LMFDB - Embedded newform 930.2.o.e.161.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.16
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.20548 + 1.24372i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.24372 + 1.20548i) q^{6} +(1.75266 + 3.03570i) q^{7} -1.00000i q^{8} +(-0.0936563 + 2.99854i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.20548 + 1.24372i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.24372 + 1.20548i) q^{6} +(1.75266 + 3.03570i) q^{7} -1.00000i q^{8} +(-0.0936563 + 2.99854i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.508798 + 0.881264i) q^{11} +(-1.20548 - 1.24372i) q^{12} +(-0.482279 - 0.278444i) q^{13} +(-3.03570 + 1.75266i) q^{14} +(-0.422115 - 1.67983i) q^{15} +1.00000 q^{16} +(-0.748115 - 1.29577i) q^{17} +(-2.99854 - 0.0936563i) q^{18} +(2.58309 + 4.47405i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.66275 + 5.83927i) q^{21} +(-0.881264 - 0.508798i) q^{22} -3.21814 q^{23} +(1.24372 - 1.20548i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.278444 - 0.482279i) q^{26} +(-3.84223 + 3.49818i) q^{27} +(-1.75266 - 3.03570i) q^{28} -2.64442 q^{29} +(1.67983 - 0.422115i) q^{30} +(5.39138 - 1.39033i) q^{31} +1.00000i q^{32} +(-1.70939 + 0.429543i) q^{33} +(1.29577 - 0.748115i) q^{34} -3.50532i q^{35} +(0.0936563 - 2.99854i) q^{36} +(2.08724 - 1.20507i) q^{37} +(-4.47405 + 2.58309i) q^{38} +(-0.235071 - 0.935475i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-7.86397 - 4.54027i) q^{41} +(-5.83927 - 1.66275i) q^{42} +(-5.69715 + 3.28925i) q^{43} +(0.508798 - 0.881264i) q^{44} +(1.58038 - 2.54998i) q^{45} -3.21814i q^{46} +8.95636i q^{47} +(1.20548 + 1.24372i) q^{48} +(-2.64364 + 4.57892i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(0.709739 - 2.49247i) q^{51} +(0.482279 + 0.278444i) q^{52} +(-1.80684 + 3.12954i) q^{53} +(-3.49818 - 3.84223i) q^{54} +(0.881264 - 0.508798i) q^{55} +(3.03570 - 1.75266i) q^{56} +(-2.45059 + 8.60599i) q^{57} -2.64442i q^{58} +(8.22333 - 4.74774i) q^{59} +(0.422115 + 1.67983i) q^{60} +0.662787i q^{61} +(1.39033 + 5.39138i) q^{62} +(-9.26680 + 4.97111i) q^{63} -1.00000 q^{64} +(0.278444 + 0.482279i) q^{65} +(-0.429543 - 1.70939i) q^{66} +(0.768714 - 1.33145i) q^{67} +(0.748115 + 1.29577i) q^{68} +(-3.87939 - 4.00245i) q^{69} +3.50532 q^{70} +(9.71728 + 5.61027i) q^{71} +(2.99854 + 0.0936563i) q^{72} +(-5.23937 - 3.02495i) q^{73} +(1.20507 + 2.08724i) q^{74} +(-0.474351 + 1.66583i) q^{75} +(-2.58309 - 4.47405i) q^{76} -3.56700 q^{77} +(0.935475 - 0.235071i) q^{78} +(0.184595 - 0.106576i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-8.98246 - 0.561664i) q^{81} +(4.54027 - 7.86397i) q^{82} +(-1.71612 + 2.97241i) q^{83} +(1.66275 - 5.83927i) q^{84} +1.49623i q^{85} +(-3.28925 - 5.69715i) q^{86} +(-3.18778 - 3.28890i) q^{87} +(0.881264 + 0.508798i) q^{88} +0.779533 q^{89} +(2.54998 + 1.58038i) q^{90} -1.95207i q^{91} +3.21814 q^{92} +(8.22835 + 5.02933i) q^{93} -8.95636 q^{94} -5.16618i q^{95} +(-1.24372 + 1.20548i) q^{96} +13.2793 q^{97} +(-4.57892 - 2.64364i) q^{98} +(-2.59485 - 1.60819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.20548	+	1.24372i	0.695982	+	0.718059i
$3$	1.20548	+	1.24372i	0.695982	+	0.718059i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.24372	+	1.20548i	−0.507745	+	0.492133i
$7$	1.75266	+	3.03570i	0.662443	+	1.14739i	0.979972	+	0.199137i	$0.0638138\pi$
$7$	1.75266	+	3.03570i	0.662443	+	1.14739i	−0.317528	+	0.948249i	$0.602853\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.0936563	+	2.99854i	−0.0312188	+	0.999513i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−0.508798	+	0.881264i	−0.153408	+	0.265711i	−0.932478	−	0.361226i	$-0.882358\pi$
$11$	−0.508798	+	0.881264i	−0.153408	+	0.265711i	0.779070	+	0.626937i	$0.215692\pi$
$12$	−1.20548	−	1.24372i	−0.347991	−	0.359030i
$13$	−0.482279	−	0.278444i	−0.133760	−	0.0772264i	0.431627	−	0.902052i	$-0.357940\pi$
$13$	−0.482279	−	0.278444i	−0.133760	−	0.0772264i	−0.565387	+	0.824826i	$0.691273\pi$
$14$	−3.03570	+	1.75266i	−0.811324	+	0.468418i
$15$	−0.422115	−	1.67983i	−0.108990	−	0.433729i
$16$	1.00000			0.250000
$17$	−0.748115	−	1.29577i	−0.181445	−	0.314271i	0.760928	−	0.648836i	$-0.224744\pi$
$17$	−0.748115	−	1.29577i	−0.181445	−	0.314271i	−0.942373	+	0.334565i	$0.891411\pi$
$18$	−2.99854	−	0.0936563i	−0.706762	−	0.0220750i
$19$	2.58309	+	4.47405i	0.592602	+	1.02642i	0.993880	+	0.110461i	$0.0352326\pi$
$19$	2.58309	+	4.47405i	0.592602	+	1.02642i	−0.401278	+	0.915956i	$0.631434\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−1.66275	+	5.83927i	−0.362843	+	1.27423i
$22$	−0.881264	−	0.508798i	−0.187886	−	0.108476i
$23$	−3.21814			−0.671029			−0.335515	−	0.942035i	$-0.608910\pi$
$23$	−3.21814			−0.671029			−0.335515	+	0.942035i	$0.608910\pi$
$24$	1.24372	−	1.20548i	0.253872	−	0.246067i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.278444	−	0.482279i	0.0546073	−	0.0945827i
$27$	−3.84223	+	3.49818i	−0.739437	+	0.673226i
$28$	−1.75266	−	3.03570i	−0.331222	−	0.573693i
$29$	−2.64442			−0.491056			−0.245528	−	0.969389i	$-0.578961\pi$
$29$	−2.64442			−0.491056			−0.245528	+	0.969389i	$0.578961\pi$
$30$	1.67983	−	0.422115i	0.306693	−	0.0770673i
$31$	5.39138	−	1.39033i	0.968320	−	0.249711i
$31$	5.39138	−	1.39033i	0.968320	−	0.249711i
$32$			1.00000i			0.176777i
$33$	−1.70939	+	0.429543i	−0.297566	+	0.0747738i
$34$	1.29577	−	0.748115i	0.222223	−	0.128301i
$35$		−	3.50532i		−	0.592507i
$36$	0.0936563	−	2.99854i	0.0156094	−	0.499756i
$37$	2.08724	−	1.20507i	0.343140	−	0.198112i	−0.318520	−	0.947916i	$-0.603186\pi$
$37$	2.08724	−	1.20507i	0.343140	−	0.198112i	0.661660	+	0.749804i	$0.269852\pi$
$38$	−4.47405	+	2.58309i	−0.725786	+	0.419033i
$39$	−0.235071	−	0.935475i	−0.0376414	−	0.149796i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−7.86397	−	4.54027i	−1.22815	−	0.709070i	−0.261504	−	0.965202i	$-0.584219\pi$
$41$	−7.86397	−	4.54027i	−1.22815	−	0.709070i	−0.966642	+	0.256132i	$0.917552\pi$
$42$	−5.83927	−	1.66275i	−0.901019	−	0.256568i
$43$	−5.69715	+	3.28925i	−0.868807	+	0.501606i	−0.866952	−	0.498392i	$-0.833924\pi$
$43$	−5.69715	+	3.28925i	−0.868807	+	0.501606i	−0.00185547	+	0.999998i	$0.500591\pi$
$44$	0.508798	−	0.881264i	0.0767042	−	0.132856i
$45$	1.58038	−	2.54998i	0.235589	−	0.380129i
$46$		−	3.21814i		−	0.474489i
$47$			8.95636i			1.30642i	0.757177	+	0.653210i	$0.226578\pi$
$47$			8.95636i			1.30642i	−0.757177	+	0.653210i	$0.773422\pi$
$48$	1.20548	+	1.24372i	0.173995	+	0.179515i
$49$	−2.64364	+	4.57892i	−0.377663	+	0.654131i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	0.709739	−	2.49247i	0.0993833	−	0.349015i
$52$	0.482279	+	0.278444i	0.0668800	+	0.0386132i
$53$	−1.80684	+	3.12954i	−0.248189	+	0.429876i	−0.963023	−	0.269418i	$-0.913169\pi$
$53$	−1.80684	+	3.12954i	−0.248189	+	0.429876i	0.714834	+	0.699294i	$0.246502\pi$
$54$	−3.49818	−	3.84223i	−0.476042	−	0.522861i
$55$	0.881264	−	0.508798i	0.118830	−	0.0686063i
$56$	3.03570	−	1.75266i	0.405662	−	0.234209i
$57$	−2.45059	+	8.60599i	−0.324588	+	1.13989i
$58$		−	2.64442i		−	0.347229i
$59$	8.22333	−	4.74774i	1.07059	−	0.618103i	0.142245	−	0.989832i	$-0.454568\pi$
$59$	8.22333	−	4.74774i	1.07059	−	0.618103i	0.928342	+	0.371728i	$0.121235\pi$
$60$	0.422115	+	1.67983i	0.0544948	+	0.216865i
$61$			0.662787i			0.0848612i	0.999099	+	0.0424306i	$0.0135101\pi$
$61$			0.662787i			0.0848612i	−0.999099	+	0.0424306i	$0.986490\pi$
$62$	1.39033	+	5.39138i	0.176572	+	0.684706i
$63$	−9.26680	+	4.97111i	−1.16751	+	0.626301i
$64$	−1.00000			−0.125000
$65$	0.278444	+	0.482279i	0.0345367	+	0.0598193i
$66$	−0.429543	−	1.70939i	−0.0528730	−	0.210411i
$67$	0.768714	−	1.33145i	0.0939133	−	0.162663i	−0.815241	−	0.579122i	$-0.803396\pi$
$67$	0.768714	−	1.33145i	0.0939133	−	0.162663i	0.909155	+	0.416459i	$0.136729\pi$
$68$	0.748115	+	1.29577i	0.0907223	+	0.157136i
$69$	−3.87939	−	4.00245i	−0.467024	−	0.481839i
$70$	3.50532			0.418966
$71$	9.71728	+	5.61027i	1.15323	+	0.665817i	0.949672	−	0.313246i	$-0.101416\pi$
$71$	9.71728	+	5.61027i	1.15323	+	0.665817i	0.203557	+	0.979063i	$0.434750\pi$
$72$	2.99854	+	0.0936563i	0.353381	+	0.0110375i
$73$	−5.23937	−	3.02495i	−0.613222	−	0.354044i	0.161003	−	0.986954i	$-0.448527\pi$
$73$	−5.23937	−	3.02495i	−0.613222	−	0.354044i	−0.774225	+	0.632910i	$0.781860\pi$
$74$	1.20507	+	2.08724i	0.140086	+	0.242637i
$75$	−0.474351	+	1.66583i	−0.0547734	+	0.192354i
$76$	−2.58309	−	4.47405i	−0.296301	−	0.513208i
$77$	−3.56700			−0.406498
$78$	0.935475	−	0.235071i	0.105922	−	0.0266165i
$79$	0.184595	−	0.106576i	0.0207686	−	0.0119907i	−0.489580	−	0.871959i	$-0.662850\pi$
