$	2.98474	−	5.16972i	0.130514	−	0.226056i	0.923875	+	0.382695i	$0.125004\pi$
$524$	−0.307801	−	0.533127i	−0.0134464	−	0.0232898i
$525$	0.520671	−	1.33091i	0.0227239	−	0.0580857i
$526$	26.6566	+	7.14261i	1.16228	+	0.311433i
$527$	−0.0114078	−	0.00305671i	−0.000496931	−	0.000133152i
$528$	−2.39350	+	6.11813i	−0.104164	+	0.266257i
$529$	5.29145	+	9.16506i	0.230063	+	0.398481i
$530$	2.45337	−	4.24936i	0.106567	−	0.184580i
$531$	12.8472	+	6.75418i	0.557522	+	0.293106i
$532$			1.00242i			0.0434605i
$533$	−17.2016	−	0.934185i	−0.745084	−	0.0404641i
$534$	11.3939	−	4.98591i	0.493064	−	0.215761i
$535$	0.202490	+	0.755704i	0.00875441	+	0.0326719i
$536$	−10.0512	−	5.80308i	−0.434147	−	0.250655i
$537$	6.70883	+	4.94006i	0.289507	+	0.213179i
$538$	−14.7899	+	14.7899i	−0.637639	+	0.637639i
$539$	−6.20354	+	23.1519i	−0.267205	+	0.997224i
$540$	2.91305	−	4.30281i	0.125358	−	0.185163i
$541$	22.2468	+	22.2468i	0.956465	+	0.956465i	0.999091	−	0.0426256i	$-0.0135723\pi$
$541$	22.2468	+	22.2468i	0.956465	+	0.956465i	−0.0426256	+	0.999091i	$0.513572\pi$
$542$	−13.5128	+	7.80163i	−0.580425	+	0.335109i
$543$	−16.6754	−	1.86046i	−0.715608	−	0.0798401i
$544$	−2.89738	+	0.776351i	−0.124224	+	0.0332858i
$545$	−0.712318			−0.0305124
$546$	−4.68980	−	2.13477i	−0.200705	−	0.0913595i
$547$	−23.4492			−1.00261			−0.501307	−	0.865269i	$-0.667147\pi$
$547$	−23.4492			−1.00261			−0.501307	+	0.865269i	$0.667147\pi$
$548$	−10.3607	+	2.77613i	−0.442586	+	0.118590i
$549$	12.2442	+	39.3897i	0.522570	+	1.68111i
$550$	−3.28482	+	1.89649i	−0.140065	+	0.0808668i
$551$	−6.42987	−	6.42987i	−0.273922	−	0.273922i
$552$	−6.03422	+	0.916238i	−0.256833	+	0.0389977i
$553$	−1.26201	+	4.70989i	−0.0536661	+	0.200285i
$554$	−17.1892	+	17.1892i	−0.730301	+	0.730301i
$555$	−11.6844	+	15.8680i	−0.495975	+	0.673558i
$556$	20.0743	+	11.5899i	0.851340	+	0.491521i
$557$	0.216431	+	0.807730i	0.00917046	+	0.0342246i	0.970359	−	0.241666i	$-0.0776939\pi$
$557$	0.216431	+	0.807730i	0.00917046	+	0.0342246i	−0.961189	+	0.275891i	$0.911027\pi$
$558$	−0.00801519	+	0.00867616i	−0.000339310	+	0.000367291i
$559$	13.8800	−	2.92281i	0.587061	−	0.123622i
$560$			0.825110i			0.0348673i
$561$	12.3034	+	15.3936i	0.519451	+	0.649917i
$562$	11.8188	−	20.4707i	0.498545	−	0.863505i
$563$	15.1333	+	26.2117i	0.637794	+	1.10469i	0.985916	+	0.167242i	$0.0534862\pi$
$563$	15.1333	+	26.2117i	0.637794	+	1.10469i	−0.348122	+	0.937449i	$0.613180\pi$
$564$	16.0013	+	6.25995i	0.673778	+	0.263592i
$565$	6.04105	+	1.61869i	0.254149	+	0.0680989i
$566$	21.8044	+	5.84247i	0.916507	+	0.245577i
$567$	−4.81930	+	5.64975i	−0.202392	+	0.237267i
$568$	2.95085	+	5.11102i	0.123815	+	0.214454i
$569$	6.86965	−	11.8986i	0.287991	−	0.498814i	−0.685339	−	0.728224i	$-0.740346\pi$
$569$	6.86965	−	11.8986i	0.287991	−	0.498814i	0.973330	+	0.229409i	$0.0736795\pi$
$570$	−1.64375	+	1.31378i	−0.0688489	+	0.0550280i
$571$		−	26.2679i		−	1.09928i	−0.835403	−	0.549638i	$-0.814765\pi$
$571$		−	26.2679i		−	1.09928i	0.835403	−	0.549638i	$-0.185235\pi$
$572$	6.18559	+	12.1970i	0.258633	+	0.509981i
$573$	−3.65000	−	8.34108i	−0.152481	−	0.348454i
$574$	−1.02034	−	3.80796i	−0.0425882	−	0.158941i
$575$	−3.05169	−	1.76190i	−0.127264	−	0.0734761i
$576$	−0.661187	+	2.92623i	−0.0275495	+	0.121926i
$577$	17.6073	−	17.6073i	0.733000	−	0.733000i	−0.238213	−	0.971213i	$-0.576562\pi$
$577$	17.6073	−	17.6073i	0.733000	−	0.733000i	0.971213	+	0.238213i	$0.0765617\pi$
$578$	2.07119	−	7.72978i	0.0861500	−	0.321516i
$579$	−0.0458229	−	0.301784i	−0.00190434	−	0.0125417i
$580$	−5.29253	−	5.29253i	−0.219760	−	0.219760i
$581$	−5.41901	+	3.12867i	−0.224819	+	0.129799i
$582$	1.52240	−	13.6453i	0.0631056	−	0.565616i
$583$	17.9770	−	4.81693i	0.744533	−	0.199497i
$584$	−12.0073			−0.496865
$585$	−2.64593	−	10.4880i	−0.109396	−	0.433627i
$586$	−28.9292			−1.19505
$587$	6.50869	−	1.74400i	0.268643	−	0.0719826i	−0.121983	−	0.992532i	$-0.538925\pi$
$587$	6.50869	−	1.74400i	0.268643	−	0.0719826i	0.390626	+	0.920550i	$0.372259\pi$
$588$	−1.21362	+	10.8777i	−0.0500487	+	0.448588i
$589$	0.00414252	−	0.00239169i	0.000170690	−	9.85477e-5i
$590$	−3.42109	−	3.42109i	−0.140844	−	0.140844i
$591$	−1.90198	−	12.5262i	−0.0782370	−	0.515258i
$592$	2.94462	−	10.9895i	0.121023	−	0.451665i
$593$	22.4859	−	22.4859i	0.923387	−	0.923387i	−0.0738801	−	0.997267i	$-0.523538\pi$
