LMFDB - Embedded newform 805.2.u.d.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	805.71
Dual form			805.2.u.d.771.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.937084 - 0.602227i) q^{2} +(0.379948 + 2.64260i) q^{3} +(-0.315382 - 0.690589i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(1.23540 - 2.70515i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.437406 + 3.04222i) q^{8} +(-3.96049 + 1.16291i) q^{9} +O(q^{10})$	\(q+(-0.937084 - 0.602227i) q^{2} +(0.379948 + 2.64260i) q^{3} +(-0.315382 - 0.690589i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(1.23540 - 2.70515i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.437406 + 3.04222i) q^{8} +(-3.96049 + 1.16291i) q^{9} +(0.729458 + 0.841840i) q^{10} +(2.41955 - 1.55495i) q^{11} +(1.70512 - 1.09582i) q^{12} +(-1.21100 - 1.39756i) q^{13} +(-1.06879 + 0.313826i) q^{14} +(0.379948 - 2.64260i) q^{15} +(1.24766 - 1.43988i) q^{16} +(1.71853 - 3.76305i) q^{17} +(4.41165 + 1.29538i) q^{18} +(3.27386 + 7.16876i) q^{19} +(0.108045 + 0.751469i) q^{20} +(2.24596 + 1.44339i) q^{21} -3.20376 q^{22} +(4.77833 - 0.409390i) q^{23} -8.20557 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.293154 + 2.03893i) q^{26} +(-1.25069 - 2.73862i) q^{27} +(-0.728444 - 0.213890i) q^{28} +(-4.09606 + 8.96911i) q^{29} +(-1.94749 + 2.24752i) q^{30} +(-0.644101 + 4.47982i) q^{31} +(3.86172 - 1.13390i) q^{32} +(5.02842 + 5.80311i) q^{33} +(-3.87661 + 2.49135i) q^{34} +(-0.841254 + 0.540641i) q^{35} +(2.05216 + 2.36832i) q^{36} +(9.34981 - 2.74535i) q^{37} +(1.24934 - 8.68934i) q^{38} +(3.23309 - 3.73118i) q^{39} +(1.27678 - 2.79576i) q^{40} +(-8.97047 - 2.63397i) q^{41} +(-1.23540 - 2.70515i) q^{42} +(0.0537437 + 0.373796i) q^{43} +(-1.83692 - 1.18051i) q^{44} +4.12769 q^{45} +(-4.72424 - 2.49401i) q^{46} -4.70455 q^{47} +(4.27906 + 2.74999i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.462736 - 1.01325i) q^{50} +(10.5972 + 3.11161i) q^{51} +(-0.583217 + 1.27707i) q^{52} +(1.32400 - 1.52798i) q^{53} +(-0.477274 + 3.31951i) q^{54} +(-2.75962 + 0.810299i) q^{55} +(2.01272 + 2.32280i) q^{56} +(-17.7003 + 11.3753i) q^{57} +(9.23979 - 5.93805i) q^{58} +(1.13929 + 1.31482i) q^{59} +(-1.94478 + 0.571039i) q^{60} +(-1.86146 + 12.9467i) q^{61} +(3.30145 - 3.81007i) q^{62} +(-1.71471 + 3.75468i) q^{63} +(-7.95773 - 2.33660i) q^{64} +(0.768203 + 1.68213i) q^{65} +(-1.21726 - 8.46625i) q^{66} +(10.5052 + 6.75131i) q^{67} -3.14071 q^{68} +(2.89737 + 12.4717i) q^{69} +1.11391 q^{70} +(11.5978 + 7.45342i) q^{71} +(-1.80548 - 12.5574i) q^{72} +(5.43407 + 11.8990i) q^{73} +(-10.4149 - 3.05809i) q^{74} +(-1.10906 + 2.42851i) q^{75} +(3.91815 - 4.52179i) q^{76} +(0.409316 - 2.84685i) q^{77} +(-5.27669 + 1.54938i) q^{78} +(1.87580 + 2.16479i) q^{79} +(-1.60278 + 1.03004i) q^{80} +(-3.65543 + 2.34920i) q^{81} +(6.81984 + 7.87051i) q^{82} +(2.82723 - 0.830149i) q^{83} +(0.288456 - 2.00625i) q^{84} +(-2.70909 + 3.12645i) q^{85} +(0.174748 - 0.382644i) q^{86} +(-25.2581 - 7.41644i) q^{87} +(3.67218 + 8.04096i) q^{88} +(-1.06004 - 7.37274i) q^{89} +(-3.86800 - 2.48581i) q^{90} -1.84924 q^{91} +(-1.78972 - 3.17075i) q^{92} -12.0831 q^{93} +(4.40855 + 2.83321i) q^{94} +(-1.12158 - 7.80073i) q^{95} +(4.46371 + 9.77416i) q^{96} +(-4.42309 - 1.29874i) q^{97} +(-0.462736 + 1.01325i) q^{98} +(-7.77436 + 8.97209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.937084	−	0.602227i	−0.662618	−	0.425839i	0.165639	−	0.986186i	$-0.447031\pi$
$2$	−0.937084	−	0.602227i	−0.662618	−	0.425839i	−0.828258	+	0.560347i	$0.810668\pi$
$3$	0.379948	+	2.64260i	0.219363	+	1.52571i	0.740397	+	0.672170i	$0.234637\pi$