$79$	0.184595	−	0.106576i	0.0207686	−	0.0119907i	0.510348	+	0.859968i	$0.329516\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−8.98246	−	0.561664i	−0.998051	−	0.0624071i
$82$	4.54027	−	7.86397i	0.501389	−	0.868430i
$83$	−1.71612	+	2.97241i	−0.188369	+	0.326264i	−0.944707	−	0.327917i	$-0.893653\pi$
$83$	−1.71612	+	2.97241i	−0.188369	+	0.326264i	0.756338	+	0.654181i	$0.226987\pi$
$84$	1.66275	−	5.83927i	0.181421	−	0.637117i
$85$			1.49623i			0.162289i
$86$	−3.28925	−	5.69715i	−0.354689	−	0.614339i
$87$	−3.18778	−	3.28890i	−0.341766	−	0.352608i
$88$	0.881264	+	0.508798i	0.0939431	+	0.0542381i
$89$	0.779533			0.0826303			0.0413152	−	0.999146i	$-0.486845\pi$
$89$	0.779533			0.0826303			0.0413152	+	0.999146i	$0.486845\pi$
$90$	2.54998	+	1.58038i	0.268792	+	0.166586i
$91$		−	1.95207i		−	0.204633i
$92$	3.21814			0.335515
$93$	8.22835	+	5.02933i	0.853241	+	0.521518i
$94$	−8.95636			−0.923778
$95$		−	5.16618i		−	0.530039i
$96$	−1.24372	+	1.20548i	−0.126936	+	0.123033i
$97$	13.2793			1.34831			0.674155	−	0.738590i	$-0.264508\pi$
$97$	13.2793			1.34831			0.674155	+	0.738590i	$0.264508\pi$
$98$	−4.57892	−	2.64364i	−0.462540	−	0.267048i
$99$	−2.59485	−	1.60819i	−0.260792	−	0.161629i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	17.5078i		−	1.74209i	−0.491200	−	0.871047i	$-0.663442\pi$
$101$		−	17.5078i		−	1.74209i	0.491200	−	0.871047i	$-0.336558\pi$
$102$	2.49247	+	0.709739i	0.246791	+	0.0702746i
$103$	−0.217920	+	0.377449i	−0.0214723	+	0.0371911i	−0.876562	−	0.481289i	$-0.840169\pi$
$103$	−0.217920	+	0.377449i	−0.0214723	+	0.0371911i	0.855090	+	0.518480i	$0.173502\pi$
$104$	−0.278444	+	0.482279i	−0.0273037	+	0.0472913i
$105$	4.35962	−	4.22558i	0.425456	−	0.412374i
$106$	−3.12954	−	1.80684i	−0.303968	−	0.175496i
$107$	15.5778	−	8.99386i	1.50596	−	0.869469i	0.505988	−	0.862540i	$-0.331128\pi$
$107$	15.5778	−	8.99386i	1.50596	−	0.869469i	0.999976	−	0.00692852i	$-0.00220543\pi$
$108$	3.84223	−	3.49818i	0.369719	−	0.336613i
$109$	7.55577			0.723711			0.361856	−	0.932234i	$-0.382143\pi$
$109$	7.55577			0.723711			0.361856	+	0.932234i	$0.382143\pi$
$110$	0.508798	+	0.881264i	0.0485120	+	0.0840252i
$111$	4.01488	+	1.14325i	0.381075	+	0.108513i
$112$	1.75266	+	3.03570i	0.165611	+	0.286846i
$113$	−4.18028	−	2.41348i	−0.393247	−	0.227041i	0.290319	−	0.956930i	$-0.406239\pi$
$113$	−4.18028	−	2.41348i	−0.393247	−	0.227041i	−0.683566	+	0.729889i	$0.739572\pi$
$114$	−8.60599	−	2.45059i	−0.806025	−	0.229518i
$115$	2.78699	+	1.60907i	0.259888	+	0.150047i
$116$	2.64442			0.245528
$117$	0.880093	−	1.42005i	0.0813646	−	0.131284i
$118$	4.74774	+	8.22333i	0.437065	+	0.757019i
$119$	2.62238	−	4.54210i	0.240394	−	0.416374i
$120$	−1.67983	+	0.422115i	−0.153347	+	0.0385336i
$121$	4.98225	+	8.62951i	0.452932	+	0.784501i
$122$	−0.662787			−0.0600059
$123$	−3.83303	−	15.2537i	−0.345613	−	1.37538i
$124$	−5.39138	+	1.39033i	−0.484160	+	0.124855i
$125$		−	1.00000i		−	0.0894427i
$126$	−4.97111	−	9.26680i	−0.442861	−	0.825552i
$127$	16.3303	−	9.42828i	1.44908	−	0.836624i	0.450650	−	0.892701i	$-0.351192\pi$
$127$	16.3303	−	9.42828i	1.44908	−	0.836624i	0.998426	+	0.0560764i	$0.0178590\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−10.9587	−	3.12052i	−0.964857	−	0.274747i
$130$	−0.482279	+	0.278444i	−0.0422987	+	0.0244211i
$131$	0.711541	−	0.410808i	0.0621676	−	0.0358925i	−0.468594	−	0.883414i	$-0.655239\pi$
$131$	0.711541	−	0.410808i	0.0621676	−	0.0358925i	0.530762	+	0.847521i	$0.321906\pi$
$132$	1.70939	−	0.429543i	0.148783	−	0.0373869i
$133$	−9.05457	+	15.6830i	−0.785131	+	1.35989i
$134$	1.33145	+	0.768714i	0.115020	+	0.0664067i
$135$	5.07656	−	1.10840i	0.436921	−	0.0953960i
$136$	−1.29577	+	0.748115i	−0.111112	+	0.0641503i
$137$	−9.97643	+	17.2797i	−0.852344	+	1.47630i	0.0267437	+	0.999642i	$0.491486\pi$
$137$	−9.97643	+	17.2797i	−0.852344	+	1.47630i	−0.879087	+	0.476660i	$0.841847\pi$
$138$	4.00245	−	3.87939i	0.340712	−	0.330236i
$139$		−	1.22089i		−	0.103555i	−0.998659	−	0.0517773i	$-0.983511\pi$
$139$		−	1.22089i		−	0.103555i	0.998659	−	0.0517773i	$-0.0164886\pi$
$140$			3.50532i			0.296254i
$141$	−11.1392	+	10.7967i	−0.938087	+	0.909244i
$142$	−5.61027	+	9.71728i	−0.470804	+	0.815456i
$143$	0.490765	−	0.283343i	0.0410398	−	0.0236944i
$144$	−0.0936563	+	2.99854i	−0.00780469	+	0.249878i
$145$	2.29013	+	1.32221i	0.190185	+	0.109804i
$146$	3.02495	−	5.23937i	0.250347	−	0.433614i
$147$	−8.88171	+	2.23184i	−0.732551	+	0.184079i
$148$	−2.08724	+	1.20507i	−0.171570	+	0.0990560i
$149$	16.6142	−	9.59220i	1.36109	−	0.785823i	0.371317	−	0.928506i	$-0.378906\pi$
$149$	16.6142	−	9.59220i	1.36109	−	0.785823i	0.989768	+	0.142683i	$0.0455728\pi$
$150$	−1.66583	−	0.474351i	−0.136014	−	0.0387306i
$151$			23.3009i			1.89620i	0.317971	+	0.948100i	$0.396998\pi$
$151$			23.3009i			1.89620i	−0.317971	+	0.948100i	$0.603002\pi$
$152$	4.47405	−	2.58309i	0.362893	−	0.209516i
$153$	3.95549	−	2.12189i	0.319783	−	0.171545i
$154$		−	3.56700i		−	0.287437i
$155$	−5.36424	−	1.49163i	−0.430866	−	0.119810i
$156$	0.235071	+	0.935475i	0.0188207	+	0.0748979i
$157$	10.7418			0.857290			0.428645	−	0.903473i	$-0.358991\pi$
$157$	10.7418			0.857290			0.428645	+	0.903473i	$0.358991\pi$
$158$	0.106576	+	0.184595i	0.00847874	+	0.0146856i
$159$	−6.07037	+	1.52539i	−0.481411	+	0.120971i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−5.64031	−	9.76931i	−0.444519	−	0.769929i
$162$	0.561664	−	8.98246i	0.0441285	−	0.705728i
$163$	−3.56174			−0.278977			−0.139488	−	0.990224i	$-0.544546\pi$
$163$	−3.56174			−0.278977			−0.139488	+	0.990224i	$0.544546\pi$
$164$	7.86397	+	4.54027i	0.614073	+	0.354535i
$165$	1.69514	+	0.482698i	0.131967	+	0.0375780i
$166$	−2.97241	−	1.71612i	−0.230704	−	0.133197i
$167$	5.75062	+	9.96036i	0.444996	+	0.770756i	0.998052	−	0.0623883i	$-0.0198717\pi$
$167$	5.75062	+	9.96036i	0.444996	+	0.770756i	−0.553056	+	0.833144i	$0.686538\pi$
$168$	5.83927	+	1.66275i	0.450509	+	0.128284i
$169$	−6.34494	−	10.9898i	−0.488072	−	0.845366i
$170$	−1.49623			−0.114756
$171$	−13.6575	+	7.32648i	−1.04442	+	0.560270i
$172$	5.69715	−	3.28925i	0.434404	−	0.250803i
$173$	−2.03876	−	1.17708i	−0.155004	−	0.0894917i	0.420492	−	0.907296i	$-0.361858\pi$
$173$	−2.03876	−	1.17708i	−0.155004	−	0.0894917i	−0.575496	+	0.817805i	$0.695191\pi$
$174$	3.28890	−	3.18778i	0.249331	−	0.241665i
$175$	−1.75266	+	3.03570i	−0.132489	+	0.229477i
$176$	−0.508798	+	0.881264i	−0.0383521	+	0.0664278i
$177$	15.8179	+	4.50419i	1.18894	+	0.338556i
$178$			0.779533i			0.0584285i
$179$	−1.49415	−	2.58794i	−0.111678	−	0.193432i	0.804769	−	0.593588i	$-0.202289\pi$
$179$	−1.49415	−	2.58794i	−0.111678	−	0.193432i	−0.916447	+	0.400156i	$0.868956\pi$
$180$	−1.58038	+	2.54998i	−0.117794	+	0.190064i
$181$	18.9344	+	10.9318i	1.40738	+	0.812552i	0.995135	−	0.0985208i	$-0.0314111\pi$
$181$	18.9344	+	10.9318i	1.40738	+	0.812552i	0.412246	+	0.911073i	$0.364744\pi$
$182$	1.95207			0.144697
$183$	−0.824318	+	0.798974i	−0.0609354	+	0.0590618i
$184$			3.21814i			0.237245i
$185$	−2.41014			−0.177197
$186$	−5.02933	+	8.22835i	−0.368769	+	0.603332i
$187$	1.52256			0.111340
$188$		−	8.95636i		−	0.653210i
$189$	−17.3535	−	5.53271i	−1.26228	−	0.402446i
$190$	5.16618			0.374794
$191$	8.08961	+	4.67054i	0.585343	+	0.337948i	0.763254	−	0.646099i	$-0.223600\pi$
$191$	8.08961	+	4.67054i	0.585343	+	0.337948i	−0.177911	+	0.984047i	$0.556934\pi$
$192$	−1.20548	−	1.24372i	−0.0869977	−	0.0897574i
$193$	−0.846405	−	1.46602i	−0.0609256	−	0.105526i	0.833954	−	0.551834i	$-0.186072\pi$
$193$	−0.846405	−	1.46602i	−0.0609256	−	0.105526i	−0.894879	+	0.446308i	$0.852739\pi$
$194$			13.2793i			0.953400i
$195$	−0.264160	+	0.927680i	−0.0189169	+	0.0664326i
$196$	2.64364	−	4.57892i	0.188831	−	0.327065i
$197$	−7.92946	+	13.7342i	−0.564951	+	0.978524i	0.432103	+	0.901824i	$0.357772\pi$
$197$	−7.92946	+	13.7342i	−0.564951	+	0.978524i	−0.997054	+	0.0766996i	$0.975562\pi$
$198$	1.60819	−	2.59485i	0.114289	−	0.184408i
$199$	−11.7826	−	6.80268i	−0.835246	−	0.482229i	0.0203995	−	0.999792i	$-0.493506\pi$
$199$	−11.7826	−	6.80268i	−0.835246	−	0.482229i	−0.855645	+	0.517562i	$0.826840\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	2.58261	−	0.648971i	0.182163	−	0.0457749i
$202$	17.5078			1.23185
$203$	−4.63477	−	8.02765i	−0.325297	−	0.563431i
$204$	−0.709739	+	2.49247i	−0.0496917	+	0.174508i
$205$	4.54027	+	7.86397i	0.317106	+	0.549244i
$206$	−0.377449	−	0.217920i	−0.0262981	−	0.0151832i
$207$	0.301399	−	9.64972i	0.0209487	−	0.670702i
$208$	−0.482279	−	0.278444i	−0.0334400	−	0.0193066i
$209$	−5.25709			−0.363641
$210$	4.22558	+	4.35962i	0.291593	+	0.300843i
$211$	−4.46360	−	7.73118i	−0.307287	−	0.532236i	0.670481	−	0.741927i	$-0.266088\pi$
$211$	−4.46360	−	7.73118i	−0.307287	−	0.532236i	−0.977768	+	0.209690i	$0.932754\pi$
$212$	1.80684	−	3.12954i	0.124094	−	0.214938i