$593$	22.4859	−	22.4859i	0.923387	−	0.923387i	0.997267	+	0.0738801i	$0.0235382\pi$
$594$	19.3533	−	3.72741i	0.794074	−	0.152937i
$595$	2.14341	+	1.23750i	0.0878711	+	0.0507324i
$596$	1.19718	+	4.46795i	0.0490386	+	0.183014i
$597$	−13.5597	−	30.9870i	−0.554961	−	1.26821i
$598$	−6.93993	+	10.6424i	−0.283795	+	0.435198i
$599$			20.4003i			0.833532i	0.909014	+	0.416766i	$0.136837\pi$
$599$			20.4003i			0.833532i	−0.909014	+	0.416766i	$0.863163\pi$
$600$	−1.35299	+	1.08139i	−0.0552358	+	0.0441476i
$601$	6.60632	−	11.4425i	0.269477	−	0.466749i	−0.699250	−	0.714878i	$-0.746482\pi$
$601$	6.60632	−	11.4425i	0.269477	−	0.466749i	0.968727	+	0.248129i	$0.0798157\pi$
$602$	1.62301	+	2.81114i	0.0661489	+	0.114573i
$603$	1.37773	+	34.7912i	0.0561055	+	1.41681i
$604$	−7.19287	−	1.92732i	−0.292674	−	0.0784217i
$605$	−3.27136	−	0.876559i	−0.133000	−	0.0356372i
$606$	−24.8143	−	9.70769i	−1.00801	−	0.394348i
$607$	2.52615	+	4.37542i	0.102533	+	0.177593i	0.912728	−	0.408568i	$-0.133972\pi$
$607$	2.52615	+	4.37542i	0.102533	+	0.177593i	−0.810195	+	0.586161i	$0.800639\pi$
$608$	0.607447	−	1.05213i	0.0246352	−	0.0426695i
$609$	6.67841	+	8.35577i	0.270623	+	0.338593i
$610$		−	13.7496i		−	0.556706i
$611$	31.9000	−	16.1778i	1.29054	−	0.654483i
$612$	6.60989	+	6.10633i	0.267189	+	0.246834i
$613$	−3.28773	−	12.2700i	−0.132790	−	0.495579i	0.867207	−	0.497948i	$-0.165913\pi$
$613$	−3.28773	−	12.2700i	−0.132790	−	0.495579i	−0.999997	+	0.00236831i	$0.999246\pi$
$614$	−6.46430	−	3.73217i	−0.260878	−	0.150618i
$615$	4.90694	−	6.66385i	0.197867	−	0.268712i
$616$	−2.21299	+	2.21299i	−0.0891637	+	0.0891637i
$617$	1.98367	−	7.40316i	0.0798596	−	0.298040i	−0.914432	−	0.404740i	$-0.867362\pi$
$617$	1.98367	−	7.40316i	0.0798596	−	0.298040i	0.994291	+	0.106700i	$0.0340286\pi$
$618$	−28.0755	+	4.26300i	−1.12936	+	0.171483i
$619$	20.2426	+	20.2426i	0.813620	+	0.813620i	0.985175	−	0.171555i	$-0.0548791\pi$
$619$	20.2426	+	20.2426i	0.813620	+	0.813620i	−0.171555	+	0.985175i	$0.554879\pi$
$620$	0.00340978	−	0.00196864i	0.000136940	−	7.90623e-5i
$621$	11.9888	+	13.8395i	0.481094	+	0.555358i
$622$	−16.7024	+	4.47539i	−0.669705	+	0.179447i
$623$	5.92475			0.237370
$624$	3.62873	+	5.08255i	0.145266	+	0.203465i
$625$	−1.00000			−0.0400000
$626$	−3.58767	+	0.961314i	−0.143392	+	0.0384218i
$627$	−7.93222	−	0.884994i	−0.316782	−	0.0353432i
$628$	3.78254	−	2.18385i	0.150940	−	0.0871450i
$629$	−24.1313	−	24.1313i	−0.962177	−	0.962177i
$630$	2.09305	−	1.32152i	0.0833890	−	0.0526506i
$631$	−5.56480	+	20.7681i	−0.221531	+	0.826766i	0.762233	+	0.647302i	$0.224103\pi$
$631$	−5.56480	+	20.7681i	−0.221531	+	0.826766i	−0.983765	+	0.179464i	$0.942564\pi$
$632$	4.17869	−	4.17869i	0.166219	−	0.166219i
$633$	−8.49635	−	6.25630i	−0.337699	−	0.248666i
$634$	14.5524	+	8.40182i	0.577949	+	0.333679i
$635$	0.204358	+	0.762676i	0.00810972	+	0.0302659i
$636$	7.78589	−	3.40705i	0.308731	−	0.135099i
$637$	15.2135	+	16.9608i	0.602780	+	0.672011i
$638$		−	28.3896i		−	1.12396i
$639$	8.23890	−	15.6713i	0.325926	−	0.619948i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	17.0880	+	29.5973i	0.674936	+	1.16902i	0.976488	+	0.215573i	$0.0691620\pi$
$641$	17.0880	+	29.5973i	0.674936	+	1.16902i	−0.301552	+	0.953450i	$0.597505\pi$
$642$	−0.493695	+	1.26196i	−0.0194846	+	0.0498055i
$643$	29.1672	+	7.81533i	1.15024	+	0.308206i	0.783062	−	0.621943i	$-0.213657\pi$
$643$	29.1672	+	7.81533i	1.15024	+	0.308206i	0.367180	+	0.930150i	$0.380323\pi$
$644$	−2.80844	−	0.752520i	−0.110668	−	0.0296535i
$645$	−2.48251	+	6.34565i	−0.0977486	+	0.249860i
$646$	−1.82209	−	3.15596i	−0.0716893	−	0.124170i
$647$	−16.6435	+	28.8275i	−0.654325	+	1.13332i	0.327737	+	0.944769i	$0.393714\pi$
$647$	−16.6435	+	28.8275i	−0.654325	+	1.13332i	−0.982063	+	0.188555i	$0.939619\pi$
$648$	8.48191	−	3.00951i	0.333201	−	0.118225i
$649$		−	18.3511i		−	0.720343i
$650$	−0.195522	+	3.60025i	−0.00766901	+	0.141213i
$651$	−0.00515493	+	0.00225576i	−0.000202038	+	8.84104e-5i
$652$	−1.31903	−	4.92267i	−0.0516571	−	0.192787i
$653$	38.8066	+	22.4050i	1.51862	+	0.876776i	0.999760	+	0.0219166i	$0.00697684\pi$
$653$	38.8066	+	22.4050i	1.51862	+	0.876776i	0.518860	+	0.854859i	$0.326356\pi$
$654$	−0.993487	−	0.731556i	−0.0388484	−	0.0286061i
$655$	0.435297	−	0.435297i	0.0170085	−	0.0170085i
$656$	−1.23661	+	4.61510i	−0.0482816	+	0.180189i