$3$	0.379948	+	2.64260i	0.219363	+	1.52571i	−0.521034	+	0.853536i	$0.674453\pi$
$4$	−0.315382	−	0.690589i	−0.157691	−	0.345295i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	1.23540	−	2.70515i	0.504351	−	1.10437i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	−0.437406	+	3.04222i	−0.154646	+	1.07559i
$9$	−3.96049	+	1.16291i	−1.32016	+	0.387635i
$10$	0.729458	+	0.841840i	0.230675	+	0.266213i
$11$	2.41955	−	1.55495i	0.729522	−	0.468836i	−0.122415	−	0.992479i	$-0.539064\pi$
$11$	2.41955	−	1.55495i	0.729522	−	0.468836i	0.851938	+	0.523643i	$0.175428\pi$
$12$	1.70512	−	1.09582i	0.492226	−	0.316335i
$13$	−1.21100	−	1.39756i	−0.335870	−	0.387615i	0.562542	−	0.826769i	$-0.309824\pi$
$13$	−1.21100	−	1.39756i	−0.335870	−	0.387615i	−0.898412	+	0.439154i	$0.855278\pi$
$14$	−1.06879	+	0.313826i	−0.285647	+	0.0838735i
$15$	0.379948	−	2.64260i	0.0981023	−	0.682316i
$16$	1.24766	−	1.43988i	0.311915	−	0.359969i
$17$	1.71853	−	3.76305i	0.416804	−	0.912673i	−0.578483	−	0.815695i	$-0.696355\pi$
$17$	1.71853	−	3.76305i	0.416804	−	0.912673i	0.995286	−	0.0969783i	$-0.0309177\pi$
$18$	4.41165	+	1.29538i	1.03984	+	0.305323i
$19$	3.27386	+	7.16876i	0.751076	+	1.64463i	0.764422	+	0.644716i	$0.223024\pi$
$19$	3.27386	+	7.16876i	0.751076	+	1.64463i	−0.0133459	+	0.999911i	$0.504248\pi$
$20$	0.108045	+	0.751469i	0.0241596	+	0.168034i
$21$	2.24596	+	1.44339i	0.490108	+	0.314973i
$22$	−3.20376			−0.683043
$23$	4.77833	−	0.409390i	0.996350	−	0.0853637i
$23$	4.77833	−	0.409390i	0.996350	−	0.0853637i
$24$	−8.20557			−1.67495
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	0.293154	+	2.03893i	0.0574922	+	0.399867i
$27$	−1.25069	−	2.73862i	−0.240695	−	0.527048i
$28$	−0.728444	−	0.213890i	−0.137663	−	0.0404215i
$29$	−4.09606	+	8.96911i	−0.760619	+	1.66552i	−0.0143328	+	0.999897i	$0.504562\pi$
$29$	−4.09606	+	8.96911i	−0.760619	+	1.66552i	−0.746286	+	0.665625i	$0.768165\pi$
$30$	−1.94749	+	2.24752i	−0.355561	+	0.410340i
$31$	−0.644101	+	4.47982i	−0.115684	+	0.804600i	0.846537	+	0.532330i	$0.178683\pi$
$31$	−0.644101	+	4.47982i	−0.115684	+	0.804600i	−0.962221	+	0.272270i	$0.912226\pi$
$32$	3.86172	−	1.13390i	0.682663	−	0.200448i
$33$	5.02842	+	5.80311i	0.875336	+	1.01019i
$34$	−3.87661	+	2.49135i	−0.664833	+	0.427263i
$35$	−0.841254	+	0.540641i	−0.142198	+	0.0913850i
$36$	2.05216	+	2.36832i	0.342026	+	0.394719i
$37$	9.34981	−	2.74535i	1.53710	−	0.451333i	0.599885	−	0.800086i	$-0.295213\pi$
$37$	9.34981	−	2.74535i	1.53710	−	0.451333i	0.937215	+	0.348753i	$0.113395\pi$
$38$	1.24934	−	8.68934i	0.202670	−	1.40960i
$39$	3.23309	−	3.73118i	0.517708	−	0.597467i
$40$	1.27678	−	2.79576i	0.201877	−	0.442048i
$41$	−8.97047	−	2.63397i	−1.40095	−	0.411357i	−0.507941	−	0.861392i	$-0.669593\pi$
$41$	−8.97047	−	2.63397i	−1.40095	−	0.411357i	−0.893011	+	0.450035i	$0.851412\pi$
$42$	−1.23540	−	2.70515i	−0.190627	−	0.417414i
$43$	0.0537437	+	0.373796i	0.00819584	+	0.0570033i	0.993509	−	0.113754i	$-0.0362876\pi$
$43$	0.0537437	+	0.373796i	0.00819584	+	0.0570033i	−0.985313	+	0.170757i	$0.945379\pi$
$44$	−1.83692	−	1.18051i	−0.276925	−	0.177969i
$45$	4.12769			0.615320
$46$	−4.72424	−	2.49401i	−0.696551	−	0.367721i
$47$	−4.70455			−0.686229			−0.343114	−	0.939294i	$-0.611482\pi$
$47$	−4.70455			−0.686229			−0.343114	+	0.939294i	$0.611482\pi$
$48$	4.27906	+	2.74999i	0.617629	+	0.396926i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.462736	−	1.01325i	−0.0654408	−	0.143295i
$51$	10.5972	+	3.11161i	1.48390	+	0.435713i
$52$	−0.583217	+	1.27707i	−0.0808777	+	0.177097i
$53$	1.32400	−	1.52798i	0.181866	−	0.209884i	−0.657495	−	0.753459i	$-0.728384\pi$