$213$	4.73636	+	18.8486i	0.324530	+	1.29148i
$214$	8.99386	+	15.5778i	0.614807	+	1.06488i
$215$	6.57850			0.448650
$216$	3.49818	+	3.84223i	0.238021	+	0.261431i
$217$	13.6699	+	13.9298i	0.927972	+	0.945618i
$218$			7.55577i			0.511741i
$219$	−2.55376	−	10.1628i	−0.172567	−	0.686738i
$220$	−0.881264	+	0.508798i	−0.0594148	+	0.0343032i
$221$			0.833232i			0.0560493i
$222$	−1.14325	+	4.01488i	−0.0767300	+	0.269461i
$223$	6.97582	−	4.02749i	0.467136	−	0.269701i	−0.247904	−	0.968785i	$-0.579742\pi$
$223$	6.97582	−	4.02749i	0.467136	−	0.269701i	0.715040	+	0.699084i	$0.246408\pi$
$224$	−3.03570	+	1.75266i	−0.202831	+	0.117105i
$225$	−2.64364	+	1.41816i	−0.176243	+	0.0945440i
$226$	2.41348	−	4.18028i	0.160543	−	0.278068i
$227$	15.0890	+	8.71161i	1.00149	+	0.578210i	0.908689	−	0.417475i	$-0.137085\pi$
$227$	15.0890	+	8.71161i	1.00149	+	0.578210i	0.0928007	+	0.995685i	$0.470418\pi$
$228$	2.45059	−	8.60599i	0.162294	−	0.569945i
$229$	−12.2125	+	7.05087i	−0.807023	+	0.465935i	−0.845921	−	0.533308i	$-0.820949\pi$
$229$	−12.2125	+	7.05087i	−0.807023	+	0.465935i	0.0388982	+	0.999243i	$0.487615\pi$
$230$	−1.60907	+	2.78699i	−0.106099	+	0.183769i
$231$	−4.29993	−	4.43634i	−0.282915	−	0.291889i
$232$			2.64442i			0.173615i
$233$			2.39244i			0.156734i	0.996925	+	0.0783669i	$0.0249706\pi$
$233$			2.39244i			0.156734i	−0.996925	+	0.0783669i	$0.975029\pi$
$234$	1.42005	+	0.880093i	0.0928318	+	0.0575335i
$235$	4.47818	−	7.75644i	0.292124	−	0.505974i
$236$	−8.22333	+	4.74774i	−0.535293	+	0.309052i
$237$	0.355075	+	0.101109i	0.0230646	+	0.00656774i
$238$	4.54210	+	2.62238i	0.294421	+	0.169984i
$239$	5.50979	−	9.54323i	0.356398	−	0.617300i	−0.630958	−	0.775817i	$-0.717338\pi$
$239$	5.50979	−	9.54323i	0.356398	−	0.617300i	0.987356	+	0.158517i	$0.0506712\pi$
$240$	−0.422115	−	1.67983i	−0.0272474	−	0.108432i
$241$	21.5818	−	12.4602i	1.39020	−	0.802634i	0.396866	−	0.917877i	$-0.370098\pi$
$241$	21.5818	−	12.4602i	1.39020	−	0.802634i	0.993337	+	0.115243i	$0.0367646\pi$
$242$	−8.62951	+	4.98225i	−0.554726	+	0.320271i
$243$	−10.1296	−	11.8487i	−0.649813	−	0.760094i
$244$		−	0.662787i		−	0.0424306i
$245$	4.57892	−	2.64364i	0.292536	−	0.168896i
$246$	15.2537	−	3.83303i	0.972542	−	0.244385i
$247$		−	2.87698i		−	0.183058i
$248$	−1.39033	−	5.39138i	−0.0882861	−	0.342353i
$249$	−5.76557	+	1.44880i	−0.365378	+	0.0918140i
$250$	1.00000			0.0632456
$251$	−6.60787	−	11.4452i	−0.417085	−	0.722413i	0.578560	−	0.815640i	$-0.303615\pi$
$251$	−6.60787	−	11.4452i	−0.417085	−	0.722413i	−0.995645	+	0.0932274i	$0.970282\pi$
$252$	9.26680	−	4.97111i	0.583754	−	0.313150i
$253$	1.63739	−	2.83603i	0.102942	−	0.178300i
$254$	9.42828	+	16.3303i	0.591583	+	1.02465i
$255$	−1.86088	+	1.80367i	−0.116533	+	0.112950i
$256$	1.00000			0.0625000
$257$	22.1051	+	12.7624i	1.37888	+	0.796096i	0.992025	−	0.126044i	$-0.0402281\pi$
$257$	22.1051	+	12.7624i	1.37888	+	0.796096i	0.386855	+	0.922141i	$0.373561\pi$
$258$	3.12052	−	10.9587i	0.194275	−	0.682257i
$259$	7.31644	+	4.22415i	0.454622	+	0.262476i
$260$	−0.278444	−	0.482279i	−0.0172684	−	0.0299097i
$261$	0.247667	−	7.92939i	0.0153302	−	0.490817i
$262$	0.410808	+	0.711541i	0.0253798	+	0.0439591i
$263$	17.3755			1.07142			0.535709	−	0.844403i	$-0.320044\pi$
$263$	17.3755			1.07142			0.535709	+	0.844403i	$0.320044\pi$
$264$	0.429543	+	1.70939i	0.0264365	+	0.105205i
$265$	3.12954	−	1.80684i	0.192246	−	0.110993i
$266$	−15.6830	−	9.05457i	−0.961585	−	0.555171i
$267$	0.939708	+	0.969517i	0.0575092	+	0.0593335i
$268$	−0.768714	+	1.33145i	−0.0469567	+	0.0813313i
$269$	−5.43030	+	9.40555i	−0.331091	+	0.573466i	−0.982726	−	0.185066i	$-0.940750\pi$
$269$	−5.43030	+	9.40555i	−0.331091	+	0.573466i	0.651635	+	0.758533i	$0.274083\pi$
$270$	1.10840	+	5.07656i	0.0674551	+	0.308950i
$271$			0.444297i			0.0269891i	0.999909	+	0.0134945i	$0.00429558\pi$
$271$			0.444297i			0.0269891i	−0.999909	+	0.0134945i	$0.995704\pi$
$272$	−0.748115	−	1.29577i	−0.0453611	−	0.0785678i
$273$	2.42782	−	2.35317i	0.146938	−	0.142421i
$274$	−17.2797	−	9.97643i	−1.04390	−	0.602698i
$275$	−1.01760			−0.0613634
$276$	3.87939	+	4.00245i	0.233512	+	0.240919i
$277$			8.03697i			0.482895i	0.970414	+	0.241447i	$0.0776221\pi$
$277$			8.03697i			0.482895i	−0.970414	+	0.241447i	$0.922378\pi$
$278$	1.22089			0.0732242
$279$	3.66402	+	16.2965i	0.219359	+	0.975644i
$280$	−3.50532			−0.209483
$281$		−	13.9273i		−	0.830831i	−0.909632	−	0.415415i	$-0.863636\pi$
$281$		−	13.9273i		−	0.830831i	0.909632	−	0.415415i	$-0.136364\pi$
$282$	−10.7967	−	11.1392i	−0.642933	−	0.663328i
$283$	−28.1351			−1.67246			−0.836230	−	0.548379i	$-0.815245\pi$
$283$	−28.1351			−1.67246			−0.836230	+	0.548379i	$0.815245\pi$
$284$	−9.71728	−	5.61027i	−0.576614	−	0.332909i
$285$	6.42526	−	6.22771i	0.380600	−	0.368898i
$286$	0.283343	+	0.490765i	0.0167544	+	0.0290195i
$287$		−	31.8302i		−	1.87888i
$288$	−2.99854	−	0.0936563i	−0.176691	−	0.00551875i
$289$	7.38065	−	12.7837i	0.434156	−	0.751980i
$290$	−1.32221	+	2.29013i	−0.0776428	+	0.134481i
$291$	16.0079	+	16.5157i	0.938400	+	0.968167i
$292$	5.23937	+	3.02495i	0.306611	+	0.177022i
$293$	19.0627	−	11.0058i	1.11365	−	0.642968i	0.173880	−	0.984767i	$-0.444370\pi$
$293$	19.0627	−	11.0058i	1.11365	−	0.642968i	0.939773	+	0.341799i	$0.111036\pi$
$294$	−2.23184	−	8.88171i	−0.130163	−	0.517992i
$295$	−9.49548			−0.552848
$296$	−1.20507	−	2.08724i	−0.0700431	−	0.121318i
$297$	−1.12790	−	5.16589i	−0.0654477	−	0.299755i
$298$	9.59220	+	16.6142i	0.555661	+	0.962433i
$299$	1.55204	+	0.896072i	0.0897569	+	0.0518212i
$300$	0.474351	−	1.66583i	0.0273867	−	0.0961768i
$301$	−19.9703	−	11.5299i	−1.15107	−	0.664571i
$302$	−23.3009			−1.34082
$303$	21.7748	−	21.1053i	1.25093	−	1.21247i
$304$	2.58309	+	4.47405i	0.148151	+	0.256604i
$305$	0.331394	−	0.573990i	0.0189755	−	0.0328666i
$306$	2.12189	+	3.95549i	0.121301	+	0.226120i
$307$	−2.89082	−	5.00704i	−0.164988	−	0.285767i	0.771663	−	0.636031i	$-0.219425\pi$
$307$	−2.89082	−	5.00704i	−0.164988	−	0.285767i	−0.936651	+	0.350264i	$0.886092\pi$
$308$	3.56700			0.203249
$309$	−0.732136	+	0.183975i	−0.0416498	+	0.0104660i
$310$	1.49163	−	5.36424i	0.0847188	−	0.304668i
$311$		−	0.448742i		−	0.0254458i	−0.999919	−	0.0127229i	$-0.995950\pi$
$311$		−	0.448742i		−	0.0254458i	0.999919	−	0.0127229i	$-0.00404994\pi$
$312$	−0.935475	+	0.235071i	−0.0529608	+	0.0133082i
$313$	15.1343	−	8.73777i	0.855439	−	0.493888i	−0.00704303	−	0.999975i	$-0.502242\pi$
$313$	15.1343	−	8.73777i	0.855439	−	0.493888i	0.862482	+	0.506087i	$0.168909\pi$
$314$			10.7418i			0.606196i
$315$	10.5108	+	0.328295i	0.592219	+	0.0184974i
$316$	−0.184595	+	0.106576i	−0.0103843	+	0.00599537i
$317$	−1.12178	+	0.647660i	−0.0630055	+	0.0363762i	−0.531172	−	0.847264i	$-0.678248\pi$
$317$	−1.12178	+	0.647660i	−0.0630055	+	0.0363762i	0.468166	+	0.883640i	$0.344915\pi$
$318$	−1.52539	−	6.07037i	−0.0855397	−	0.340409i
$319$	1.34548	−	2.33043i	0.0753322	−	0.130479i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	29.9645	+	8.53249i	1.67245	+	0.476237i
$322$	9.76931	−	5.64031i	0.544422	−	0.314322i
$323$	3.86490	−	6.69421i	0.215049	−	0.372476i
$324$	8.98246	+	0.561664i	0.499025	+	0.0312036i
$325$		−	0.556888i		−	0.0308906i
$326$		−	3.56174i		−	0.197266i
$327$	9.10829	+	9.39723i	0.503690	+	0.519668i
$328$	−4.54027	+	7.86397i	−0.250694	+	0.434215i
$329$	−27.1888	+	15.6975i	−1.49897	+	0.865429i
$330$	−0.482698	+	1.69514i	−0.0265717	+	0.0933145i
$331$	−17.5084	−	10.1085i	−0.962351	−	0.555614i	−0.0654553	−	0.997856i	$-0.520850\pi$
$331$	−17.5084	−	10.1085i	−0.962351	−	0.555614i	−0.896896	+	0.442242i	$0.854183\pi$
$332$	1.71612	−	2.97241i	0.0941844	−	0.163132i
$333$	3.41796	+	6.37153i	0.187303	+	0.349158i
$334$	−9.96036	+	5.75062i	−0.545007	+	0.314660i
$335$	−1.33145	+	0.768714i	−0.0727449	+	0.0419993i
$336$	−1.66275	+	5.83927i	−0.0907106	+	0.318558i
$337$			11.8084i			0.643243i	0.946868	+	0.321622i	$0.104228\pi$
$337$			11.8084i			0.643243i	−0.946868	+	0.321622i	$0.895772\pi$
$338$	10.9898	−	6.34494i	0.597764	−	0.345119i
$339$	−2.03753	−	8.10847i	−0.110664	−	0.440392i
$340$		−	1.49623i		−	0.0811445i
$341$	−1.51788	+	5.45863i	−0.0821976	+	0.295601i
$342$	−7.32648	−	13.6575i	−0.396171	−	0.738514i
$343$	6.00365			0.324166
$344$	3.28925	+	5.69715i	0.177345	+	0.307170i
$345$	1.35843	+	5.40592i	0.0731352	+	0.291045i
$346$	1.17708	−	2.03876i	0.0632802	−	0.109605i
$347$	−2.75581	−	4.77321i	−0.147940	−	0.256239i	0.782526	−	0.622618i	$-0.213931\pi$
$347$	−2.75581	−	4.77321i	−0.147940	−	0.256239i	−0.930466	+	0.366379i	$0.880598\pi$
$348$	3.18778	+	3.28890i	0.170883	+	0.176304i
$349$	−21.0390			−1.12619			−0.563095	−	0.826392i	$-0.690390\pi$
$349$	−21.0390			−1.12619			−0.563095	+	0.826392i	$0.690390\pi$