$657$	19.2312	+	30.4588i	0.750281	+	1.18831i
$658$	5.78784	+	5.78784i	0.225634	+	0.225634i
$659$	15.8615	−	9.15765i	0.617877	−	0.356731i	−0.158165	−	0.987413i	$-0.550558\pi$
$659$	15.8615	−	9.15765i	0.617877	−	0.356731i	0.776042	+	0.630681i	$0.217225\pi$
$660$	−6.52914	−	0.728453i	−0.254146	−	0.0283550i
$661$	−46.0633	+	12.3426i	−1.79165	+	0.480072i	−0.992626	−	0.121221i	$-0.961319\pi$
$661$	−46.0633	+	12.3426i	−1.79165	+	0.480072i	−0.799029	+	0.601293i	$0.794653\pi$
$662$	−19.4484			−0.755883
$663$	18.6454	−	1.80366i	0.724128	−	0.0700482i
$664$	7.58364			0.294302
$665$	−0.968265	+	0.259446i	−0.0375477	+	0.0100609i
$666$	−32.5931	+	10.1315i	−1.26296	+	0.392586i
$667$	22.8412	−	13.1874i	0.884415	−	0.510617i
$668$	−6.51943	−	6.51943i	−0.252244	−	0.252244i
$669$	14.2335	−	2.16122i	0.550298	−	0.0835574i
$670$	3.00389	−	11.2107i	0.116051	−	0.433106i
$671$	36.8772	−	36.8772i	1.42363	−	1.42363i
$672$	−0.847394	+	1.15080i	−0.0326889	+	0.0443931i
$673$	23.3095	+	13.4577i	0.898514	+	0.518757i	0.876718	−	0.481005i	$-0.159728\pi$
$673$	23.3095	+	13.4577i	0.898514	+	0.518757i	0.0217965	+	0.999762i	$0.493061\pi$
$674$	7.61297	+	28.4120i	0.293241	+	1.09439i
$675$	4.91015	+	1.70014i	0.188992	+	0.0654383i
$676$	12.9235	+	1.40786i	0.497059	+	0.0541483i
$677$			35.2263i			1.35385i	0.736050	+	0.676927i	$0.236689\pi$
$677$			35.2263i			1.35385i	−0.736050	+	0.676927i	$0.763311\pi$
$678$	6.76318	+	8.46183i	0.259738	+	0.324975i
$679$	3.27033	−	5.66437i	0.125504	−	0.217379i
$680$	−1.49980	−	2.59772i	−0.0575145	−	0.0996181i
$681$	−32.9214	−	12.8793i	−1.26155	−	0.493537i
$682$	0.0144252	+	0.00386521i	0.000552368	+	0.000148007i
$683$	−25.9255	−	6.94671i	−0.992010	−	0.265808i	−0.273915	−	0.961754i	$-0.588319\pi$
$683$	−25.9255	−	6.94671i	−0.992010	−	0.265808i	−0.718095	+	0.695945i	$0.754986\pi$
$684$	−3.64183	+	0.144216i	−0.139249	+	0.00551425i
$685$	−5.36308	−	9.28912i	−0.204913	−	0.354919i
$686$	−5.49490	+	9.51745i	−0.209796	+	0.363378i
$687$	1.38806	−	1.10942i	0.0529579	−	0.0423270i
$688$		−	3.93404i		−	0.149984i
$689$	5.49884	−	16.8152i	0.209489	−	0.640609i
$690$	−2.44679	−	5.59147i	−0.0931477	−	0.212864i
$691$	−3.82546	−	14.2768i	−0.145527	−	0.543116i	−0.999731	−	0.0231778i	$-0.992622\pi$
$691$	−3.82546	−	14.2768i	−0.145527	−	0.543116i	0.854204	−	0.519938i	$-0.174045\pi$
$692$	4.76186	+	2.74926i	0.181019	+	0.104511i
$693$	9.15803	+	2.06927i	0.347885	+	0.0786052i
$694$	14.9972	−	14.9972i	0.569285	−	0.569285i
$695$	−5.99937	+	22.3900i	−0.227569	+	0.849300i
$696$	−1.94615	−	12.8171i	−0.0737687	−	0.485831i
$697$	10.1341	+	10.1341i	0.383855	+	0.383855i
$698$	−13.9214	+	8.03752i	−0.526932	+	0.304225i
$699$	−2.24352	+	20.1087i	−0.0848576	+	0.760581i
$700$	−0.796995	+	0.213554i	−0.0301236	+	0.00807159i
$701$	−19.3599			−0.731215			−0.365608	−	0.930769i	$-0.619139\pi$
$701$	−19.3599			−0.731215			−0.365608	+	0.930769i	$0.619139\pi$
$702$	7.08096	−	17.3453i	0.267253	−	0.654657i
$703$	13.8220			0.521308
$704$	3.66375	−	0.981698i	0.138083	−	0.0369991i
$705$	−1.90520	+	17.0763i	−0.0717538	+	0.643131i
$706$	28.2971	−	16.3373i	1.06498	−	0.614864i
$707$	−8.97556	−	8.97556i	−0.337561	−	0.337561i
$708$	−1.25799	−	8.28497i	−0.0472783	−	0.311368i
$709$	7.45717	−	27.8305i	0.280060	−	1.04520i	−0.672314	−	0.740266i	$-0.734700\pi$
$709$	7.45717	−	27.8305i	0.280060	−	1.04520i	0.952374	−	0.304932i	$-0.0986338\pi$
$710$	−4.17313	+	4.17313i	−0.156615	+	0.156615i
$711$	−17.2927	−	3.90732i	−0.648528	−	0.146536i
$712$	−6.21854	−	3.59028i	−0.233050	−	0.134551i
$713$	0.00359089	+	0.0134014i	0.000134480	+	0.000501885i
$714$	1.71854	+	3.92726i	0.0643149	+	0.146974i
$715$	−10.1804	+	9.13163i	−0.380727	+	0.341504i
$716$		−	4.81015i		−	0.179764i
$717$	−27.5301	+	22.0036i	−1.02813	+	0.821740i
$718$	3.38314	−	5.85977i	0.126258	−	0.218685i
$719$	3.77091	+	6.53140i	0.140631	+	0.243580i	0.927734	−	0.373241i	$-0.121754\pi$
$719$	3.77091	+	6.53140i	0.140631	+	0.243580i	−0.787103	+	0.616821i	$0.788420\pi$
$720$	−2.99765	+	0.118707i	−0.111716	+	0.00442395i
$721$	−13.0669	−	3.50126i	−0.486637	−	0.130394i
$722$	−16.9269	−	4.53555i	−0.629955	−	0.168796i
$723$	−29.0962	−	11.3829i	−1.08210	−	0.423333i
$724$	4.84363	+	8.38941i	0.180012	+	0.311790i
$725$	3.74239	−	6.48200i	0.138989	−	0.240735i
$726$	−3.66241	−	4.58227i	−0.135925	−	0.170064i
$727$			18.8445i			0.698904i	0.936954	+	0.349452i	$0.113632\pi$