$53$	1.32400	−	1.52798i	0.181866	−	0.209884i	0.839361	+	0.543574i	$0.182929\pi$
$54$	−0.477274	+	3.31951i	−0.0649488	+	0.451729i
$55$	−2.75962	+	0.810299i	−0.372108	+	0.109261i
$56$	2.01272	+	2.32280i	0.268961	+	0.310397i
$57$	−17.7003	+	11.3753i	−2.34446	+	1.50669i
$58$	9.23979	−	5.93805i	1.21324	−	0.779705i
$59$	1.13929	+	1.31482i	0.148324	+	0.171174i	0.825049	−	0.565061i	$-0.191147\pi$
$59$	1.13929	+	1.31482i	0.148324	+	0.171174i	−0.676726	+	0.736235i	$0.736602\pi$
$60$	−1.94478	+	0.571039i	−0.251070	+	0.0737208i
$61$	−1.86146	+	12.9467i	−0.238335	+	1.65766i	0.421933	+	0.906627i	$0.361352\pi$
$61$	−1.86146	+	12.9467i	−0.238335	+	1.65766i	−0.660268	+	0.751030i	$0.729557\pi$
$62$	3.30145	−	3.81007i	0.419284	−	0.483880i
$63$	−1.71471	+	3.75468i	−0.216033	+	0.473046i
$64$	−7.95773	−	2.33660i	−0.994716	−	0.292075i
$65$	0.768203	+	1.68213i	0.0952839	+	0.208643i
$66$	−1.21726	−	8.46625i	−0.149835	−	1.04212i
$67$	10.5052	+	6.75131i	1.28342	+	0.824804i	0.991306	−	0.131580i	$-0.0420050\pi$
$67$	10.5052	+	6.75131i	1.28342	+	0.824804i	0.292114	+	0.956384i	$0.405641\pi$
$68$	−3.14071			−0.380867
$69$	2.89737	+	12.4717i	0.348803	+	1.50141i
$70$	1.11391			0.133138
$71$	11.5978	+	7.45342i	1.37640	+	0.884559i	0.999137	−	0.0415471i	$-0.0132287\pi$
$71$	11.5978	+	7.45342i	1.37640	+	0.884559i	0.377264	+	0.926106i	$0.376865\pi$
$72$	−1.80548	−	12.5574i	−0.212777	−	1.47990i
$73$	5.43407	+	11.8990i	0.636010	+	1.39267i	0.903282	+	0.429047i	$0.141151\pi$
$73$	5.43407	+	11.8990i	0.636010	+	1.39267i	−0.267272	+	0.963621i	$0.586122\pi$
$74$	−10.4149	−	3.05809i	−1.21071	−	0.355495i
$75$	−1.10906	+	2.42851i	−0.128064	+	0.280420i
$76$	3.91815	−	4.52179i	0.449443	−	0.518685i
$77$	0.409316	−	2.84685i	0.0466458	−	0.324429i
$78$	−5.27669	+	1.54938i	−0.597468	+	0.175432i
$79$	1.87580	+	2.16479i	0.211044	+	0.243558i	0.851396	−	0.524524i	$-0.175757\pi$
$79$	1.87580	+	2.16479i	0.211044	+	0.243558i	−0.640351	+	0.768082i	$0.721211\pi$
$80$	−1.60278	+	1.03004i	−0.179196	+	0.115162i
$81$	−3.65543	+	2.34920i	−0.406159	+	0.261023i
$82$	6.81984	+	7.87051i	0.753125	+	0.869152i
$83$	2.82723	−	0.830149i	0.310329	−	0.0911207i	−0.122860	−	0.992424i	$-0.539207\pi$
$83$	2.82723	−	0.830149i	0.310329	−	0.0911207i	0.433189	+	0.901303i	$0.357388\pi$
$84$	0.288456	−	2.00625i	0.0314731	−	0.218900i
$85$	−2.70909	+	3.12645i	−0.293842	+	0.339111i
$86$	0.174748	−	0.382644i	0.0188435	−	0.0412616i
$87$	−25.2581	−	7.41644i	−2.70795	−	0.795126i
$88$	3.67218	+	8.04096i	0.391456	+	0.857169i
$89$	−1.06004	−	7.37274i	−0.112364	−	0.781509i	−0.965609	−	0.259999i	$-0.916278\pi$
$89$	−1.06004	−	7.37274i	−0.112364	−	0.781509i	0.853245	−	0.521510i	$-0.174631\pi$
$90$	−3.86800	−	2.48581i	−0.407723	−	0.262027i
$91$	−1.84924			−0.193853
$92$	−1.78972	−	3.17075i	−0.186591	−	0.330573i
$93$	−12.0831			−1.25296
$94$	4.40855	+	2.83321i	0.454708	+	0.292223i
$95$	−1.12158	−	7.80073i	−0.115071	−	0.800338i
$96$	4.46371	+	9.77416i	0.455576	+	0.997571i
$97$	−4.42309	−	1.29874i	−0.449097	−	0.131867i	0.0493604	−	0.998781i	$-0.484282\pi$
$97$	−4.42309	−	1.29874i	−0.449097	−	0.131867i	−0.498457	+	0.866914i	$0.666100\pi$
$98$	−0.462736	+	1.01325i	−0.0467434	+	0.102354i
$99$	−7.77436	+	8.97209i	−0.781353	+	0.901729i
$100$	0.108045	−	0.751469i	0.0108045	−	0.0751469i
$101$	0.126806	−	0.0372336i	0.0126177	−	0.00370488i	−0.275418	−	0.961325i	$-0.588816\pi$
$101$	0.126806	−	0.0372336i	0.0126177	−	0.00370488i	0.288035	+	0.957620i	$0.406998\pi$
$102$	−8.05655	−	9.29775i	−0.797717	−	0.920614i
$103$	8.15092	−	5.23828i	0.803134	−	0.516143i	−0.0735030	−	0.997295i	$-0.523418\pi$