$350$	−3.03570	−	1.75266i	−0.162265	−	0.0936836i
$351$	2.82707	−	0.617255i	0.150898	−	0.0329466i
$352$	−0.881264	−	0.508798i	−0.0469715	−	0.0271190i
$353$	12.9487	+	22.4278i	0.689189	+	1.19371i	0.972101	+	0.234564i	$0.0753664\pi$
$353$	12.9487	+	22.4278i	0.689189	+	1.19371i	−0.282912	+	0.959146i	$0.591300\pi$
$354$	−4.50419	+	15.8179i	−0.239395	+	0.840710i
$355$	−5.61027	−	9.71728i	−0.297762	−	0.515740i
$356$	−0.779533			−0.0413152
$357$	8.81030	−	2.21389i	0.466291	−	0.117172i
$358$	2.58794	−	1.49415i	0.136777	−	0.0789683i
$359$	−7.88537	−	4.55262i	−0.416174	−	0.240278i	0.277265	−	0.960793i	$-0.410572\pi$
$359$	−7.88537	−	4.55262i	−0.416174	−	0.240278i	−0.693439	+	0.720515i	$0.743905\pi$
$360$	−2.54998	−	1.58038i	−0.134396	−	0.0832932i
$361$	−3.84473	+	6.65927i	−0.202354	+	0.350488i
$362$	−10.9318	+	18.9344i	−0.574561	+	0.995169i
$363$	−4.72667	+	16.5992i	−0.248086	+	0.871230i
$364$			1.95207i			0.102316i
$365$	3.02495	+	5.23937i	0.158333	+	0.274241i
$366$	−0.798974	−	0.824318i	−0.0417630	−	0.0430878i
$367$	−29.0390	−	16.7657i	−1.51582	−	0.875162i	−0.999828	−	0.0185717i	$-0.994088\pi$
$367$	−29.0390	−	16.7657i	−1.51582	−	0.875162i	−0.515997	−	0.856590i	$-0.672579\pi$
$368$	−3.21814			−0.167757
$369$	14.3507	−	23.1552i	0.747066	−	1.20541i
$370$		−	2.41014i		−	0.125297i
$371$	−12.6671			−0.657645
$372$	−8.22835	−	5.02933i	−0.426620	−	0.260759i
$373$	−23.3875			−1.21096			−0.605479	−	0.795862i	$-0.707018\pi$
$373$	−23.3875			−1.21096			−0.605479	+	0.795862i	$0.707018\pi$
$374$			1.52256i			0.0787296i
$375$	1.24372	−	1.20548i	0.0642252	−	0.0622505i
$376$	8.95636			0.461889
$377$	1.27535	+	0.736322i	0.0656837	+	0.0379225i
$378$	5.53271	−	17.3535i	0.284572	−	0.892570i
$379$	−5.80353	−	10.0520i	−0.298107	−	0.516337i	0.677596	−	0.735435i	$-0.263022\pi$
$379$	−5.80353	−	10.0520i	−0.298107	−	0.516337i	−0.975703	+	0.219098i	$0.929689\pi$
$380$			5.16618i			0.265020i
$381$	31.4118	+	8.94463i	1.60928	+	0.458247i
$382$	−4.67054	+	8.08961i	−0.238965	+	0.413900i
$383$	−1.14352	+	1.98063i	−0.0584311	+	0.101206i	−0.893761	−	0.448543i	$-0.851943\pi$
$383$	−1.14352	+	1.98063i	−0.0584311	+	0.101206i	0.835330	+	0.549749i	$0.185276\pi$
$384$	1.24372	−	1.20548i	0.0634681	−	0.0615167i
$385$	3.08911	+	1.78350i	0.157436	+	0.0908956i
$386$	1.46602	−	0.846405i	0.0746183	−	0.0430809i
$387$	−9.32937	−	17.3912i	−0.474238	−	0.884043i
$388$	−13.2793			−0.674155
$389$	−1.40760	−	2.43804i	−0.0713684	−	0.123614i	0.828133	−	0.560532i	$-0.189403\pi$
$389$	−1.40760	−	2.43804i	−0.0713684	−	0.123614i	−0.899501	+	0.436918i	$0.856070\pi$
$390$	−0.927680	−	0.264160i	−0.0469749	−	0.0133763i
$391$	2.40754	+	4.16998i	0.121755	+	0.210885i
$392$	4.57892	+	2.64364i	0.231270	+	0.133524i
$393$	1.36867	+	0.389735i	0.0690405	+	0.0196595i
$394$	−13.7342	−	7.92946i	−0.691921	−	0.399481i
$395$	−0.213152			−0.0107248
$396$	2.59485	+	1.60819i	0.130396	+	0.0808144i
$397$	−2.67976	−	4.64148i	−0.134493	−	0.232949i	0.790910	−	0.611932i	$-0.209607\pi$
$397$	−2.67976	−	4.64148i	−0.134493	−	0.232949i	−0.925404	+	0.378983i	$0.876274\pi$
$398$	6.80268	−	11.7826i	0.340988	−	0.590608i
$399$	−30.4202	+	7.64414i	−1.52292	+	0.382685i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−11.7824			−0.588384			−0.294192	−	0.955746i	$-0.595050\pi$
$401$	−11.7824			−0.588384			−0.294192	+	0.955746i	$0.595050\pi$
$402$	0.648971	+	2.58261i	0.0323677	+	0.128809i
$403$	−2.98728	−	0.830669i	−0.148807	−	0.0413786i
$404$			17.5078i			0.871047i
$405$	7.49820	+	4.97764i	0.372589	+	0.247341i
$406$	8.02765	−	4.63477i	0.398406	−	0.230020i
$407$			2.45255i			0.121568i
$408$	−2.49247	−	0.709739i	−0.123395	−	0.0351373i
$409$	−0.573155	+	0.330911i	−0.0283407	+	0.0163625i	−0.514103	−	0.857728i	$-0.671875\pi$
$409$	−0.573155	+	0.330911i	−0.0283407	+	0.0163625i	0.485763	+	0.874091i	$0.338542\pi$
$410$	−7.86397	+	4.54027i	−0.388374	+	0.224228i
$411$	−33.5173	+	8.42240i	−1.65329	+	0.415446i
$412$	0.217920	−	0.377449i	0.0107362	−	0.0185956i
$413$	28.8254	+	16.6424i	1.41841	+	0.818917i
$414$	9.64972	+	0.301399i	0.474258	+	0.0148130i
$415$	2.97241	−	1.71612i	0.145910	−	0.0842411i
$416$	0.278444	−	0.482279i	0.0136518	−	0.0236457i
$417$	1.51844	−	1.47176i	0.0743584	−	0.0720722i
$418$		−	5.25709i		−	0.257133i
$419$		−	4.45152i		−	0.217471i	−0.994071	−	0.108736i	$-0.965320\pi$
$419$		−	4.45152i		−	0.217471i	0.994071	−	0.108736i	$-0.0346802\pi$
$420$	−4.35962	+	4.22558i	−0.212728	+	0.206187i
$421$	5.24985	−	9.09301i	0.255862	−	0.443166i	−0.709267	−	0.704940i	$-0.750974\pi$
$421$	5.24985	−	9.09301i	0.255862	−	0.443166i	0.965129	+	0.261774i	$0.0843073\pi$
$422$	7.73118	−	4.46360i	0.376348	−	0.217285i
$423$	−26.8560	−	0.838820i	−1.30578	−	0.0407848i
$424$	3.12954	+	1.80684i	0.151984	+	0.0877480i
$425$	0.748115	−	1.29577i	0.0362889	−	0.0628542i
$426$	−18.8486	+	4.73636i	−0.913217	+	0.229477i
$427$	−2.01202	+	1.16164i	−0.0973685	+	0.0562157i
$428$	−15.5778	+	8.99386i	−0.752982	+	0.434734i
$429$	0.944004	+	0.268809i	0.0455769	+	0.0129782i
$430$			6.57850i			0.317244i
$431$	−10.1716	+	5.87257i	−0.489948	+	0.282872i	−0.724553	−	0.689219i	$-0.757954\pi$
$431$	−10.1716	+	5.87257i	−0.489948	+	0.282872i	0.234605	+	0.972091i	$0.424620\pi$
$432$	−3.84223	+	3.49818i	−0.184859	+	0.168306i
$433$		−	0.986441i		−	0.0474053i	−0.999719	−	0.0237027i	$-0.992455\pi$
$433$		−	0.986441i		−	0.0474053i	0.999719	−	0.0237027i	$-0.00754550\pi$
$434$	−13.9298	+	13.6699i	−0.668653	+	0.656175i
$435$	1.11625	+	4.44217i	0.0535200	+	0.212986i
$436$	−7.55577			−0.361856
$437$	−8.31276	−	14.3981i	−0.397653	−	0.688756i
$438$	10.1628	−	2.55376i	0.485597	−	0.122023i
$439$	−0.755941	+	1.30933i	−0.0360791	+	0.0624909i	−0.883501	−	0.468429i	$-0.844820\pi$
$439$	−0.755941	+	1.30933i	−0.0360791	+	0.0624909i	0.847422	+	0.530920i	$0.178153\pi$
$440$	−0.508798	−	0.881264i	−0.0242560	−	0.0420126i
$441$	−13.4825	−	8.35589i	−0.642022	−	0.397900i
$442$	−0.833232			−0.0396328
$443$	−32.6594	−	18.8559i	−1.55169	−	0.895871i	−0.998004	−	0.0631476i	$-0.979886\pi$
$443$	−32.6594	−	18.8559i	−1.55169	−	0.895871i	−0.553690	−	0.832723i	$-0.686781\pi$
$444$	−4.01488	−	1.14325i	−0.190538	−	0.0542563i
$445$	−0.675095	−	0.389767i	−0.0320026	−	0.0184767i
$446$	4.02749	+	6.97582i	0.190707	+	0.330315i
$447$	31.9579	+	9.10014i	1.51156	+	0.430422i
$448$	−1.75266	−	3.03570i	−0.0828054	−	0.143423i
$449$	−19.1329			−0.902938			−0.451469	−	0.892287i	$-0.649100\pi$
$449$	−19.1329			−0.902938			−0.451469	+	0.892287i	$0.649100\pi$
$450$	−1.41816	−	2.64364i	−0.0668527	−	0.124622i
$451$	8.00235	−	4.62016i	0.376816	−	0.217555i
$452$	4.18028	+	2.41348i	0.196624	+	0.113521i
$453$	−28.9797	+	28.0887i	−1.36158	+	1.31972i
$454$	−8.71161	+	15.0890i	−0.408856	+	0.708160i
$455$	−0.976035	+	1.69054i	−0.0457572	+	0.0792538i
$456$	8.60599	+	2.45059i	0.403012	+	0.114759i
$457$			33.8765i			1.58468i	0.610082	+	0.792338i	$0.291136\pi$
$457$			33.8765i			1.58468i	−0.610082	+	0.792338i	$0.708864\pi$
$458$	−7.05087	−	12.2125i	−0.329466	−	0.570651i
$459$	7.40728	+	2.36161i	0.345742	+	0.110231i
$460$	−2.78699	−	1.60907i	−0.129944	−	0.0750233i
$461$	20.2187			0.941678			0.470839	−	0.882219i	$-0.343951\pi$
$461$	20.2187			0.941678			0.470839	+	0.882219i	$0.343951\pi$
$462$	4.43634	−	4.29993i	0.206397	−	0.200051i
$463$			4.75152i			0.220822i	0.993886	+	0.110411i	$0.0352167\pi$
$463$			4.75152i			0.220822i	−0.993886	+	0.110411i	$0.964783\pi$
$464$	−2.64442			−0.122764
$465$	−4.61130	−	8.46971i	−0.213844	−	0.392773i
$466$	−2.39244			−0.110828
$467$		−	4.46882i		−	0.206792i	−0.994640	−	0.103396i	$-0.967029\pi$
$467$		−	4.46882i		−	0.206792i	0.994640	−	0.103396i	$-0.0329709\pi$
$468$	−0.880093	+	1.42005i	−0.0406823	+	0.0656420i
$469$	5.38918			0.248849
$470$	7.75644	+	4.47818i	0.357778	+	0.206563i
$471$	12.9490	+	13.3598i	0.596658	+	0.615585i
$472$	−4.74774	−	8.22333i	−0.218533	−	0.378509i
$473$		−	6.69426i		−	0.307802i
$474$	−0.101109	+	0.355075i	−0.00464409	+	0.0163092i
$475$	−2.58309	+	4.47405i	−0.118520	+	0.205283i
$476$	−2.62238	+	4.54210i	−0.120197	+	0.208187i
$477$	−9.21483	−	5.71099i	−0.421918	−	0.261488i
$478$	9.54323	+	5.50979i	0.436497	+	0.252012i
$479$	7.32007	−	4.22624i	0.334463	−	0.193102i	−0.323358	−	0.946277i	$-0.604812\pi$
$479$	7.32007	−	4.22624i	0.334463	−	0.193102i	0.657821	+	0.753175i	$0.271478\pi$
$480$	1.67983	−	0.422115i	0.0766733	−	0.0192668i
$481$	−1.34217			−0.0611979
$482$	12.4602	+	21.5818i	0.567548	+	0.983022i
$483$	5.35098	−	18.7916i	0.243478	−	0.855048i
$484$	−4.98225	−	8.62951i	−0.226466	−	0.392250i
$485$	−11.5002	−	6.63966i	−0.522198	−	0.301491i
$486$	11.8487	−	10.1296i	0.537468	−	0.459487i
$487$	−29.2380	−	16.8806i	−1.32490	−	0.764931i	−0.340394	−	0.940283i	$-0.610560\pi$