$727$			18.8445i			0.698904i	−0.936954	+	0.349452i	$0.886368\pi$
$728$	0.613018	+	2.91113i	0.0227199	+	0.107894i
$729$	−21.2191	−	16.6958i	−0.785891	−	0.618365i
$730$	−3.10772	−	11.5982i	−0.115022	−	0.429267i
$731$	−10.2196	−	5.90026i	−0.377984	−	0.218229i
$732$	14.1210	−	19.1769i	0.521926	−	0.708800i
$733$	−26.3274	+	26.3274i	−0.972424	+	0.972424i	−0.999630	−	0.0272063i	$-0.991339\pi$
$733$	−26.3274	+	26.3274i	−0.972424	+	0.972424i	0.0272063	+	0.999630i	$0.491339\pi$
$734$	3.48622	−	13.0107i	0.128679	−	0.480235i
$735$	−10.8211	+	1.64308i	−0.399143	+	0.0606061i
$736$	2.49170	+	2.49170i	0.0918451	+	0.0918451i
$737$	38.1242	−	22.0110i	1.40432	−	0.810786i
$738$	13.6876	−	4.25477i	0.503849	−	0.156620i
$739$	−22.7470	+	6.09505i	−0.836763	+	0.224210i	−0.651662	−	0.758509i	$-0.725928\pi$
$739$	−22.7470	+	6.09505i	−0.836763	+	0.224210i	−0.185101	+	0.982719i	$0.559261\pi$
$740$	11.3771			0.418232
$741$	−4.82335	+	5.85646i	−0.177190	+	0.215142i
$742$	4.04860			0.148629
$743$	−40.3372	+	10.8083i	−1.47983	+	0.396519i	−0.906288	−	0.422660i	$-0.861097\pi$
$743$	−40.3372	+	10.8083i	−1.47983	+	0.396519i	−0.573539	+	0.819178i	$0.694430\pi$
$744$	0.00677750		0.000756163i	0.000248475		2.77223e-5i
$745$	−4.00586	+	2.31278i	−0.146763	+	0.0847338i
$746$	−24.0925	−	24.0925i	−0.882089	−	0.882089i
$747$	−12.1462	−	19.2373i	−0.444405	−	0.703857i
$748$	2.94469	−	10.9897i	0.107669	−	0.401825i
$749$	−0.456462	+	0.456462i	−0.0166788	+	0.0166788i
$750$	−1.39472	−	1.02701i	−0.0509281	−	0.0375010i
$751$	−5.24153	−	3.02620i	−0.191266	−	0.110428i	0.401309	−	0.915943i	$-0.368555\pi$
$751$	−5.24153	−	3.02620i	−0.191266	−	0.110428i	−0.592575	+	0.805515i	$0.701889\pi$
$752$	−2.56753	−	9.58216i	−0.0936283	−	0.349425i
$753$	46.7712	−	20.4668i	1.70444	−	0.745850i
$754$	−22.6051	−	14.7409i	−0.823228	−	0.536831i
$755$		−	7.44661i		−	0.271010i
$756$	4.27643	+	0.306419i	0.155532	+	0.0111444i
$757$	−5.09098	+	8.81784i	−0.185035	+	0.320490i	−0.943588	−	0.331121i	$-0.892573\pi$
$757$	−5.09098	+	8.81784i	−0.185035	+	0.320490i	0.758553	+	0.651611i	$0.225906\pi$
$758$	−11.9487	−	20.6958i	−0.433997	−	0.751705i
$759$	8.43418	−	21.5590i	0.306141	−	0.782542i
$760$	1.17350	+	0.314438i	0.0425673	+	0.0114059i
$761$	47.4705	+	12.7197i	1.72080	+	0.461088i	0.978031	−	0.208457i	$-0.0668442\pi$
$761$	47.4705	+	12.7197i	1.72080	+	0.461088i	0.742772	+	0.669545i	$0.233511\pi$
$762$	−0.498250	+	1.27360i	−0.0180497	+	0.0461377i
$763$	−0.293870	−	0.508999i	−0.0106388	−	0.0184270i
$764$	−2.62831	+	4.55237i	−0.0950889	+	0.164699i
$765$	−4.18750	+	7.96510i	−0.151399	+	0.287979i
$766$			22.6973i			0.820086i
$767$	−14.6119	−	9.52851i	−0.527606	−	0.344055i
$768$	1.58678	−	0.694363i	0.0572579	−	0.0250557i
$769$	−0.157880	−	0.589218i	−0.00569331	−	0.0212477i	0.963021	−	0.269427i	$-0.0868344\pi$
$769$	−0.157880	−	0.589218i	−0.00569331	−	0.0212477i	−0.968714	+	0.248180i	$0.920168\pi$
$770$	−2.71034	−	1.56482i	−0.0976740	−	0.0563921i
$771$	18.0124	+	13.2634i	0.648700	+	0.477671i
$772$	−0.124615	+	0.124615i	−0.00448499	+	0.00448499i
$773$	8.94546	−	33.3849i	0.321746	−	1.20077i	−0.595797	−	0.803135i	$-0.703164\pi$
$773$	8.94546	−	33.3849i	0.321746	−	1.20077i	0.917543	−	0.397637i	$-0.130170\pi$
$774$	−9.97944	+	6.30088i	−0.358704	+	0.226480i
$775$	0.00278407	+	0.00278407i	0.000100007	+	0.000100007i
$776$	−6.86499	+	3.96350i	−0.246439	+	0.142281i
$777$	−16.1592	−	1.80287i	−0.579707	−	0.0646777i
$778$	9.46711	−	2.53671i	0.339412	−	0.0909453i
$779$	−5.80464			−0.207973
$780$	−3.97018	+	4.82055i	−0.142155	+	0.172603i
$781$	−22.3851			−0.801001
$782$	10.2098	−	2.73570i	0.365101	−	0.0978284i
$783$	−29.3960	+	25.4650i	−1.05053	+	0.910045i
$784$	5.47258	−	3.15960i	0.195449	−	0.112843i
$785$	3.08843	+	3.08843i	0.110231	+	0.110231i
$786$	1.05417	−	0.160066i	0.0376011	−	0.00570936i
$787$	−5.66965	+	21.1594i	−0.202101	+	0.754252i	0.788212	+	0.615403i	$0.211007\pi$
$787$	−5.66965	+	21.1594i	−0.202101	+	0.754252i	−0.990314	+	0.138849i	$0.955660\pi$
$788$	−5.17241	+	5.17241i	−0.184259	+	0.184259i
$789$	−28.3423	+	38.4901i	−1.00901	+	1.37028i
$790$	5.11782	+	2.95478i	0.182084	+	0.105126i
$791$	1.33560	+	4.98453i	0.0474885	+	0.177229i
$792$	−8.35822	−	7.72146i	−0.296996	−	0.274370i
$793$	−10.2153	−	48.5111i	−0.362757	−	1.72268i
$794$		−	25.0689i		−	0.889664i
$795$	5.30610	+	6.63879i	0.188188	+	0.235453i