$103$	8.15092	−	5.23828i	0.803134	−	0.516143i	0.876637	+	0.481152i	$0.159781\pi$
$104$	4.78140	−	3.07282i	0.468855	−	0.301315i
$105$	−1.74833	−	2.01768i	−0.170620	−	0.196905i
$106$	−2.16089	+	0.634496i	−0.209885	+	0.0616277i
$107$	0.147620	−	1.02672i	0.0142710	−	0.0992567i	−0.981441	−	0.191764i	$-0.938579\pi$
$107$	0.147620	−	1.02672i	0.0142710	−	0.0992567i	0.995712	+	0.0925075i	$0.0294882\pi$
$108$	−1.49682	+	1.72742i	−0.144031	+	0.166221i
$109$	6.24652	−	13.6780i	0.598308	−	1.31011i	−0.331982	−	0.943286i	$-0.607717\pi$
$109$	6.24652	−	13.6780i	0.598308	−	1.31011i	0.930290	−	0.366826i	$-0.119556\pi$
$110$	3.07398	+	0.902603i	0.293093	+	0.0860598i
$111$	10.8073	+	23.6647i	1.02579	+	2.24616i
$112$	−0.271142	−	1.88584i	−0.0256205	−	0.178195i
$113$	−1.99892	−	1.28463i	−0.188042	−	0.120847i	0.443233	−	0.896407i	$-0.353832\pi$
$113$	−1.99892	−	1.28463i	−0.188042	−	0.120847i	−0.631275	+	0.775559i	$0.717468\pi$
$114$	23.4371			2.19509
$115$	−4.70011	−	0.953403i	−0.438287	−	0.0889053i
$116$	7.48580			0.695039
$117$	6.42138	+	4.12677i	0.593657	+	0.381520i
$118$	−0.275797	−	1.91821i	−0.0253891	−	0.176585i
$119$	−1.71853	−	3.76305i	−0.157537	−	0.344958i
$120$	7.87319	+	2.31178i	0.718720	+	0.211035i
$121$	−1.13321	+	2.48138i	−0.103019	+	0.225580i
$122$	9.54121	−	11.0111i	0.863820	−	0.996902i
$123$	3.55221	−	24.7061i	0.320292	−	2.22768i
$124$	3.29686	−	0.968044i	0.296066	−	0.0869329i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	3.86800	−	2.48581i	0.344588	−	0.221454i
$127$	17.8528	−	11.4733i	1.58418	−	1.01809i	0.609975	−	0.792421i	$-0.291180\pi$
$127$	17.8528	−	11.4733i	1.58418	−	1.01809i	0.974204	−	0.225669i	$-0.0724568\pi$
$128$	0.778591	+	0.898542i	0.0688184	+	0.0794206i
$129$	−0.967373	+	0.284046i	−0.0851724	+	0.0250089i
$130$	0.293154	−	2.03893i	0.0257113	−	0.178826i
$131$	−2.99136	+	3.45221i	−0.261356	+	0.301621i	−0.871228	−	0.490879i	$-0.836676\pi$
$131$	−2.99136	+	3.45221i	−0.261356	+	0.301621i	0.609871	+	0.792500i	$0.291221\pi$
$132$	2.42169	−	5.30277i	0.210781	−	0.461547i
$133$	7.56172	+	2.22032i	0.655684	+	0.192526i
$134$	−5.77847	−	12.6531i	−0.499184	−	1.09306i
$135$	0.428466	+	2.98005i	0.0368765	+	0.256482i
$136$	10.6963	+	6.87412i	0.917203	+	0.589451i
$137$	−15.2886			−1.30619			−0.653097	−	0.757274i	$-0.726531\pi$
$137$	−15.2886			−1.30619			−0.653097	+	0.757274i	$0.726531\pi$
$138$	4.79569	−	13.4319i	0.408236	−	1.14340i
$139$	0.276495			0.0234520			0.0117260	−	0.999931i	$-0.496267\pi$
$139$	0.276495			0.0234520			0.0117260	+	0.999931i	$0.496267\pi$
$140$	0.638677	+	0.410453i	0.0539780	+	0.0346896i
$141$	−1.78749	−	12.4322i	−0.150533	−	1.04698i
$142$	−6.37941	−	13.9690i	−0.535348	−	1.17225i
$143$	−5.10322	−	1.49844i	−0.426752	−	0.125306i
$144$	−3.26691	+	7.15353i	−0.272242	+	0.596127i
$145$	6.45703	−	7.45181i	0.536227	−	0.618839i
$146$	2.07370	−	14.4229i	0.171620	−	1.19365i
$147$	2.56163	−	0.752162i	0.211280	−	0.0620373i
$148$	−4.84467	−	5.59105i	−0.398229	−	0.459581i
$149$	−1.93833	+	1.24569i	−0.158794	+	0.102051i	−0.617625	−	0.786473i	$-0.711905\pi$
$149$	−1.93833	+	1.24569i	−0.158794	+	0.102051i	0.458831	+	0.888524i	$0.348269\pi$
$150$	2.50180	−	1.60781i	0.204271	−	0.131277i
$151$	−4.82208	−	5.56498i	−0.392415	−	0.452871i	0.524822	−	0.851212i	$-0.324132\pi$
$151$	−4.82208	−	5.56498i	−0.392415	−	0.452871i	−0.917238	+	0.398340i	$0.869586\pi$
$152$	−23.2410	+	6.82417i	−1.88509	+	0.553513i
$153$	−2.43014	+	16.9020i	−0.196465	+	1.36645i
$154$	−2.09801	+	2.42124i	−0.169063	+	0.195109i
$155$	1.88012	−	4.11689i	0.151015	−	0.330677i
$156$	−3.59637	−	1.05599i	−0.287940	−	0.0845468i