$487$	−29.2380	−	16.8806i	−1.32490	−	0.764931i	−0.984506	+	0.175352i	$0.943894\pi$
$488$	0.662787			0.0300030
$489$	−4.29359	−	4.42979i	−0.194163	−	0.200322i
$490$	2.64364	+	4.57892i	0.119427	+	0.206854i
$491$	−3.86335	+	6.69152i	−0.174351	+	0.301984i	−0.939936	−	0.341350i	$-0.889116\pi$
$491$	−3.86335	+	6.69152i	−0.174351	+	0.301984i	0.765586	+	0.643334i	$0.222449\pi$
$492$	3.83303	+	15.2537i	0.172806	+	0.687691i
$493$	1.97833	+	3.42657i	0.0890995	+	0.154325i
$494$	2.87698			0.129442
$495$	1.44311	+	2.69016i	0.0648632	+	0.120914i
$496$	5.39138	−	1.39033i	0.242080	−	0.0624277i
$497$			39.3316i			1.76426i
$498$	−1.44880	−	5.76557i	−0.0649223	−	0.258362i
$499$	28.3347	−	16.3590i	1.26843	−	0.732330i	0.293742	−	0.955885i	$-0.405099\pi$
$499$	28.3347	−	16.3590i	1.26843	−	0.732330i	0.974691	+	0.223554i	$0.0717660\pi$
$500$			1.00000i			0.0447214i
$501$	−5.45563	+	19.1591i	−0.243739	+	0.855966i
$502$	11.4452	−	6.60787i	0.510823	−	0.294924i
$503$	−25.7137	+	14.8458i	−1.14652	+	0.661942i	−0.948036	−	0.318162i	$-0.896934\pi$
$503$	−25.7137	+	14.8458i	−1.14652	+	0.661942i	−0.198482	+	0.980105i	$0.563601\pi$
$504$	4.97111	+	9.26680i	0.221431	+	0.412776i
$505$	−8.75391	+	15.1622i	−0.389544	+	0.674710i
$506$	2.83603	+	1.63739i	0.126077	+	0.0727906i
$507$	6.01946	−	21.1392i	0.267334	−	0.938824i
$508$	−16.3303	+	9.42828i	−0.724538	+	0.418312i
$509$	13.1355	−	22.7513i	0.582219	−	1.00843i	−0.412997	−	0.910733i	$-0.635518\pi$
$509$	13.1355	−	22.7513i	0.582219	−	1.00843i	0.995216	−	0.0977008i	$-0.0311488\pi$
$510$	−1.80367	−	1.86088i	−0.0798678	−	0.0824014i
$511$		−	21.2069i		−	0.938137i
$512$			1.00000i			0.0441942i
$513$	−25.5759	−	8.15418i	−1.12920	−	0.360016i
$514$	−12.7624	+	22.1051i	−0.562925	+	0.975015i
$515$	0.377449	−	0.217920i	0.0166324	−	0.00960271i
$516$	10.9587	+	3.12052i	0.482428	+	0.137373i
$517$	−7.89292	−	4.55698i	−0.347130	−	0.200416i
$518$	−4.22415	+	7.31644i	−0.185598	+	0.321466i
$519$	−0.993726	−	3.95458i	−0.0436197	−	0.173587i
$520$	0.482279	−	0.278444i	0.0211493	−	0.0122106i
$521$	−33.3101	+	19.2316i	−1.45934	+	0.842552i	−0.998979	−	0.0451783i	$-0.985614\pi$
$521$	−33.3101	+	19.2316i	−1.45934	+	0.842552i	−0.460364	+	0.887730i	$0.652281\pi$
$522$	7.92939	+	0.247667i	0.347060	+	0.0108401i
$523$		−	7.33956i		−	0.320937i	−0.987041	−	0.160468i	$-0.948700\pi$
$523$		−	7.33956i		−	0.320937i	0.987041	−	0.160468i	$-0.0513004\pi$
$524$	−0.711541	+	0.410808i	−0.0310838	+	0.0179462i
$525$	−5.88833	+	1.47965i	−0.256988	+	0.0645771i
$526$			17.3755i			0.757607i
$527$	−5.83493	−	5.94588i	−0.254173	−	0.259007i
$528$	−1.70939	+	0.429543i	−0.0743915	+	0.0186934i
$529$	−12.6436			−0.549720
$530$	1.80684	+	3.12954i	0.0784842	+	0.135939i
$531$	13.4661	+	25.1026i	0.584380	+	1.08936i
$532$	9.05457	−	15.6830i	0.392565	−	0.679943i
$533$	2.52842	+	4.37935i	0.109518	+	0.189691i
$534$	−0.969517	+	0.939708i	−0.0419551	+	0.0406651i
$535$	−17.9877			−0.777677
$536$	−1.33145	−	0.768714i	−0.0575099	−	0.0332034i
$537$	1.41750	−	4.97800i	0.0611698	−	0.214817i
$538$	−9.40555	−	5.43030i	−0.405502	−	0.234117i
$539$	−2.69016	−	4.65949i	−0.115873	−	0.200698i
$540$	−5.07656	+	1.10840i	−0.218460	+	0.0476980i
$541$	−13.7846	−	23.8755i	−0.592644	−	1.02649i	−0.993875	−	0.110513i	$-0.964751\pi$
$541$	−13.7846	−	23.8755i	−0.592644	−	1.02649i	0.401231	−	0.915977i	$-0.368583\pi$
$542$	−0.444297			−0.0190842
$543$	9.22892	+	36.7270i	0.396051	+	1.57610i
$544$	1.29577	−	0.748115i	0.0555558	−	0.0320752i
$545$	−6.54349	−	3.77788i	−0.280292	−	0.161827i
$546$	2.35317	+	2.42782i	0.100707	+	0.103901i
$547$	17.8437	−	30.9062i	0.762941	−	1.32145i	−0.178387	−	0.983960i	$-0.557088\pi$
$547$	17.8437	−	30.9062i	0.762941	−	1.32145i	0.941328	−	0.337493i	$-0.109579\pi$
$548$	9.97643	−	17.2797i	0.426172	−	0.738151i
$549$	−1.98739	−	0.0620742i	−0.0848198	−	0.00264926i
$550$		−	1.01760i		−	0.0433905i
$551$	−6.83078	−	11.8313i	−0.291001	−	0.504028i
$552$	−4.00245	+	3.87939i	−0.170356	+	0.165118i
$553$	0.647065	+	0.373583i	0.0275160	+	0.0158864i
$554$	−8.03697			−0.341458
$555$	−2.90536	−	2.99752i	−0.123326	−	0.127238i
$556$			1.22089i			0.0517773i
$557$	7.54761			0.319803			0.159901	−	0.987133i	$-0.448882\pi$
$557$	7.54761			0.319803			0.159901	+	0.987133i	$0.448882\pi$
$558$	−16.2965	+	3.66402i	−0.689885	+	0.155110i
$559$	3.66349			0.154949
$560$		−	3.50532i		−	0.148127i
$561$	1.83541	+	1.89363i	0.0774910	+	0.0799491i
$562$	13.9273			0.587486
$563$	14.7599	+	8.52162i	0.622054	+	0.359143i	0.777668	−	0.628675i	$-0.216402\pi$
$563$	14.7599	+	8.52162i	0.622054	+	0.359143i	−0.155614	+	0.987818i	$0.549736\pi$
$564$	11.1392	−	10.7967i	0.469043	−	0.454622i
$565$	2.41348	+	4.18028i	0.101536	+	0.175866i
$566$		−	28.1351i		−	1.18261i
$567$	−14.0382	−	28.2524i	−0.589547	−	1.18649i
$568$	5.61027	−	9.71728i	0.235402	−	0.407728i
$569$	16.3440	−	28.3087i	0.685178	−	1.18676i	−0.288203	−	0.957569i	$-0.593058\pi$
$569$	16.3440	−	28.3087i	0.685178	−	1.18676i	0.973381	−	0.229194i	$-0.0736090\pi$
$570$	6.22771	+	6.42526i	0.260850	+	0.269125i
$571$	−36.0942	−	20.8390i	−1.51049	−	0.872084i	−0.999925	−	0.0122468i	$-0.996102\pi$
$571$	−36.0942	−	20.8390i	−1.51049	−	0.872084i	−0.510569	−	0.859837i	$-0.670565\pi$
$572$	−0.490765	+	0.283343i	−0.0205199	+	0.0118472i
$573$	3.94301	+	15.6914i	0.164721	+	0.655517i
$574$	31.8302			1.32857
$575$	−1.60907	−	2.78699i	−0.0671029	−	0.116226i
$576$	0.0936563	−	2.99854i	0.00390235	−	0.124939i
$577$	−18.9525	−	32.8266i	−0.789002	−	1.36659i	−0.926579	−	0.376100i	$-0.877265\pi$
$577$	−18.9525	−	32.8266i	−0.789002	−	1.36659i	0.137577	−	0.990491i	$-0.456069\pi$
$578$	12.7837	+	7.38065i	0.531730	+	0.306994i
$579$	0.802986	−	2.81993i	0.0333710	−	0.117192i
$580$	−2.29013	−	1.32221i	−0.0950926	−	0.0549018i
$581$	−12.0311			−0.499135
$582$	−16.5157	+	16.0079i	−0.684598	+	0.663549i
$583$	−1.83864	−	3.18461i	−0.0761485	−	0.131893i
$584$	−3.02495	+	5.23937i	−0.125173	+	0.216807i
$585$	−1.47221	+	0.789756i	−0.0608684	+	0.0326524i
$586$	11.0058	+	19.0627i	0.454647	+	0.787471i
$587$	−26.0324			−1.07447			−0.537237	−	0.843431i	$-0.680532\pi$
$587$	−26.0324			−1.07447			−0.537237	+	0.843431i	$0.680532\pi$
$588$	8.88171	−	2.23184i	0.366276	−	0.0920394i
$589$	20.1468	+	20.5299i	0.830136	+	0.845921i
$590$		−	9.49548i		−	0.390923i
$591$	−26.6403	+	6.69429i	−1.09583	+	0.275366i
$592$	2.08724	−	1.20507i	0.0857850	−	0.0495280i
$593$			16.4572i			0.675817i	0.941179	+	0.337908i	$0.109719\pi$
$593$			16.4572i			0.675817i	−0.941179	+	0.337908i	$0.890281\pi$
$594$	5.16589	−	1.12790i	0.211959	−	0.0462785i
$595$	−4.54210	+	2.62238i	−0.186208	+	0.107507i
$596$	−16.6142	+	9.59220i	−0.680543	+	0.392912i
$597$	−5.74303	−	22.8547i	−0.235047	−	0.935379i
$598$	−0.896072	+	1.55204i	−0.0366431	+	0.0634677i
$599$	17.7128	+	10.2265i	0.723724	+	0.417842i	0.816122	−	0.577880i	$-0.196120\pi$
$599$	17.7128	+	10.2265i	0.723724	+	0.417842i	−0.0923976	+	0.995722i	$0.529453\pi$
$600$	1.66583	+	0.474351i	0.0680072	+	0.0193653i
$601$	−10.8743	+	6.27830i	−0.443573	+	0.256097i	−0.705112	−	0.709096i	$-0.749103\pi$
$601$	−10.8743	+	6.27830i	−0.443573	+	0.256097i	0.261539	+	0.965193i	$0.415770\pi$
$602$	11.5299	−	19.9703i	0.469923	−	0.813930i
$603$	3.92041	+	2.42972i	0.159651	+	0.0989457i
$604$		−	23.3009i		−	0.948100i
$605$		−	9.96450i		−	0.405114i
$606$	21.1053	+	21.7748i	0.857343	+	0.884539i
$607$	−8.27295	+	14.3292i	−0.335789	+	0.581603i	−0.983636	−	0.180167i	$-0.942336\pi$
$607$	−8.27295	+	14.3292i	−0.335789	+	0.581603i	0.647847	+	0.761770i	$0.275669\pi$
$608$	−4.47405	+	2.58309i	−0.181447	+	0.104758i
$609$	4.39702	−	15.4415i	0.178176	−	0.625720i
$610$	0.573990	+	0.331394i	0.0232402	+	0.0134177i
$611$	2.49384	−	4.31946i	0.100890	−	0.174747i
$612$	−3.95549	+	2.12189i	−0.159891	+	0.0857725i
$613$	28.1131	−	16.2311i	1.13548	−	0.655568i	0.190171	−	0.981751i	$-0.439096\pi$
$613$	28.1131	−	16.2311i	1.13548	−	0.655568i	0.945307	+	0.326183i	$0.105763\pi$
$614$	5.00704	−	2.89082i	0.202068	−	0.116664i
$615$	−4.30736	+	15.1266i	−0.173690	+	0.609964i
$616$			3.56700i			0.143719i
$617$	0.546152	−	0.315321i	0.0219873	−	0.0126943i	−0.488966	−	0.872303i	$-0.662626\pi$
$617$	0.546152	−	0.315321i	0.0219873	−	0.0126943i	0.510953	+	0.859608i	$0.329292\pi$
$618$	−0.183975	−	0.732136i	−0.00740055	−	0.0294508i
$619$		−	45.8973i		−	1.84477i	−0.386274	−	0.922384i	$-0.626238\pi$
$619$		−	45.8973i		−	1.84477i	0.386274	−	0.922384i	$-0.373762\pi$
$620$	5.36424	+	1.49163i	0.215433	+	0.0599052i
$621$	12.3648	−	11.2577i	0.496184	−	0.451754i
$622$	0.448742			0.0179929
$623$	1.36626	+	2.36643i	0.0547379	+	0.0948089i
$624$	−0.235071	−	0.935475i	−0.00941035	−	0.0374490i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.73777	+	15.1343i	0.349232	+	0.604887i