$796$	−9.76412	+	16.9120i	−0.346080	+	0.599428i
$797$	5.47802	+	9.48820i	0.194041	+	0.336089i	0.946586	−	0.322452i	$-0.104507\pi$
$797$	5.47802	+	9.48820i	0.194041	+	0.336089i	−0.752545	+	0.658541i	$0.771174\pi$
$798$	−1.61692	−	0.632560i	−0.0572382	−	0.0223924i
$799$	−28.7426	−	7.70155i	−1.01684	−	0.272461i
$800$	0.965926	+	0.258819i	0.0341506	+	0.00915064i
$801$	0.852382	+	21.5248i	0.0301174	+	0.760541i
$802$	−15.9007	−	27.5409i	−0.561474	−	0.972502i
$803$	22.7718	−	39.4418i	0.803598	−	1.39187i
$804$	15.7031	−	12.5508i	0.553804	−	0.442632i
$805$		−	2.90752i		−	0.102476i
$806$	0.0105677	−	0.00947899i	0.000372231	−	0.000333883i
$807$	−14.5234	−	33.1892i	−0.511247	−	1.16832i
$808$	3.98163	+	14.8596i	0.140073	+	0.522760i
$809$	−7.08136	−	4.08842i	−0.248967	−	0.143741i	0.370324	−	0.928903i	$-0.379247\pi$
$809$	−7.08136	−	4.08842i	−0.248967	−	0.143741i	−0.619291	+	0.785161i	$0.712580\pi$
$810$	5.10224	+	7.41398i	0.179275	+	0.260501i
$811$	−25.8013	+	25.8013i	−0.906006	+	0.906006i	−0.995947	−	0.0899413i	$-0.971332\pi$
$811$	−25.8013	+	25.8013i	−0.906006	+	0.906006i	0.0899413	+	0.995947i	$0.471332\pi$
$812$	1.59840	−	5.96533i	0.0560930	−	0.209342i
$813$	−4.05708	−	26.7194i	−0.142288	−	0.937089i
$814$	30.5140	+	30.5140i	1.06952	+	1.06952i
$815$	4.41355	−	2.54816i	0.154600	−	0.0892583i
$816$	0.576079	−	5.16341i	0.0201668	−	0.180755i
$817$	4.61659	−	1.23701i	0.161514	−	0.0432776i
$818$	22.4973			0.786600
$819$	6.40281	−	6.21759i	0.223732	−	0.217260i
$820$	−4.77790			−0.166851
$821$	−10.5495	+	2.82674i	−0.368181	+	0.0986539i	−0.438166	−	0.898894i	$-0.644372\pi$
$821$	−10.5495	+	2.82674i	−0.368181	+	0.0986539i	0.0699844	+	0.997548i	$0.477705\pi$
$822$	2.05998	−	18.4637i	0.0718502	−	0.643995i
$823$	41.3492	−	23.8730i	1.44134	−	0.832159i	0.443403	−	0.896322i	$-0.353771\pi$
$823$	41.3492	−	23.8730i	1.44134	−	0.832159i	0.997939	+	0.0641632i	$0.0204378\pi$
$824$	11.5932	+	11.5932i	0.403867	+	0.403867i
$825$	−0.986234	−	6.49520i	−0.0343363	−	0.226134i
$826$	1.03321	−	3.85599i	0.0359499	−	0.134167i
$827$	11.8144	−	11.8144i	0.410828	−	0.410828i	−0.471199	−	0.882027i	$-0.656179\pi$
$827$	11.8144	−	11.8144i	0.410828	−	0.410828i	0.882027	+	0.471199i	$0.156179\pi$
$828$	2.32988	−	10.3114i	0.0809691	−	0.358347i
$829$	−16.8509	−	9.72886i	−0.585255	−	0.337897i	0.177964	−	0.984037i	$-0.443049\pi$
$829$	−16.8509	−	9.72886i	−0.585255	−	0.337897i	−0.763219	+	0.646140i	$0.776382\pi$
$830$	1.96279	+	7.32523i	0.0681295	+	0.254263i
$831$	−16.8795	−	38.5734i	−0.585542	−	1.33810i
$832$	1.12067	−	3.42697i	0.0388523	−	0.118809i
$833$		−	18.9550i		−	0.656752i
$834$	−31.3621	+	25.0664i	−1.08598	+	0.867979i
$835$	4.60993	−	7.98464i	0.159533	−	0.276320i
$836$	2.30404	+	3.99072i	0.0796869	+	0.138022i
$837$	−0.00893689	−	0.0184035i	−0.000308904	−	0.000636118i
$838$	−18.1696	−	4.86852i	−0.627658	−	0.168180i
$839$	−1.11041	−	0.297534i	−0.0383357	−	0.0102720i	0.239600	−	0.970872i	$-0.422984\pi$
$839$	−1.11041	−	0.297534i	−0.0383357	−	0.0102720i	−0.277936	+	0.960600i	$0.589650\pi$
$840$	−1.33091	−	0.520671i	−0.0459208	−	0.0179649i
$841$	13.5109	+	23.4016i	0.465893	+	0.806950i
$842$	16.2347	−	28.1193i	0.559484	−	0.969055i
$843$	25.5614	+	31.9815i	0.880382	+	1.10150i
$844$			6.09178i			0.209688i
$845$	1.98497	+	12.8476i	0.0682852	+	0.441970i
$846$	−20.1947	+	21.8601i	−0.694309	+	0.751565i
$847$	−0.723258	−	2.69923i	−0.0248514	−	0.0927468i
$848$	−4.24936	−	2.45337i	−0.145924	−	0.0842490i
$849$	−23.1832	+	31.4839i	−0.795646	+	1.08053i
$850$	2.12103	−	2.12103i	0.0727508	−	0.0727508i
$851$	−10.3762	+	38.7246i	−0.355692	+	1.32746i
$852$	−10.1062	+	1.53453i	−0.346233	+	0.0525721i
$853$	−35.2653	−	35.2653i	−1.20746	−	1.20746i	−0.971847	−	0.235613i	$-0.924290\pi$
$853$	−35.2653	−	35.2653i	−1.20746	−	1.20746i	−0.235613	−	0.971847i	$-0.575710\pi$
$854$	9.82502	−	5.67248i	0.336205	−	0.194108i
$855$	−1.08188	−	3.48041i	−0.0369994	−	0.119028i
$856$	0.755704	−	0.202490i	0.0258294	−	0.00692097i
$857$	39.7560			1.35804			0.679020	−	0.734120i	$-0.262405\pi$
$857$	39.7560			1.35804			0.679020	+	0.734120i	$0.262405\pi$
$858$	−23.5772	+	2.28073i	−0.804911	+	0.0778628i
$859$	−38.7074			−1.32068			−0.660340	−	0.750967i	$-0.729588\pi$
$859$	−38.7074			−1.32068			−0.660340	+	0.750967i	$0.729588\pi$
$860$	3.79999	−	1.01821i	0.129579	−	0.0347205i