$157$	7.81915	+	17.1215i	0.624036	+	1.36645i	0.912547	+	0.408972i	$0.134113\pi$
$157$	7.81915	+	17.1215i	0.624036	+	1.36645i	−0.288511	+	0.957477i	$0.593160\pi$
$158$	−0.454088	−	3.15825i	−0.0361253	−	0.251257i
$159$	4.54090	+	2.91826i	0.360116	+	0.231433i
$160$	−4.02475			−0.318185
$161$	2.81974	−	3.87931i	0.222227	−	0.305733i
$162$	4.84020			0.380282
$163$	−9.51108	−	6.11240i	−0.744965	−	0.478760i	0.112275	−	0.993677i	$-0.464186\pi$
$163$	−9.51108	−	6.11240i	−0.744965	−	0.478760i	−0.857240	+	0.514917i	$0.827823\pi$
$164$	1.01013	+	7.02562i	0.0788780	+	0.548608i
$165$	−3.18981	−	6.98471i	−0.248326	−	0.543759i
$166$	−3.14929	−	0.924715i	−0.244432	−	0.0717718i
$167$	−4.56283	+	9.99121i	−0.353083	+	0.773143i	0.646862	+	0.762607i	$0.276081\pi$
$167$	−4.56283	+	9.99121i	−0.353083	+	0.773143i	−0.999944	+	0.0105358i	$0.996646\pi$
$168$	−5.37350	+	6.20136i	−0.414575	+	0.478445i
$169$	1.36342	−	9.48279i	0.104878	−	0.729445i
$170$	4.42148	−	1.29826i	0.339112	−	0.0995722i
$171$	−21.3027	−	24.5846i	−1.62906	−	1.88004i
$172$	0.241190	−	0.155003i	0.0183905	−	0.0118189i
$173$	10.6979	−	6.87514i	0.813349	−	0.522708i	−0.0665980	−	0.997780i	$-0.521214\pi$
$173$	10.6979	−	6.87514i	0.813349	−	0.522708i	0.879947	+	0.475072i	$0.157578\pi$
$174$	19.2025	+	22.1609i	1.45574	+	1.68002i
$175$	0.959493	−	0.281733i	0.0725309	−	0.0212970i
$176$	0.779840	−	5.42390i	0.0587826	−	0.408842i
$177$	−3.04166	+	3.51026i	−0.228625	+	0.263847i
$178$	−3.44672	+	7.54726i	−0.258343	+	0.565691i
$179$	0.886849	+	0.260402i	0.0662862	+	0.0194634i	0.314708	−	0.949189i	$-0.398094\pi$
$179$	0.886849	+	0.260402i	0.0662862	+	0.0194634i	−0.248421	+	0.968652i	$0.579912\pi$
$180$	−1.30180	−	2.85054i	−0.0970304	−	0.212467i
$181$	−2.09734	−	14.5873i	−0.155894	−	1.08427i	−0.906101	−	0.423062i	$-0.860955\pi$
$181$	−2.09734	−	14.5873i	−0.155894	−	1.08427i	0.750207	−	0.661203i	$-0.229954\pi$
$182$	1.73290	+	1.11366i	0.128451	+	0.0825503i
$183$	−34.9202			−2.58138
$184$	−0.844612	+	14.7158i	−0.0622656	+	1.08486i
$185$	−9.74453			−0.716432
$186$	11.3229	+	7.27677i	0.830234	+	0.533559i
$187$	−1.69329	−	11.7771i	−0.123826	−	0.861228i
$188$	1.48373	+	3.24891i	0.108212	+	0.236951i
$189$	−2.88874	−	0.848210i	−0.210125	−	0.0616982i
$190$	−3.64680	+	7.98538i	−0.264567	+	0.579321i
$191$	5.49907	−	6.34627i	0.397899	−	0.459200i	−0.521079	−	0.853508i	$-0.674470\pi$
$191$	5.49907	−	6.34627i	0.397899	−	0.459200i	0.918978	+	0.394309i	$0.129016\pi$
$192$	3.15117	−	21.9169i	0.227416	−	1.58172i
$193$	21.5346	−	6.32314i	1.55010	−	0.455149i	0.608967	−	0.793195i	$-0.291584\pi$
$193$	21.5346	−	6.32314i	1.55010	−	0.455149i	0.941130	+	0.338046i	$0.109766\pi$
$194$	3.36267	+	3.88073i	0.241426	+	0.278620i
$195$	−4.15332	+	2.66918i	−0.297425	+	0.191144i
$196$	−0.638677	+	0.410453i	−0.0456198	+	0.0293180i
$197$	−14.8632	−	17.1531i	−1.05896	−	1.22210i	−0.974196	−	0.225704i	$-0.927532\pi$
$197$	−14.8632	−	17.1531i	−1.05896	−	1.22210i	−0.0847638	−	0.996401i	$-0.527014\pi$
$198$	12.6885	−	3.72567i	0.901730	−	0.264772i
$199$	3.06497	−	21.3173i	0.217270	−	1.51114i	−0.530785	−	0.847507i	$-0.678103\pi$
$199$	3.06497	−	21.3173i	0.217270	−	1.51114i	0.748054	−	0.663637i	$-0.230988\pi$
$200$	−2.01272	+	2.32280i	−0.142321	+	0.164247i
$201$	−13.8496	+	30.3263i	−0.976872	+	2.13905i
$202$	−0.141251	−	0.0414750i	−0.00993837	−	0.00291817i
$203$	4.09606	+	8.96911i	0.287487	+	0.629508i
$204$	−1.19331	−	8.29964i	−0.0835483	−	0.581091i
$205$	7.86503	+	5.05455i	0.549317	+	0.353025i
$206$	−10.7927			−0.751965
$207$	−18.4485	+	7.17813i	−1.28226	+	0.498915i
$208$	−3.52323			−0.244292
$209$	19.0684	+	12.2545i	1.31899	+	0.847661i