$627$	−6.33730	−	6.53832i	−0.253087	−	0.261116i
$628$	−10.7418			−0.428645
$629$	−3.12299	−	1.80306i	−0.124522	−	0.0718927i
$630$	−0.328295	+	10.5108i	−0.0130796	+	0.418762i
$631$	16.2083	+	9.35789i	0.645244	+	0.372532i	0.786632	−	0.617423i	$-0.211823\pi$
$631$	16.2083	+	9.35789i	0.645244	+	0.372532i	−0.141388	+	0.989954i	$0.545156\pi$
$632$	−0.106576	−	0.184595i	−0.00423937	−	0.00734280i
$633$	4.23463	−	14.8712i	0.168311	−	0.591077i
$634$	−0.647660	−	1.12178i	−0.0257219	−	0.0445516i
$635$	−18.8566			−0.748300
$636$	6.07037	−	1.52539i	0.240706	−	0.0604857i
$637$	2.54994	−	1.47221i	0.101032	−	0.0583311i
$638$	2.33043	+	1.34548i	0.0922627	+	0.0532679i
$639$	−17.7327	+	28.6122i	−0.701495	+	1.13188i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−3.71167	+	6.42881i	−0.146602	+	0.253923i	−0.929970	−	0.367636i	$-0.880167\pi$
$641$	−3.71167	+	6.42881i	−0.146602	+	0.253923i	0.783367	+	0.621559i	$0.213500\pi$
$642$	−8.53249	+	29.9645i	−0.336751	+	1.18260i
$643$			17.2741i			0.681222i	0.940204	+	0.340611i	$0.110634\pi$
$643$			17.2741i			0.681222i	−0.940204	+	0.340611i	$0.889366\pi$
$644$	5.64031	+	9.76931i	0.222259	+	0.384965i
$645$	7.93022	+	8.18178i	0.312252	+	0.322157i
$646$	6.69421	+	3.86490i	0.263380	+	0.152062i
$647$	8.93872			0.351418			0.175709	−	0.984442i	$-0.443778\pi$
$647$	8.93872			0.351418			0.175709	+	0.984442i	$0.443778\pi$
$648$	−0.561664	+	8.98246i	−0.0220642	+	0.352864i
$649$			9.66257i			0.379289i
$650$	0.556888			0.0218429
$651$	−0.846021	+	33.7935i	−0.0331582	+	1.32447i
$652$	3.56174			0.139488
$653$			22.3040i			0.872823i	0.899747	+	0.436411i	$0.143751\pi$
$653$			22.3040i			0.872823i	−0.899747	+	0.436411i	$0.856249\pi$
$654$	−9.39723	+	9.10829i	−0.367461	+	0.356163i
$655$	−0.821617			−0.0321032
$656$	−7.86397	−	4.54027i	−0.307037	−	0.177268i
$657$	9.56114	−	15.4272i	0.373016	−	0.601871i
$658$	−15.6975	−	27.1888i	−0.611951	−	1.05993i
$659$		−	23.8067i		−	0.927377i	−0.885998	−	0.463688i	$-0.846526\pi$
$659$		−	23.8067i		−	0.927377i	0.885998	−	0.463688i	$-0.153474\pi$
$660$	−1.69514	−	0.482698i	−0.0659833	−	0.0187890i
$661$	−20.5693	+	35.6271i	−0.800054	+	1.38573i	0.119527	+	0.992831i	$0.461862\pi$
$661$	−20.5693	+	35.6271i	−0.800054	+	1.38573i	−0.919580	+	0.392902i	$0.871471\pi$
$662$	10.1085	−	17.5084i	0.392878	−	0.680485i
$663$	−1.03630	+	1.00444i	−0.0402467	+	0.0390093i
$664$	2.97241	+	1.71612i	0.115352	+	0.0665984i
$665$	15.6830	−	9.05457i	0.608160	−	0.351121i
$666$	−6.37153	+	3.41796i	−0.246892	+	0.132443i
$667$	8.51012			0.329513
$668$	−5.75062	−	9.96036i	−0.222498	−	0.385378i
$669$	13.4182	+	3.82089i	0.518779	+	0.147724i
$670$	−0.768714	−	1.33145i	−0.0296980	−	0.0514384i
$671$	−0.584090	−	0.337225i	−0.0225486	−	0.0130184i
$672$	−5.83927	−	1.66275i	−0.225255	−	0.0641421i
$673$	−40.8232	−	23.5693i	−1.57362	−	0.908529i	−0.995720	−	0.0924207i	$-0.970540\pi$
$673$	−40.8232	−	23.5693i	−1.57362	−	0.908529i	−0.577899	−	0.816109i	$-0.696127\pi$
$674$	−11.8084			−0.454842
$675$	−4.95063	−	1.57838i	−0.190550	−	0.0607517i
$676$	6.34494	+	10.9898i	0.244036	+	0.422683i
$677$	−9.59632	+	16.6213i	−0.368816	+	0.638809i	−0.989381	−	0.145347i	$-0.953570\pi$
$677$	−9.59632	+	16.6213i	−0.368816	+	0.638809i	0.620564	+	0.784155i	$0.286904\pi$
$678$	8.10847	−	2.03753i	0.311404	−	0.0782511i
$679$	23.2741	+	40.3120i	0.893179	+	1.54703i
$680$	1.49623			0.0573778
$681$	7.35460	+	29.2680i	0.281829	+	1.12155i
$682$	−5.45863	−	1.51788i	−0.209022	−	0.0581225i
$683$			28.8541i			1.10407i	0.833821	+	0.552035i	$0.186148\pi$
$683$			28.8541i			1.10407i	−0.833821	+	0.552035i	$0.813852\pi$
$684$	13.6575	−	7.32648i	0.522208	−	0.280135i
$685$	17.2797	−	9.97643i	0.660223	−	0.381180i
$686$			6.00365i			0.229220i
$687$	−23.4911	−	6.68918i	−0.896242	−	0.255208i
$688$	−5.69715	+	3.28925i	−0.217202	+	0.125402i
$689$	1.74280	−	1.00621i	0.0663955	−	0.0383335i
$690$	−5.40592	+	1.35843i	−0.205800	+	0.0517144i
$691$	20.3713	−	35.2841i	0.774959	−	1.34227i	−0.159858	−	0.987140i	$-0.551104\pi$
$691$	20.3713	−	35.2841i	0.774959	−	1.34227i	0.934817	−	0.355129i	$-0.115563\pi$
$692$	2.03876	+	1.17708i	0.0775021	+	0.0447459i
$693$	0.334072	−	10.6958i	0.0126904	−	0.406299i
$694$	4.77321	−	2.75581i	0.181188	−	0.104609i
$695$	−0.610446	+	1.05732i	−0.0231555	+	0.0401065i
$696$	−3.28890	+	3.18778i	−0.124666	+	0.120833i
$697$			13.5866i			0.514628i
$698$		−	21.0390i		−	0.796337i
$699$	−2.97551	+	2.88403i	−0.112544	+	0.109084i
$700$	1.75266	−	3.03570i	0.0662443	−	0.114739i
$701$	6.09463	−	3.51874i	0.230191	−	0.132901i	−0.380469	−	0.924794i	$-0.624237\pi$
$701$	6.09463	−	3.51874i	0.230191	−	0.132901i	0.610660	+	0.791893i	$0.290904\pi$
$702$	0.617255	+	2.82707i	0.0232968	+	0.106701i
$703$	10.7831	+	6.22560i	0.406691	+	0.234803i
$704$	0.508798	−	0.881264i	0.0191761	−	0.0332139i
$705$	15.0451	−	3.78061i	0.566633	−	0.142386i
$706$	−22.4278	+	12.9487i	−0.844081	+	0.487330i
$707$	53.1485	−	30.6853i	1.99885	−	1.15404i
$708$	−15.8179	−	4.50419i	−0.594472	−	0.169278i
$709$		−	22.0251i		−	0.827169i	−0.910466	−	0.413585i	$-0.864277\pi$
$709$		−	22.0251i		−	0.827169i	0.910466	−	0.413585i	$-0.135723\pi$
$710$	9.71728	−	5.61027i	0.364683	−	0.210550i
$711$	0.302284	+	0.563497i	0.0113365	+	0.0211328i
$712$		−	0.779533i		−	0.0292142i
$713$	−17.3502	+	4.47428i	−0.649771	+	0.167563i
$714$	2.21389	+	8.81030i	0.0828529	+	0.329717i
$715$	−0.566687			−0.0211929
$716$	1.49415	+	2.58794i	0.0558390	+	0.0967160i
$717$	18.5110	−	4.65153i	0.691305	−	0.173714i
$718$	4.55262	−	7.88537i	0.169902	−	0.294279i
$719$	18.1976	+	31.5191i	0.678656	+	1.17547i	0.975386	+	0.220505i	$0.0707704\pi$
$719$	18.1976	+	31.5191i	0.678656	+	1.17547i	−0.296730	+	0.954961i	$0.595896\pi$
$720$	1.58038	−	2.54998i	0.0588972	−	0.0950322i
$721$	−1.52776			−0.0568968
$722$	−6.65927	−	3.84473i	−0.247832	−	0.143086i
$723$	41.5133	+	11.8211i	1.54389	+	0.439630i
$724$	−18.9344	−	10.9318i	−0.703690	−	0.406276i
$725$	−1.32221	−	2.29013i	−0.0491056	−	0.0850534i
$726$	−16.5992	−	4.72667i	−0.616053	−	0.175423i
$727$	3.84543	+	6.66048i	0.142619	+	0.247024i	0.928482	−	0.371377i	$-0.121114\pi$
$727$	3.84543	+	6.66048i	0.142619	+	0.247024i	−0.785863	+	0.618401i	$0.787781\pi$
$728$	−1.95207			−0.0723485
$729$	2.52543	−	26.8816i	0.0935346	−	0.995616i
$730$	−5.23937	+	3.02495i	−0.193918	+	0.111959i
$731$	8.52425	+	4.92148i	0.315281	+	0.182027i
$732$	0.824318	−	0.798974i	0.0304677	−	0.0295309i
$733$	2.30501	−	3.99239i	0.0851374	−	0.147462i	−0.820312	−	0.571916i	$-0.806200\pi$
$733$	2.30501	−	3.99239i	0.0851374	−	0.147462i	0.905450	+	0.424454i	$0.139534\pi$
$734$	16.7657	−	29.0390i	0.618833	−	1.07185i
$735$	8.80770	+	2.50803i	0.324877	+	0.0925099i
$736$		−	3.21814i		−	0.118622i
$737$	0.782240	+	1.35488i	0.0288142	+	0.0499076i
$738$	23.1552	+	14.3507i	0.852354	+	0.528255i
$739$	2.74609	+	1.58546i	0.101017	+	0.0583220i	0.549657	−	0.835390i	$-0.314758\pi$
$739$	2.74609	+	1.58546i	0.101017	+	0.0583220i	−0.448641	+	0.893712i	$0.648092\pi$
$740$	2.41014			0.0885984
$741$	3.57815	−	3.46813i	0.131447	−	0.127405i
$742$		−	12.6671i		−	0.465025i
$743$	30.5226			1.11977			0.559883	−	0.828571i	$-0.310846\pi$
$743$	30.5226			1.11977			0.559883	+	0.828571i	$0.310846\pi$
$744$	5.02933	−	8.22835i	0.184384	−	0.301666i
$745$	−19.1844			−0.702862
$746$		−	23.3875i		−	0.856276i
$747$	−8.75216	−	5.42424i	−0.320225	−	0.198463i
$748$	−1.52256			−0.0556702
$749$	54.6052	+	31.5264i	1.99523	+	1.15195i
$750$	1.20548	+	1.24372i	0.0440178	+	0.0454141i
$751$	19.5846	+	33.9216i	0.714654	+	1.23782i	0.963093	+	0.269169i	$0.0867490\pi$
$751$	19.5846	+	33.9216i	0.714654	+	1.23782i	−0.248439	+	0.968647i	$0.579918\pi$
$752$			8.95636i			0.326605i
$753$	6.26890	−	22.0152i	0.228452	−	0.802278i
$754$	−0.736322	+	1.27535i	−0.0268153	+	0.0464454i
$755$	11.6505	−	20.1792i	0.424003	−	0.734395i
$756$	17.3535	+	5.53271i	0.631142	+	0.201223i
$757$	37.5703	+	21.6912i	1.36552	+	0.788382i	0.990352	−	0.138576i	$-0.0442526\pi$
$757$	37.5703	+	21.6912i	1.36552	+	0.788382i	0.375165	+	0.926958i	$0.377586\pi$
$758$	10.0520	−	5.80353i	0.365105	−	0.210794i
$759$	5.50105	−	1.38233i	0.199675	−	0.0501754i
$760$	−5.16618			−0.187397
$761$	−20.1815	−	34.9553i	−0.731577	−	1.26713i	−0.956209	−	0.292685i	$-0.905451\pi$
$761$	−20.1815	−	34.9553i	−0.731577	−	1.26713i	0.224632	−	0.974444i	$-0.427882\pi$
$762$	−8.94463	+	31.4118i	−0.324030	+	1.13793i
$763$	13.2427	+	22.9370i	0.479418	+	0.830376i
$764$	−8.08961	−	4.67054i	−0.292672	−	0.168974i
$765$	−4.48650	−	0.140131i	−0.162210	−	0.00506646i
$766$	−1.98063	−	1.14352i	−0.0715632	−	0.0413170i
$767$	−5.28792			−0.190936
$768$	1.20548	+	1.24372i	0.0434989	+	0.0448787i
$769$	7.20267	+	12.4754i	0.259735	+	0.449874i	0.966171	−	0.257903i	$-0.0830315\pi$