$861$	6.78615	+	0.757127i	0.231271	+	0.0258028i
$862$	−18.9532	+	10.9426i	−0.645547	+	0.372707i
$863$	2.57323	+	2.57323i	0.0875939	+	0.0875939i	0.749546	−	0.661952i	$-0.230272\pi$
$863$	2.57323	+	2.57323i	0.0875939	+	0.0875939i	−0.661952	+	0.749546i	$0.730272\pi$
$864$	−4.30281	−	2.91305i	−0.146385	−	0.0991038i
$865$	−1.42312	+	5.31117i	−0.0483876	+	0.180585i
$866$	−4.77724	+	4.77724i	−0.162337	+	0.162337i
$867$	11.1612	+	8.21858i	0.379055	+	0.279118i
$868$	0.00281344	+	0.00162434i	9.54945e−5	+	5.51337e-5i
$869$	5.80139	+	21.6511i	0.196799	+	0.734463i
$870$	11.8767	−	5.19715i	0.402656	−	0.176200i
$871$	2.26926	−	41.7850i	0.0768910	−	1.41583i
$872$			0.712318i			0.0241221i
$873$	21.0493	+	11.0663i	0.712412	+	0.374537i
$874$	−2.14052	+	3.70748i	−0.0724041	+	0.125408i
$875$	−0.412555	−	0.714566i	−0.0139469	−	0.0241568i
$876$	7.57698	−	19.3679i	0.256003	−	0.654380i
$877$	46.1278	+	12.3599i	1.55763	+	0.417365i	0.931911	−	0.362687i	$-0.118141\pi$
$877$	46.1278	+	12.3599i	1.55763	+	0.417365i	0.625715	+	0.780051i	$0.284807\pi$
$878$	−26.2378	−	7.03041i	−0.885484	−	0.237265i
$879$	18.2553	−	46.6631i	0.615734	−	1.57391i
$880$	1.89649	+	3.28482i	0.0639308	+	0.110731i
$881$	−22.1331	+	38.3356i	−0.745682	+	1.29156i	0.204193	+	0.978931i	$0.434543\pi$
$881$	−22.1331	+	38.3356i	−0.745682	+	1.29156i	−0.949875	+	0.312629i	$0.898790\pi$
$882$	−16.7800	−	8.82173i	−0.565010	−	0.297043i
$883$		−	30.2826i		−	1.01909i	−0.860444	−	0.509545i	$-0.829814\pi$
$883$		−	30.2826i		−	1.01909i	0.860444	−	0.509545i	$-0.170186\pi$
$884$	−7.22153	−	8.05094i	−0.242886	−	0.270783i
$885$	7.67708	−	3.35944i	0.258062	−	0.112926i
$886$	−7.90533	−	29.5031i	−0.265585	−	0.991176i
$887$	−25.8425	−	14.9201i	−0.867705	−	0.500970i	−0.00111997	−	0.999999i	$-0.500356\pi$
$887$	−25.8425	−	14.9201i	−0.867705	−	0.500970i	−0.866585	+	0.499030i	$0.833690\pi$
$888$	15.8680	+	11.6844i	0.532494	+	0.392103i
$889$	−0.460674	+	0.460674i	−0.0154505	+	0.0154505i
$890$	1.85846	−	6.93588i	0.0622959	−	0.232491i
$891$	−6.20018	+	33.5691i	−0.207714	+	1.12461i
$892$	−5.87739	−	5.87739i	−0.196790	−	0.196790i
$893$	10.4373	−	6.02599i	0.349272	−	0.201652i
$894$	−7.96231	−	0.888351i	−0.266299	−	0.0297109i
$895$	4.64624	−	1.24496i	0.155307	−	0.0416143i
$896$	0.825110			0.0275650
$897$	−12.7869	−	17.9098i	−0.426942	−	0.597992i
$898$	15.2586			0.509188
$899$	−0.0284654	+	0.00762729i	−0.000949375	+	0.000254384i
$900$	−0.890511	−	2.86478i	−0.0296837	−	0.0954928i
$901$	−12.7463	+	7.35910i	−0.424642	+	0.245167i
$902$	−12.8146	−	12.8146i	−0.426678	−	0.426678i
$903$	−5.55856	+	0.844014i	−0.184977	+	0.0280870i
$904$	1.61869	−	6.04105i	0.0538369	−	0.200922i
$905$	−6.84993	+	6.84993i	−0.227699	+	0.227699i
$906$	7.64772	−	10.3860i	0.254079	−	0.345050i
$907$	31.8087	+	18.3647i	1.05619	+	0.609791i	0.924376	−	0.381483i	$-0.124587\pi$
$907$	31.8087	+	18.3647i	1.05619	+	0.609791i	0.131814	+	0.991274i	$0.457920\pi$
$908$	5.28248	+	19.7145i	0.175305	+	0.654248i
$909$	31.3172	−	33.8998i	1.03873	−	1.12438i
$910$	−2.65328	+	1.34559i	−0.0879553	+	0.0446058i
$911$			35.9584i			1.19136i	0.803223	+	0.595678i	$0.203117\pi$
$911$			35.9584i			1.19136i	−0.803223	+	0.595678i	$0.796883\pi$
$912$	1.31378	+	1.64375i	0.0435035	+	0.0544299i
$913$	−14.3823	+	24.9109i	−0.475986	+	0.824431i
$914$	1.83877	+	3.18485i	0.0608212	+	0.105345i
$915$	22.1783	+	8.67645i	0.733191	+	0.286835i
$916$	−0.990963	−	0.265528i	−0.0327423	−	0.00877328i
$917$	0.490632	+	0.131465i	0.0162021	+	0.00434134i
$918$	−14.0206	+	6.80853i	−0.462749	+	0.224715i
$919$	−4.72834	−	8.18972i	−0.155974	−	0.270154i	0.777440	−	0.628958i	$-0.216518\pi$
$919$	−4.72834	−	8.18972i	−0.155974	−	0.270154i	−0.933413	+	0.358804i	$0.883185\pi$
$920$	−1.76190	+	3.05169i	−0.0580880	+	0.100611i
$921$	10.0992	−	8.07186i	0.332780	−	0.265977i
$922$		−	19.1292i		−	0.629985i
$923$	−11.6231	+	17.8240i	−0.382579	+	0.586683i
$924$	−2.17310	−	4.96603i	−0.0714898	−	0.163370i
$925$	2.94462	+	10.9895i	0.0968185	+	0.361332i
$926$	34.4914	+	19.9136i	1.13346	+	0.654401i
$927$	10.8403	−	47.9761i	0.356042	−	1.57574i
$928$	−5.29253	+	5.29253i	−0.173736	+	0.173736i
$929$	6.29712	−	23.5012i	0.206602	−	0.771048i	−0.782354	−	0.622834i	$-0.785981\pi$
$929$	6.29712	−	23.5012i	0.206602	−	0.771048i	0.988955	−	0.148214i	$-0.0473523\pi$
$930$	0.00102375	+	0.00674227i	3.35701e−5	+	0.000221088i
$931$	5.42857	+	5.42857i	0.177914	+	0.177914i