$210$	0.423230	+	2.94363i	0.0292056	+	0.203130i
$211$	−2.20547	−	4.82930i	−0.151831	−	0.332463i	0.818399	−	0.574651i	$-0.194862\pi$
$211$	−2.20547	−	4.82930i	−0.151831	−	0.332463i	−0.970229	+	0.242188i	$0.922135\pi$
$212$	−1.47277	−	0.432445i	−0.101151	−	0.0297005i
$213$	−15.2899	+	33.4801i	−1.04764	+	2.29402i
$214$	−0.756650	+	0.873221i	−0.0517236	+	0.0596922i
$215$	0.0537437	−	0.373796i	0.00366529	−	0.0254927i
$216$	8.87855	−	2.60698i	0.604109	−	0.177382i
$217$	2.96383	+	3.42044i	0.201198	+	0.232195i
$218$	−14.0908	+	9.05558i	−0.954346	+	0.613321i
$219$	−29.3795	+	18.8811i	−1.98528	+	1.27586i
$220$	1.42992	+	1.65021i	0.0964051	+	0.111257i
$221$	−7.34023	+	2.15529i	−0.493757	+	0.144980i
$222$	4.12418	−	28.6843i	0.276797	−	1.92516i
$223$	−13.9083	+	16.0511i	−0.931370	+	1.07486i	0.0656601	+	0.997842i	$0.479085\pi$
$223$	−13.9083	+	16.0511i	−0.931370	+	1.07486i	−0.997030	+	0.0770160i	$0.975461\pi$
$224$	1.67194	−	3.66104i	0.111711	−	0.244614i
$225$	−3.96049	−	1.16291i	−0.264033	−	0.0775271i
$226$	1.09952	+	2.40760i	0.0731387	+	0.160151i
$227$	1.38029	+	9.60012i	0.0916130	+	0.637182i	0.982954	+	0.183850i	$0.0588559\pi$
$227$	1.38029	+	9.60012i	0.0916130	+	0.637182i	−0.891341	+	0.453333i	$0.850235\pi$
$228$	13.4380	+	8.63607i	0.889952	+	0.571938i
$229$	28.1851			1.86252			0.931262	−	0.364351i	$-0.118709\pi$
$229$	28.1851			1.86252			0.931262	+	0.364351i	$0.118709\pi$
$230$	3.83023	+	3.72395i	0.252558	+	0.245550i
$231$	7.67861			0.505215
$232$	−25.4944	−	16.3843i	−1.67379	−	1.07568i
$233$	−0.996084	−	6.92791i	−0.0652556	−	0.453863i	−0.996084	−	0.0884072i	$-0.971822\pi$
$233$	−0.996084	−	6.92791i	−0.0652556	−	0.453863i	0.930829	−	0.365455i	$-0.119087\pi$
$234$	−3.53212	−	7.73426i	−0.230902	−	0.505604i
$235$	4.51398	+	1.32542i	0.294460	+	0.0864611i
$236$	0.548685	−	1.20145i	0.0357164	−	0.0782079i
$237$	−5.00797	+	5.77951i	−0.325303	+	0.375419i
$238$	−0.655806	+	4.56123i	−0.0425096	+	0.295661i
$239$	−18.9548	+	5.56562i	−1.22608	+	0.360010i	−0.829769	−	0.558106i	$-0.811528\pi$
$239$	−18.9548	+	5.56562i	−1.22608	+	0.360010i	−0.396311	+	0.918116i	$0.629710\pi$
$240$	−3.33097	−	3.84414i	−0.215013	−	0.248138i
$241$	−9.07767	+	5.83387i	−0.584744	+	0.375792i	−0.799312	−	0.600917i	$-0.794802\pi$
$241$	−9.07767	+	5.83387i	−0.584744	+	0.375792i	0.214567	+	0.976709i	$0.431166\pi$
$242$	2.55626	−	1.64281i	0.164323	−	0.105604i
$243$	−13.5116	−	15.5933i	−0.866771	−	1.00031i
$244$	9.52793	−	2.79765i	0.609963	−	0.179101i
$245$	−0.142315	+	0.989821i	−0.00909216	+	0.0632374i
$246$	−18.2074	+	21.0125i	−1.16086	+	1.33971i
$247$	6.05417	−	13.2568i	0.385218	−	0.843509i
$248$	−13.3469	−	3.91900i	−0.847528	−	0.248857i
$249$	3.26795	+	7.15582i	0.207098	+	0.453482i
$250$	0.158526	+	1.10258i	0.0100261	+	0.0697330i
$251$	−23.9653	−	15.4016i	−1.51268	−	0.972140i	−0.993043	−	0.117753i	$-0.962431\pi$
$251$	−23.9653	−	15.4016i	−1.51268	−	0.972140i	−0.519636	−	0.854387i	$-0.673933\pi$
$252$	3.13373			0.197406
$253$	10.9248	−	8.42061i	0.686838	−	0.529399i
$254$	−23.6391			−1.48325
$255$	−9.29128	−	5.97114i	−0.581842	−	0.373927i
$256$	2.17215	+	15.1076i	0.135759	+	0.944227i
$257$	−3.75061	−	8.21268i	−0.233956	−	0.512293i	0.755844	−	0.654751i	$-0.227227\pi$
$257$	−3.75061	−	8.21268i	−0.233956	−	0.512293i	−0.989801	+	0.142458i	$0.954499\pi$
$258$	1.07757	+	0.316403i	0.0670866	+	0.0196984i
$259$	4.04803	−	8.86394i	0.251532	−	0.550778i
$260$	0.919384	−	1.06103i	0.0570178	−	0.0658020i
$261$	5.79217	−	40.2855i	0.358527	−	2.49361i
$262$	4.88217	−	1.43353i	0.301621	−	0.0885640i
$263$	1.61085	+	1.85902i	0.0993294	+	0.114632i	0.803238	−	0.595659i	$-0.203109\pi$