$769$	7.20267	+	12.4754i	0.259735	+	0.449874i	−0.706436	+	0.707777i	$0.749698\pi$
$770$	−1.78350	+	3.08911i	−0.0642729	+	0.111324i
$771$	10.7744	+	42.8772i	0.388030	+	1.54419i
$772$	0.846405	+	1.46602i	0.0304628	+	0.0527631i
$773$	−0.596764			−0.0214641			−0.0107321	−	0.999942i	$-0.503416\pi$
$773$	−0.596764			−0.0214641			−0.0107321	+	0.999942i	$0.503416\pi$
$774$	17.3912	−	9.32937i	0.625113	−	0.335337i
$775$	3.89975	+	3.97391i	0.140083	+	0.142747i
$776$		−	13.2793i		−	0.476700i
$777$	3.56615	+	14.1917i	0.127935	+	0.509124i
$778$	2.43804	−	1.40760i	0.0874080	−	0.0504650i
$779$		−	46.9117i		−	1.68079i
$780$	0.264160	−	0.927680i	0.00945846	−	0.0332163i
$781$	−9.88827	+	5.70899i	−0.353830	+	0.204284i
$782$	−4.16998	+	2.40754i	−0.149118	+	0.0860935i
$783$	10.1605	−	9.25066i	0.363105	−	0.330592i
$784$	−2.64364	+	4.57892i	−0.0944156	+	0.163533i
$785$	−9.30268	−	5.37091i	−0.332027	−	0.191696i
$786$	−0.389735	+	1.36867i	−0.0139014	+	0.0488190i
$787$	−44.6959	+	25.8052i	−1.59324	+	0.919856i	−0.600490	+	0.799632i	$0.705028\pi$
$787$	−44.6959	+	25.8052i	−1.59324	+	0.919856i	−0.992747	+	0.120224i	$0.961639\pi$
$788$	7.92946	−	13.7342i	0.282475	−	0.489262i
$789$	20.9457	+	21.6101i	0.745687	+	0.769342i
$790$		−	0.213152i		−	0.00758361i
$791$		−	16.9201i		−	0.601608i
$792$	−1.60819	+	2.59485i	−0.0571444	+	0.0922040i
$793$	0.184549	−	0.319648i	0.00655353	−	0.0113510i
$794$	4.64148	−	2.67976i	0.164720	−	0.0951011i
$795$	6.01979	+	1.71416i	0.213500	+	0.0607949i
$796$	11.7826	+	6.80268i	0.417623	+	0.241115i
$797$	−23.5456	+	40.7822i	−0.834028	+	1.44458i	0.0607919	+	0.998150i	$0.480637\pi$
$797$	−23.5456	+	40.7822i	−0.834028	+	1.44458i	−0.894820	+	0.446428i	$0.852696\pi$
$798$	−7.64414	−	30.4202i	−0.270600	−	1.07686i
$799$	11.6054	−	6.70039i	0.410570	−	0.237043i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−0.0730082	+	2.33746i	−0.00257962	+	0.0825901i
$802$		−	11.7824i		−	0.416050i
$803$	5.33157	−	3.07818i	0.188147	−	0.108627i
$804$	−2.58261	+	0.648971i	−0.0910817	+	0.0228874i
$805$			11.2806i			0.397590i
$806$	0.830669	−	2.98728i	0.0292591	−	0.105222i
$807$	−18.2439	+	4.58442i	−0.642216	+	0.161379i
$808$	−17.5078			−0.615923
$809$	4.47657	+	7.75365i	0.157388	+	0.272604i	0.933926	−	0.357467i	$-0.116359\pi$
$809$	4.47657	+	7.75365i	0.157388	+	0.272604i	−0.776538	+	0.630070i	$0.783026\pi$
$810$	−4.97764	+	7.49820i	−0.174897	+	0.263460i
$811$	19.0738	−	33.0368i	0.669772	−	1.16008i	−0.308195	−	0.951323i	$-0.599725\pi$
$811$	19.0738	−	33.0368i	0.669772	−	1.16008i	0.977968	−	0.208756i	$-0.0669416\pi$
$812$	4.63477	+	8.02765i	0.162648	+	0.281715i
$813$	−0.552579	+	0.535589i	−0.0193798	+	0.0187839i
$814$	−2.45255			−0.0859617
$815$	3.08456	+	1.78087i	0.108047	+	0.0623811i
$816$	0.709739	−	2.49247i	0.0248458	−	0.0872538i
$817$	−29.4325	−	16.9929i	−1.02971	−	0.594506i
$818$	−0.330911	−	0.573155i	−0.0115700	−	0.0200399i
$819$	5.85336	+	0.182824i	0.204533	+	0.00638838i
$820$	−4.54027	−	7.86397i	−0.158553	−	0.274622i
$821$	−1.33931			−0.0467422			−0.0233711	−	0.999727i	$-0.507440\pi$
$821$	−1.33931			−0.0467422			−0.0233711	+	0.999727i	$0.507440\pi$
$822$	−8.42240	−	33.5173i	−0.293765	−	1.16905i
$823$	−21.0797	+	12.1704i	−0.734792	+	0.424233i	−0.820173	−	0.572116i	$-0.806123\pi$
$823$	−21.0797	+	12.1704i	−0.734792	+	0.424233i	0.0853804	+	0.996348i	$0.472789\pi$
$824$	0.377449	+	0.217920i	0.0131491	+	0.00759161i
$825$	−1.22669	−	1.26560i	−0.0427078	−	0.0440625i
$826$	−16.6424	+	28.8254i	−0.579062	+	1.00296i
$827$	17.0711	−	29.5680i	0.593621	−	1.02818i	−0.400119	−	0.916463i	$-0.631031\pi$
$827$	17.0711	−	29.5680i	0.593621	−	1.02818i	0.993740	−	0.111718i	$-0.0356353\pi$
$828$	−0.301399	+	9.64972i	−0.0104744	+	0.335351i
$829$			32.3395i			1.12320i	0.827409	+	0.561599i	$0.189814\pi$
$829$			32.3395i			1.12320i	−0.827409	+	0.561599i	$0.810186\pi$
$830$	1.71612	+	2.97241i	0.0595674	+	0.103174i
$831$	−9.99570	+	9.68837i	−0.346747	+	0.336086i
$832$	0.482279	+	0.278444i	0.0167200	+	0.00965330i
$833$	7.91098			0.274099
$834$	1.47176	+	1.51844i	0.0509627	+	0.0525793i
$835$		−	11.5012i		−	0.398017i
$836$	5.25709			0.181820
$837$	−15.8513	+	24.2020i	−0.547900	+	0.836544i
$838$	4.45152			0.153775
$839$		−	23.2464i		−	0.802555i	−0.915956	−	0.401278i	$-0.868566\pi$
$839$		−	23.2464i		−	0.802555i	0.915956	−	0.401278i	$-0.131434\pi$
$840$	−4.22558	−	4.35962i	−0.145796	−	0.150421i
$841$	−22.0070			−0.758864
$842$	9.09301	+	5.24985i	0.313366	+	0.180922i
$843$	17.3216	−	16.7890i	0.596586	−	0.578243i
$844$	4.46360	+	7.73118i	0.153643	+	0.266118i
$845$			12.6899i			0.436545i
$846$	0.838820	−	26.8560i	0.0288392	−	0.923328i
$847$	−17.4644	+	30.2492i	−0.600083	+	1.03937i
$848$	−1.80684	+	3.12954i	−0.0620472	+	0.107469i
$849$	−33.9162	−	34.9921i	−1.16400	−	1.20093i
$850$	1.29577	+	0.748115i	0.0444447	+	0.0256601i
$851$	−6.71703	+	3.87808i	−0.230257	+	0.132939i
$852$	−4.73636	−	18.8486i	−0.162265	−	0.645742i
$853$	27.9332			0.956415			0.478207	−	0.878247i	$-0.341287\pi$
$853$	27.9332			0.956415			0.478207	+	0.878247i	$0.341287\pi$
$854$	−1.16164	−	2.01202i	−0.0397505	−	0.0688499i
$855$	15.4910	+	0.483846i	0.529781	+	0.0165472i
$856$	−8.99386	−	15.5778i	−0.307404	−	0.532439i
$857$	30.8970	+	17.8384i	1.05542	+	0.609348i	0.924162	−	0.382000i	$-0.124765\pi$
$857$	30.8970	+	17.8384i	1.05542	+	0.609348i	0.131259	+	0.991348i	$0.458098\pi$
$858$	−0.268809	+	0.944004i	−0.00917697	+	0.0322278i
$859$	−27.9755	−	16.1517i	−0.954512	−	0.551088i	−0.0600327	−	0.998196i	$-0.519120\pi$
$859$	−27.9755	−	16.1517i	−0.954512	−	0.551088i	−0.894480	+	0.447108i	$0.852454\pi$
$860$	−6.57850			−0.224325
$861$	39.5877	−	38.3705i	1.34914	−	1.30766i
$862$	−5.87257	−	10.1716i	−0.200020	−	0.346446i
$863$	10.9154	−	18.9061i	0.371565	−	0.643570i	−0.618241	−	0.785988i	$-0.712155\pi$
$863$	10.9154	−	18.9061i	0.371565	−	0.643570i	0.989807	+	0.142418i	$0.0454879\pi$
$864$	−3.49818	−	3.84223i	−0.119011	−	0.130715i
$865$	1.17708	+	2.03876i	0.0400219	+	0.0693200i
$866$	0.986441			0.0335206
$867$	24.7964	−	6.23096i	0.842131	−	0.211615i
$868$	−13.6699	−	13.9298i	−0.463986	−	0.472809i
$869$			0.216903i			0.00735792i
$870$	−4.44217	+	1.11625i	−0.150604	+	0.0378444i
$871$	−0.741469	+	0.428087i	−0.0251237	+	0.0145052i
$872$		−	7.55577i		−	0.255871i
$873$	−1.24369	+	39.8185i	−0.0420926	+	1.34765i
$874$	14.3981	−	8.31276i	0.487024	−	0.281183i
$875$	3.03570	−	1.75266i	0.102625	−	0.0592507i
$876$	2.55376	+	10.1628i	0.0862834	+	0.343369i
$877$	−14.0024	+	24.2529i	−0.472829	+	0.818963i	−0.999516	−	0.0310954i	$-0.990100\pi$
$877$	−14.0024	+	24.2529i	−0.472829	+	0.818963i	0.526688	+	0.850059i	$0.323434\pi$
$878$	−1.30933	−	0.755941i	−0.0441877	−	0.0255118i
$879$	36.6677	+	10.4413i	1.23677	+	0.352175i
$880$	0.881264	−	0.508798i	0.0297074	−	0.0171516i
$881$	6.16441	−	10.6771i	0.207684	−	0.359720i	−0.743300	−	0.668958i	$-0.766741\pi$
$881$	6.16441	−	10.6771i	0.207684	−	0.359720i	0.950985	+	0.309238i	$0.100074\pi$
$882$	8.35589	−	13.4825i	0.281358	−	0.453978i
$883$			26.1480i			0.879951i	0.898010	+	0.439976i	$0.145013\pi$
$883$			26.1480i			0.879951i	−0.898010	+	0.439976i	$0.854987\pi$
$884$		−	0.833232i		−	0.0280246i
$885$	−11.4466	−	11.8097i	−0.384772	−	0.396978i
$886$	18.8559	−	32.6594i	0.633476	−	1.09721i
$887$	−7.69703	+	4.44388i	−0.258441	+	0.149211i	−0.623623	−	0.781725i	$-0.714340\pi$
$887$	−7.69703	+	4.44388i	−0.258441	+	0.149211i	0.365182	+	0.930936i	$0.381007\pi$
$888$	1.14325	−	4.01488i	0.0383650	−	0.134730i
$889$	57.2428	+	33.0491i	1.91986	+	1.10843i
$890$	0.389767	−	0.675095i	0.0130650	−	0.0226292i
$891$	5.06523	−	7.63014i	0.169692	−	0.255619i
$892$	−6.97582	+	4.02749i	−0.233568	+	0.134850i
$893$	−40.0712	+	23.1351i	−1.34093	+	0.774187i
$894$	−9.10014	+	31.9579i	−0.304354	+	1.06883i
$895$			2.98830i			0.0998878i
$896$	3.03570	−	1.75266i	0.101416	−	0.0585523i
$897$	0.756491	+	3.01049i	0.0252585	+	0.100517i
$898$		−	19.1329i		−	0.638474i
$899$	−14.2571	+	3.67662i	−0.475500	+	0.122622i
$900$	2.64364	−	1.41816i	0.0881213	−	0.0472720i
$901$	5.40691			0.180130
$902$	4.62016	+	8.00235i	0.153834	+	0.266449i
$903$	−9.73387	−	38.7364i	−0.323923	−	1.28907i
$904$	−2.41348	+	4.18028i	−0.0802713	+	0.139034i
$905$	−10.9318	−	18.9344i	−0.363384	−	0.629400i
$906$	−28.0887	−	28.9797i	−0.933184	−	0.962786i
$907$	−22.6580			−0.752347			−0.376174	−	0.926549i	$-0.622760\pi$
$907$	−22.6580			−0.752347			−0.376174	+	0.926549i	$0.622760\pi$
$908$	−15.0890	−	8.71161i	−0.500745	−	0.289105i
$909$	52.4979	+	1.63972i	1.74124	+	0.0543860i
$910$	−1.69054	−	0.976035i	−0.0560409	−	0.0323552i
$911$	20.8726	+	36.1524i	0.691539	+	1.19778i	0.971333	+	0.237721i	$0.0764004\pi$
$911$	20.8726	+	36.1524i	0.691539	+	1.19778i	−0.279794	+	0.960060i	$0.590266\pi$