$932$	10.1167	−	5.84090i	0.331385	−	0.191325i
$933$	3.32089	−	29.7652i	0.108721	−	0.974470i
$934$	−30.6054	+	8.20070i	−1.00144	+	0.268335i
$935$	11.3774			0.372081
$936$	−10.4880	+	2.64593i	−0.342812	+	0.0864849i
$937$	−33.2229			−1.08534			−0.542672	−	0.839945i	$-0.682587\pi$
$937$	−33.2229			−1.08534			−0.542672	+	0.839945i	$0.682587\pi$
$938$	9.25005	−	2.47854i	0.302025	−	0.0809273i
$939$	0.713327	−	6.39357i	0.0232786	−	0.208646i
$940$	8.59113	−	4.96009i	0.280212	−	0.161780i
$941$	5.22787	+	5.22787i	0.170424	+	0.170424i	0.787166	−	0.616742i	$-0.211548\pi$
$941$	5.22787	+	5.22787i	0.170424	+	0.170424i	−0.616742	+	0.787166i	$0.711548\pi$
$942$	1.13567	+	7.47934i	0.0370020	+	0.243690i
$943$	4.35756	−	16.2626i	0.141902	−	0.529584i
$944$	−3.42109	+	3.42109i	−0.111347	+	0.111347i
$945$	0.810844	+	4.21003i	0.0263768	+	0.136952i
$946$	12.9226	+	7.46089i	0.420151	+	0.242574i
$947$	−4.28531	−	15.9930i	−0.139254	−	0.519703i	−0.999944	−	0.0105737i	$-0.996634\pi$
$947$	−4.28531	−	15.9930i	−0.139254	−	0.519703i	0.860690	−	0.509129i	$-0.170032\pi$
$948$	4.10337	+	9.37714i	0.133271	+	0.304555i
$949$	−19.5814	−	38.6114i	−0.635640	−	1.25338i
$950$			1.21489i			0.0394164i
$951$	−22.7352	+	18.1713i	−0.737240	+	0.589245i
$952$	1.23750	−	2.14341i	0.0401075	−	0.0694682i
$953$	3.83233	+	6.63779i	0.124141	+	0.215019i	0.921397	−	0.388623i	$-0.127049\pi$
$953$	3.83233	+	6.63779i	0.124141	+	0.215019i	−0.797256	+	0.603642i	$0.793716\pi$
$954$	0.582463	+	14.7087i	0.0188580	+	0.476211i
$955$	−5.07751	−	1.36051i	−0.164304	−	0.0440252i
$956$	19.6542	+	5.26633i	0.635662	+	0.170325i
$957$	45.7928	+	17.9148i	1.48027	+	0.579102i
$958$	−12.8383	−	22.2366i	−0.414788	−	0.718433i
$959$	4.42513	−	7.66455i	0.142895	−	0.247501i
$960$	1.08139	+	1.35299i	0.0349017	+	0.0436677i
$961$			31.0000i			0.999999i
$962$	40.1405	−	8.45267i	1.29418	−	0.272525i
$963$	−1.72401	−	1.59267i	−0.0555555	−	0.0513231i
$964$	4.66870	+	17.4238i	0.150369	+	0.561184i
$965$	−0.152621	−	0.0881160i	−0.00491306	−	0.00283655i
$966$	2.98604	−	4.05518i	0.0960743	−	0.130473i
$967$	−19.4699	+	19.4699i	−0.626110	+	0.626110i	−0.947087	−	0.320977i	$-0.895989\pi$
$967$	−19.4699	+	19.4699i	−0.626110	+	0.626110i	0.320977	+	0.947087i	$0.395989\pi$
$968$	−0.876559	+	3.27136i	−0.0281737	+	0.105146i
$969$	6.24039	−	0.947543i	0.200470	−	0.0304395i
$970$	−5.60524	−	5.60524i	−0.179973	−	0.179973i
$971$	43.2649	−	24.9790i	1.38844	−	0.801613i	0.395296	−	0.918554i	$-0.370642\pi$
$971$	43.2649	−	24.9790i	1.38844	−	0.801613i	0.993139	+	0.116940i	$0.0373086\pi$
$972$	−0.497989	+	15.5805i	−0.0159730	+	0.499745i
$973$	−18.4742	+	4.95014i	−0.592255	+	0.158694i
$974$	−24.0727			−0.771340
$975$	−5.68385	−	2.58725i	−0.182029	−	0.0828583i
$976$	−13.7496			−0.440115
$977$	27.6307	−	7.40363i	0.883985	−	0.236863i	0.211859	−	0.977300i	$-0.432048\pi$
$977$	27.6307	−	7.40363i	0.883985	−	0.236863i	0.672126	+	0.740437i	$0.265382\pi$
$978$	8.77267	+	0.978762i	0.280519	+	0.0312974i
$979$	23.5869	−	13.6179i	0.753839	−	0.435229i
$980$	4.46834	+	4.46834i	0.142736	+	0.142736i
$981$	1.80693	−	1.14087i	0.0576908	−	0.0364251i
$982$	−2.59493	+	9.68440i	−0.0828074	+	0.309042i
$983$	−31.5486	+	31.5486i	−1.00624	+	1.00624i	−0.00626241	+	0.999980i	$0.501993\pi$
$983$	−31.5486	+	31.5486i	−1.00624	+	1.00624i	−0.999980	+	0.00626241i	$0.998007\pi$
$984$	−6.66385	−	4.90694i	−0.212436	−	0.156427i
$985$	−6.33488	−	3.65744i	−0.201846	−	0.116536i
$986$	5.81081	+	21.6862i	0.185054	+	0.690631i
$987$	−12.9882	+	5.68353i	−0.413418	+	0.180909i
$988$	4.37392	+	0.237539i	0.139153	+	0.00755712i
$989$			13.8627i			0.440810i
$990$	5.29510	−	10.0719i	0.168289	−	0.320105i
$991$	16.8825	−	29.2414i	0.536291	−	0.928883i	−0.462809	−	0.886458i	$-0.653158\pi$
$991$	16.8825	−	29.2414i	0.536291	−	0.928883i	0.999100	−	0.0424251i	$-0.0135084\pi$
$992$	−0.00196864	−	0.00340978i	−6.25043e−5	−	0.000108261i
$993$	12.2726	−	31.3704i	0.389458	−	0.995511i
$994$	−4.70362	−	1.26033i	−0.149190	−	0.0399753i
$995$	−18.8628	−	5.05428i	−0.597992	−	0.160231i
$996$	−4.78552	+	12.2325i	−0.151635	+	0.387601i
$997$	−3.58159	−	6.20350i	−0.113430	−	0.196467i	0.803721	−	0.595006i	$-0.202850\pi$
$997$	−3.58159	−	6.20350i	−0.113430	−	0.196467i	−0.917151	+	0.398540i	$0.869517\pi$
$998$	−10.7600	+	18.6369i	−0.340603	+	0.589942i