$263$	1.61085	+	1.85902i	0.0993294	+	0.114632i	−0.703908	+	0.710291i	$0.748563\pi$
$264$	−19.8538	+	12.7593i	−1.22192	+	0.785278i
$265$	−1.70085	+	1.09307i	−0.104483	+	0.0671469i
$266$	−5.74882	−	6.63450i	−0.352483	−	0.406787i
$267$	19.0805	−	5.60253i	1.16770	−	0.342869i
$268$	1.34922	−	9.38405i	0.0824169	−	0.573222i
$269$	1.45667	−	1.68109i	0.0888148	−	0.102498i	−0.709603	−	0.704602i	$-0.751125\pi$
$269$	1.45667	−	1.68109i	0.0888148	−	0.102498i	0.798417	+	0.602104i	$0.205671\pi$
$270$	1.39316	−	3.05059i	0.0847848	−	0.185653i
$271$	10.9112	+	3.20382i	0.662808	+	0.194618i	0.595798	−	0.803134i	$-0.296836\pi$
$271$	10.9112	+	3.20382i	0.662808	+	0.194618i	0.0670099	+	0.997752i	$0.478654\pi$
$272$	−3.27418	−	7.16946i	−0.198527	−	0.434713i
$273$	−0.702617	−	4.88681i	−0.0425243	−	0.295763i
$274$	14.3267	+	9.20721i	0.865508	+	0.556228i
$275$	2.87613			0.173437
$276$	7.69902	−	5.93422i	0.463426	−	0.357198i
$277$	−2.93843			−0.176553			−0.0882765	−	0.996096i	$-0.528136\pi$
$277$	−2.93843			−0.176553			−0.0882765	+	0.996096i	$0.528136\pi$
$278$	−0.259099	−	0.166513i	−0.0155397	−	0.00998678i
$279$	−2.65865	−	18.4913i	−0.159169	−	1.10705i
$280$	−1.27678	−	2.79576i	−0.0763022	−	0.167079i
$281$	−17.3448	−	5.09290i	−1.03470	−	0.303817i	−0.280082	−	0.959976i	$-0.590362\pi$
$281$	−17.3448	−	5.09290i	−1.03470	−	0.303817i	−0.754623	+	0.656159i	$0.772180\pi$
$282$	−5.81201	+	12.7265i	−0.346100	+	0.757853i
$283$	−9.76221	+	11.2662i	−0.580303	+	0.669706i	−0.967670	−	0.252220i	$-0.918839\pi$
$283$	−9.76221	+	11.2662i	−0.580303	+	0.669706i	0.387367	+	0.921926i	$0.373385\pi$
$284$	1.48954	−	10.3600i	0.0883878	−	0.614750i
$285$	20.1881	−	5.92775i	1.19584	−	0.351130i
$286$	3.87974	+	4.47746i	0.229414	+	0.264758i
$287$	−7.86503	+	5.05455i	−0.464258	+	0.298361i
$288$	−13.9757	+	8.98164i	−0.823526	+	0.529248i
$289$	−0.0745571	−	0.0860435i	−0.00438571	−	0.00506138i
$290$	−10.5385	+	3.09437i	−0.618840	+	0.181708i
$291$	1.75149	−	12.1819i	0.102674	−	0.714116i
$292$	6.50349	−	7.50543i	0.380588	−	0.439222i
$293$	0.793142	−	1.73674i	0.0463358	−	0.101461i	−0.885048	−	0.465499i	$-0.845875\pi$
$293$	0.793142	−	1.73674i	0.0463358	−	0.101461i	0.931384	+	0.364038i	$0.118602\pi$
$294$	−2.85343	−	0.837844i	−0.166416	−	0.0488640i
$295$	−0.722719	−	1.58253i	−0.0420783	−	0.0921386i
$296$	4.26231	+	29.6450i	0.247742	+	1.72308i
$297$	−7.28452	−	4.68148i	−0.422691	−	0.271647i
$298$	2.56656			0.148677
$299$	−6.35869	−	6.18225i	−0.367732	−	0.357529i
$300$	2.02688			0.117022
$301$	0.317691	+	0.204167i	0.0183114	+	0.0117680i
$302$	1.16731	+	8.11884i	0.0671713	+	0.467187i
$303$	0.146573	+	0.320950i	0.00842041	+	0.0184381i
$304$	14.4068	+	4.23022i	0.826286	+	0.242620i
$305$	5.43357	−	11.8979i	0.311125	−	0.681269i
$306$	12.4561	−	14.3751i	0.712068	−	0.821770i
$307$	1.77804	−	12.3665i	0.101478	−	0.705795i	−0.874036	−	0.485860i	$-0.838506\pi$
$307$	1.77804	−	12.3665i	0.101478	−	0.705795i	0.975515	−	0.219935i	$-0.0705845\pi$
$308$	−2.09510	+	0.615176i	−0.119379	+	0.0350529i
$309$	16.9396	+	19.5493i	0.963661	+	1.11212i
$310$	−4.24114	+	2.72561i	−0.240880	+	0.154804i
$311$	16.5596	−	10.6422i	0.939011	−	0.603466i	0.0208966	−	0.999782i	$-0.493348\pi$
$311$	16.5596	−	10.6422i	0.939011	−	0.603466i	0.918114	+	0.396316i	$0.129712\pi$
$312$	9.93692	+	11.4678i	0.562567	+	0.649237i
$313$	−8.77028	+	2.57519i	−0.495725	+	0.145558i	−0.520033	−	0.854146i	$-0.674080\pi$
$313$	−8.77028	+	2.57519i	−0.495725	+	0.145558i	0.0243072	+	0.999705i	$0.492262\pi$
$314$	2.98386	−	20.7532i	0.168389	−	1.17117i
$315$	2.70307	−	3.11950i	0.152300	−	0.175764i