$912$	−2.45059	+	8.60599i	−0.0811470	+	0.284973i
$913$	−1.74632	−	3.02471i	−0.0577947	−	0.100103i
$914$	−33.8765			−1.12054
$915$	1.11337	−	0.279772i	0.0368068	−	0.00924899i
$916$	12.2125	−	7.05087i	0.403511	−	0.232967i
$917$	2.49418	+	1.44001i	0.0823650	+	0.0475535i
$918$	−2.36161	+	7.40728i	−0.0779449	+	0.244477i
$919$	27.6822	−	47.9471i	0.913153	−	1.58163i	0.103570	−	0.994622i	$-0.466973\pi$
$919$	27.6822	−	47.9471i	0.913153	−	1.58163i	0.809583	−	0.587005i	$-0.199693\pi$
$920$	1.60907	−	2.78699i	0.0530495	−	0.0918845i
$921$	2.74252	−	9.63122i	0.0903693	−	0.317359i
$922$			20.2187i			0.665867i
$923$	−3.12429	−	5.41143i	−0.102837	−	0.178119i
$924$	4.29993	+	4.43634i	0.141457	+	0.145945i
$925$	2.08724	+	1.20507i	0.0686280	+	0.0396224i
$926$	−4.75152			−0.156145
$927$	−1.11138	−	0.688792i	−0.0365027	−	0.0226229i
$928$		−	2.64442i		−	0.0868073i
$929$	13.1951			0.432917			0.216459	−	0.976292i	$-0.430549\pi$
$929$	13.1951			0.432917			0.216459	+	0.976292i	$0.430549\pi$
$930$	8.46971	−	4.61130i	0.277733	−	0.151210i
$931$	−27.3150			−0.895214
$932$		−	2.39244i		−	0.0783669i
$933$	0.558107	−	0.540947i	0.0182716	−	0.0177098i
$934$	4.46882			0.146224
$935$	−1.31857	−	0.761279i	−0.0431220	−	0.0248965i
$936$	−1.42005	−	0.880093i	−0.0464159	−	0.0287667i
$937$	−12.0937	−	20.9469i	−0.395083	−	0.684304i	0.598029	−	0.801475i	$-0.295951\pi$
$937$	−12.0937	−	20.9469i	−0.395083	−	0.684304i	−0.993112	+	0.117171i	$0.962618\pi$
$938$			5.38918i			0.175963i
$939$	29.1113	+	8.28955i	0.950011	+	0.270519i
$940$	−4.47818	+	7.75644i	−0.146062	+	0.252987i
$941$	23.1741	−	40.1388i	0.755455	−	1.30849i	−0.189693	−	0.981843i	$-0.560749\pi$
$941$	23.1741	−	40.1388i	0.755455	−	1.30849i	0.945148	−	0.326643i	$-0.105917\pi$
$942$	−13.3598	+	12.9490i	−0.435284	+	0.421901i
$943$	25.3074	+	14.6112i	0.824122	+	0.475807i
$944$	8.22333	−	4.74774i	0.267647	−	0.154526i
$945$	12.2623	+	13.4682i	0.398891	+	0.438122i
$946$	6.69426			0.217649
$947$	−12.4511	−	21.5659i	−0.404605	−	0.700796i	0.589670	−	0.807644i	$-0.299258\pi$
$947$	−12.4511	−	21.5659i	−0.404605	−	0.700796i	−0.994275	+	0.106848i	$0.965924\pi$
$948$	−0.355075	−	0.101109i	−0.0115323	−	0.00328387i
$949$	1.68456	+	2.91774i	0.0546831	+	0.0947139i
$950$	−4.47405	−	2.58309i	−0.145157	−	0.0838066i
$951$	−2.15778	−	0.614437i	−0.0699710	−	0.0199245i
$952$	−4.54210	−	2.62238i	−0.147210	−	0.0849919i
$953$	−54.5547			−1.76720			−0.883600	−	0.468243i	$-0.844887\pi$
$953$	−54.5547			−1.76720			−0.883600	+	0.468243i	$0.844887\pi$
$954$	5.71099	−	9.21483i	0.184900	−	0.298341i
$955$	−4.67054	−	8.08961i	−0.151135	−	0.261773i
$956$	−5.50979	+	9.54323i	−0.178199	+	0.308650i
$957$	4.52033	−	1.13589i	0.146122	−	0.0367181i
$958$	4.22624	+	7.32007i	0.136544	+	0.236501i
$959$	−69.9412			−2.25852
$960$	0.422115	+	1.67983i	0.0136237	+	0.0542162i
$961$	27.1340	−	14.9916i	0.875289	−	0.483600i
$962$		−	1.34217i		−	0.0432735i
$963$	25.5095	+	47.5530i	0.822031	+	1.53237i
$964$	−21.5818	+	12.4602i	−0.695101	+	0.401317i
$965$			1.69281i			0.0544935i
$966$	18.7916	+	5.35098i	0.604610	+	0.172165i
$967$	−35.0773	+	20.2519i	−1.12801	+	0.651257i	−0.943434	−	0.331561i	$-0.892425\pi$
$967$	−35.0773	+	20.2519i	−1.12801	+	0.651257i	−0.184576	+	0.982818i	$0.559091\pi$
$968$	8.62951	−	4.98225i	0.277363	−	0.160136i
$969$	12.9847	−	3.26286i	0.417130	−	0.104818i
$970$	6.63966	−	11.5002i	0.213187	−	0.369250i
$971$	47.5688	+	27.4639i	1.52656	+	0.881358i	0.999503	+	0.0315255i	$0.0100365\pi$
$971$	47.5688	+	27.4639i	1.52656	+	0.881358i	0.527053	+	0.849832i	$0.323297\pi$
$972$	10.1296	+	11.8487i	0.324907	+	0.380047i
$973$	3.70626	−	2.13981i	0.118817	−	0.0685991i
$974$	16.8806	−	29.2380i	0.540888	−	0.936846i
$975$	0.692610	−	0.671315i	0.0221813	−	0.0214993i
$976$			0.662787i			0.0212153i
$977$			9.01668i			0.288469i	0.989544	+	0.144235i	$0.0460720\pi$
$977$			9.01668i			0.288469i	−0.989544	+	0.144235i	$0.953928\pi$
$978$	4.42979	−	4.29359i	0.141649	−	0.137294i
$979$	−0.396625	+	0.686975i	−0.0126762	+	0.0219558i
$980$	−4.57892	+	2.64364i	−0.146268	+	0.0844479i
$981$	−0.707645	+	22.6563i	−0.0225934	+	0.723359i
$982$	−6.69152	−	3.86335i	−0.213535	−	0.123284i
$983$	−10.0029	+	17.3255i	−0.319042	+	0.552596i	−0.980288	−	0.197572i	$-0.936694\pi$
$983$	−10.0029	+	17.3255i	−0.319042	+	0.552596i	0.661247	+	0.750168i	$0.270028\pi$
$984$	−15.2537	+	3.83303i	−0.486271	+	0.122192i
$985$	13.7342	−	7.92946i	0.437609	−	0.252654i
$986$	−3.42657	+	1.97833i	−0.109124	+	0.0630029i
$987$	−52.2986	−	14.8922i	−1.66468	−	0.474025i
$988$			2.87698i			0.0915291i
$989$	18.3342	−	10.5853i	0.582995	−	0.336592i
$990$	−2.69016	+	1.44311i	−0.0854988	+	0.0458652i
$991$			53.7889i			1.70866i	0.519730	+	0.854330i	$0.326032\pi$
$991$			53.7889i			1.70866i	−0.519730	+	0.854330i	$0.673968\pi$
$992$	1.39033	+	5.39138i	0.0441430	+	0.171176i
$993$	−8.53390	−	33.9611i	−0.270815	−	1.07772i
$994$	−39.3316			−1.24752
$995$	6.80268	+	11.7826i	0.215660	+	0.373533i
$996$	5.76557	−	1.44880i	0.182689	−	0.0459070i
$997$	5.51236	−	9.54769i	0.174578	−	0.302378i	−0.765437	−	0.643511i	$-0.777477\pi$
$997$	5.51236	−	9.54769i	0.174578	−	0.302378i	0.940015	+	0.341133i	$0.110810\pi$
$998$	16.3590	+	28.3347i	0.517836	+	0.896918i
$999$	−3.80410	+	11.9317i	−0.120356	+	0.377502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.16	yes	40
3.2	odd	2	inner	930.2.o.e.161.4	✓	40
31.26	odd	6	inner	930.2.o.e.491.14	yes	40
93.26	even	6	inner	930.2.o.e.491.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.4	✓	40	3.2	odd	2	inner
930.2.o.e.161.16	yes	40	1.1	even	1	trivial
930.2.o.e.491.6	yes	40	93.26	even	6	inner
930.2.o.e.491.14	yes	40	31.26	odd	6	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.20548 + 1.24372i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.24372 + 1.20548i) q^{6} +(1.75266 + 3.03570i) q^{7} -1.00000i q^{8} +(-0.0936563 + 2.99854i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.20548 + 1.24372i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.24372 + 1.20548i) q^{6} +(1.75266 + 3.03570i) q^{7} -1.00000i q^{8} +(-0.0936563 + 2.99854i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.508798 + 0.881264i) q^{11} +(-1.20548 - 1.24372i) q^{12} +(-0.482279 - 0.278444i) q^{13} +(-3.03570 + 1.75266i) q^{14} +(-0.422115 - 1.67983i) q^{15} +1.00000 q^{16} +(-0.748115 - 1.29577i) q^{17} +(-2.99854 - 0.0936563i) q^{18} +(2.58309 + 4.47405i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.66275 + 5.83927i) q^{21} +(-0.881264 - 0.508798i) q^{22} -3.21814 q^{23} +(1.24372 - 1.20548i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.278444 - 0.482279i) q^{26} +(-3.84223 + 3.49818i) q^{27} +(-1.75266 - 3.03570i) q^{28} -2.64442 q^{29} +(1.67983 - 0.422115i) q^{30} +(5.39138 - 1.39033i) q^{31} +1.00000i q^{32} +(-1.70939 + 0.429543i) q^{33} +(1.29577 - 0.748115i) q^{34} -3.50532i q^{35} +(0.0936563 - 2.99854i) q^{36} +(2.08724 - 1.20507i) q^{37} +(-4.47405 + 2.58309i) q^{38} +(-0.235071 - 0.935475i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-7.86397 - 4.54027i) q^{41} +(-5.83927 - 1.66275i) q^{42} +(-5.69715 + 3.28925i) q^{43} +(0.508798 - 0.881264i) q^{44} +(1.58038 - 2.54998i) q^{45} -3.21814i q^{46} +8.95636i q^{47} +(1.20548 + 1.24372i) q^{48} +(-2.64364 + 4.57892i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(0.709739 - 2.49247i) q^{51} +(0.482279 + 0.278444i) q^{52} +(-1.80684 + 3.12954i) q^{53} +(-3.49818 - 3.84223i) q^{54} +(0.881264 - 0.508798i) q^{55} +(3.03570 - 1.75266i) q^{56} +(-2.45059 + 8.60599i) q^{57} -2.64442i q^{58} +(8.22333 - 4.74774i) q^{59} +(0.422115 + 1.67983i) q^{60} +0.662787i q^{61} +(1.39033 + 5.39138i) q^{62} +(-9.26680 + 4.97111i) q^{63} -1.00000 q^{64} +(0.278444 + 0.482279i) q^{65} +(-0.429543 - 1.70939i) q^{66} +(0.768714 - 1.33145i) q^{67} +(0.748115 + 1.29577i) q^{68} +(-3.87939 - 4.00245i) q^{69} +3.50532 q^{70} +(9.71728 + 5.61027i) q^{71} +(2.99854 + 0.0936563i) q^{72} +(-5.23937 - 3.02495i) q^{73} +(1.20507 + 2.08724i) q^{74} +(-0.474351 + 1.66583i) q^{75} +(-2.58309 - 4.47405i) q^{76} -3.56700 q^{77} +(0.935475 - 0.235071i) q^{78} +(0.184595 - 0.106576i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-8.98246 - 0.561664i) q^{81} +(4.54027 - 7.86397i) q^{82} +(-1.71612 + 2.97241i) q^{83} +(1.66275 - 5.83927i) q^{84} +1.49623i q^{85} +(-3.28925 - 5.69715i) q^{86} +(-3.18778 - 3.28890i) q^{87} +(0.881264 + 0.508798i) q^{88} +0.779533 q^{89} +(2.54998 + 1.58038i) q^{90} -1.95207i q^{91} +3.21814 q^{92} +(8.22835 + 5.02933i) q^{93} -8.95636 q^{94} -5.16618i q^{95} +(-1.24372 + 1.20548i) q^{96} +13.2793 q^{97} +(-4.57892 - 2.64364i) q^{98} +(-2.59485 - 1.60819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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