$999$	4.22510	−	58.9662i	0.133676	−	1.86561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bh.c.71.7	yes	40
3.2	odd	2	inner	390.2.bh.c.71.2	yes	40
13.11	odd	12	inner	390.2.bh.c.11.2	✓	40
39.11	even	12	inner	390.2.bh.c.11.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bh.c.11.2	✓	40	13.11	odd	12	inner
390.2.bh.c.11.7	yes	40	39.11	even	12	inner
390.2.bh.c.71.2	yes	40	3.2	odd	2	inner
390.2.bh.c.71.7	yes	40	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.192053 + 1.72137i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(0.260015 + 1.71242i) q^{6} +(-0.213554 + 0.796995i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.92623 - 0.661187i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.192053 + 1.72137i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(0.260015 + 1.71242i) q^{6} +(-0.213554 + 0.796995i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.92623 - 0.661187i) q^{9} +(0.866025 + 0.500000i) q^{10} +(0.981698 + 3.66375i) q^{11} +(0.694363 + 1.58678i) q^{12} +(3.42697 + 1.12067i) q^{13} +0.825110i q^{14} +(-1.35299 + 1.08139i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.49980 - 2.59772i) q^{17} +(-2.99765 + 0.118707i) q^{18} +(1.17350 + 0.314438i) q^{19} +(0.965926 + 0.258819i) q^{20} +(-1.33091 - 0.520671i) q^{21} +(1.89649 + 3.28482i) q^{22} +(-1.76190 + 3.05169i) q^{23} +(1.08139 + 1.35299i) q^{24} +1.00000i q^{25} +(3.60025 + 0.195522i) q^{26} +(1.70014 - 4.91015i) q^{27} +(0.213554 + 0.796995i) q^{28} +(-6.48200 - 3.74239i) q^{29} +(-1.02701 + 1.39472i) q^{30} +(0.00278407 - 0.00278407i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-6.49520 + 0.986234i) q^{33} +(-2.12103 - 2.12103i) q^{34} +(-0.714566 + 0.412555i) q^{35} +(-2.86478 + 0.890511i) q^{36} +(10.9895 - 2.94462i) q^{37} +1.21489 q^{38} +(-2.58725 + 5.68385i) q^{39} +1.00000 q^{40} +(-4.61510 + 1.23661i) q^{41} +(-1.42032 - 0.158464i) q^{42} +(3.40698 - 1.96702i) q^{43} +(2.68205 + 2.68205i) q^{44} +(-1.60163 - 2.53669i) q^{45} +(-0.912024 + 3.40372i) q^{46} +(7.01463 - 7.01463i) q^{47} +(1.39472 + 1.02701i) q^{48} +(5.47258 + 3.15960i) q^{49} +(0.258819 + 0.965926i) q^{50} +(4.75968 - 2.08280i) q^{51} +(3.52818 - 0.742952i) q^{52} -4.90674i q^{53} +(0.371368 - 5.18286i) q^{54} +(-1.89649 + 3.28482i) q^{55} +(0.412555 + 0.714566i) q^{56} +(-0.766637 + 1.95964i) q^{57} +(-7.22973 - 1.93720i) q^{58} +(-4.67330 - 1.25221i) q^{59} +(-0.631032 + 1.61301i) q^{60} +(-6.87481 - 11.9075i) q^{61} +(0.00196864 - 0.00340978i) q^{62} +(1.15187 - 2.19099i) q^{63} -1.00000i q^{64} +(1.63080 + 3.21567i) q^{65} +(-6.01863 + 2.63371i) q^{66} +(-3.00389 - 11.2107i) q^{67} +(-2.59772 - 1.49980i) q^{68} +(-4.91472 - 3.61896i) q^{69} +(-0.583441 + 0.583441i) q^{70} +(-1.52747 + 5.70060i) q^{71} +(-2.53669 + 1.60163i) q^{72} +(-8.49044 - 8.49044i) q^{73} +(9.85289 - 5.68857i) q^{74} +(-1.72137 - 0.192053i) q^{75} +(1.17350 - 0.314438i) q^{76} -3.12963 q^{77} +(-1.02800 + 6.15981i) q^{78} +5.90955 q^{79} +(0.965926 - 0.258819i) q^{80} +(8.12566 + 3.86957i) q^{81} +(-4.13778 + 2.38895i) q^{82} +(5.36244 + 5.36244i) q^{83} +(-1.41294 + 0.214541i) q^{84} +(0.776351 - 2.89738i) q^{85} +(2.78179 - 2.78179i) q^{86} +(7.68692 - 10.4392i) q^{87} +(3.28482 + 1.89649i) q^{88} +(-1.85846 - 6.93588i) q^{89} +(-2.20360 - 2.03572i) q^{90} +(-1.62501 + 2.49195i) q^{91} +3.52379i q^{92} +(0.00425773 + 0.00532711i) q^{93} +(4.96009 - 8.59113i) q^{94} +(0.607447 + 1.05213i) q^{95} +(1.61301 + 0.631032i) q^{96} +(-7.65690 - 2.05166i) q^{97} +(6.10387 + 1.63553i) q^{98} +(-0.450254 - 11.3701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9	\( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) \) 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9 + 8 * q^13 + 4 * q^15 + 20 * q^16 - 8 * q^18 - 16 * q^19 + 4 * q^21 - 8 * q^22 + 8 * q^24 - 48 * q^27 + 8 * q^28 + 36 * q^31 + 12 * q^33 + 16 * q^34 - 12 * q^36 - 64 * q^37 - 60 * q^39 + 40 * q^40 - 12 * q^42 + 8 * q^45 - 32 * q^46 + 48 * q^49 + 24 * q^52 - 28 * q^54 + 8 * q^55 - 76 * q^57 - 28 * q^58 + 4 * q^60 - 40 * q^61 + 80 * q^63 + 40 * q^66 - 28 * q^67 - 36 * q^69 + 16 * q^70 + 16 * q^72 + 8 * q^73 - 16 * q^76 - 28 * q^78 + 40 * q^79 + 12 * q^81 + 20 * q^84 + 44 * q^85 + 40 * q^87 + 12 * q^88 + 120 * q^91 - 8 * q^93 - 16 * q^94 + 4 * q^96 - 160 * q^97 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more