$316$	0.903389	−	1.97815i	0.0508196	−	0.111279i
$317$	22.6760	+	6.65827i	1.27361	+	0.373966i	0.847543	−	0.530726i	$-0.178081\pi$
$317$	22.6760	+	6.65827i	1.27361	+	0.373966i	0.426066	+	0.904692i	$0.359899\pi$
$318$	−2.49775	−	5.46930i	−0.140067	−	0.306703i
$319$	4.03592	+	28.0704i	0.225968	+	1.57164i
$320$	6.97709	+	4.48390i	0.390031	+	0.250658i
$321$	2.76930			0.154567
$322$	−4.97856	+	1.93711i	−0.277444	+	0.107951i
$323$	32.6026			1.81406
$324$	2.77519	+	1.78351i	0.154177	+	0.0990837i
$325$	−0.263175	−	1.83042i	−0.0145983	−	0.101533i
$326$	5.23163	+	11.4557i	0.289753	+	0.634471i
$327$	38.5188	+	11.3101i	2.13009	+	0.625451i
$328$	11.9369	−	26.1381i	0.659102	−	1.44323i
$329$	−3.08082	+	3.55546i	−0.169851	+	0.196019i
$330$	−1.21726	+	8.46625i	−0.0670081	+	0.466052i
$331$	−21.0437	+	6.17898i	−1.15666	+	0.339627i	−0.803135	−	0.595796i	$-0.796837\pi$
$331$	−21.0437	+	6.17898i	−1.15666	+	0.339627i	−0.353529	+	0.935424i	$0.615018\pi$
$332$	−1.46495	−	1.69064i	−0.0803995	−	0.0927859i
$333$	−33.8373	+	21.7459i	−1.85427	+	1.19167i
$334$	10.2927	−	6.61474i	0.563193	−	0.361942i
$335$	−8.17764	−	9.43750i	−0.446792	−	0.515626i
$336$	4.88049	−	1.43304i	0.266253	−	0.0781788i
$337$	−2.14755	+	14.9365i	−0.116984	+	0.813643i	0.843862	+	0.536561i	$0.180277\pi$
$337$	−2.14755	+	14.9365i	−0.116984	+	0.813643i	−0.960846	+	0.277083i	$0.910632\pi$
$338$	−6.98843	+	8.06508i	−0.380120	+	0.438682i
$339$	2.63527	−	5.77043i	0.143128	−	0.313407i
$340$	3.01349	+	0.884841i	0.163429	+	0.0479872i
$341$	5.40747	+	11.8407i	0.292831	+	0.641211i
$342$	5.15689	+	35.8670i	0.278853	+	1.93946i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	−1.16068			−0.0625796
$345$	0.733664	−	12.7828i	0.0394992	−	0.688200i
$346$	−14.1653			−0.761529
$347$	2.27339	+	1.46102i	0.122042	+	0.0784316i	0.600238	−	0.799822i	$-0.295073\pi$
$347$	2.27339	+	1.46102i	0.122042	+	0.0784316i	−0.478196	+	0.878253i	$0.658709\pi$
$348$	2.84422	+	19.7820i	0.152466	+	1.06042i
$349$	11.7205	+	25.6643i	0.627383	+	1.37378i	0.910026	+	0.414552i	$0.136062\pi$
$349$	11.7205	+	25.6643i	0.627383	+	1.37378i	−0.282642	+	0.959225i	$0.591211\pi$
$350$	−1.06879	−	0.313826i	−0.0571294	−	0.0167747i
$351$	−2.31282	+	5.06438i	−0.123449	+	0.270316i
$352$	7.58047	−	8.74833i	0.404041	−	0.466288i
$353$	−1.22118	+	8.49353i	−0.0649971	+	0.452065i	0.931169	+	0.364587i	$0.118790\pi$
$353$	−1.22118	+	8.49353i	−0.0649971	+	0.452065i	−0.996166	+	0.0874779i	$0.972119\pi$
$354$	4.96426	−	1.45764i	0.263848	−	0.0774727i
$355$	−9.02809	−	10.4190i	−0.479161	−	0.552982i
$356$	−4.75722	+	3.05728i	−0.252132	+	0.162036i
$357$	9.29128	−	5.97114i	0.491746	−	0.316026i
$358$	−0.674230	−	0.778103i	−0.0356342	−	0.0411240i
$359$	16.6797	−	4.89759i	0.880319	−	0.258485i	0.189820	−	0.981819i	$-0.439209\pi$
$359$	16.6797	−	4.89759i	0.880319	−	0.258485i	0.690498	+	0.723334i	$0.257391\pi$
$360$	−1.80548	+	12.5574i	−0.0951570	+	0.661831i
$361$	−28.2306	+	32.5799i	−1.48582	+	1.71473i
$362$	−6.81949	+	14.9326i	−0.358424	+	0.784840i
$363$	−6.98785	−	2.05182i	−0.366767	−	0.107693i
$364$	0.583217	+	1.27707i	0.0305689	+	0.0669365i
$365$	−1.86163	−	12.9479i	−0.0974422	−	0.677725i
$366$	32.7232	+	21.0299i	1.71047	+	1.09925i
$367$	−28.2451			−1.47438			−0.737191	−	0.675684i	$-0.763848\pi$
$367$	−28.2451			−1.47438			−0.737191	+	0.675684i	$0.763848\pi$
$368$	5.37225	−	7.39097i	0.280048	−	0.385281i
$369$	38.5906			2.00894
$370$	9.13145	+	5.86842i	0.474721	+	0.305085i
$371$	−0.287733	−	2.00123i	−0.0149384	−	0.103899i
$372$	3.81079	+	8.34446i	0.197580	+	0.432640i
$373$	32.4165	+	9.51834i	1.67846	+	0.492841i	0.975797	−	0.218679i	$-0.0701748\pi$
$373$	32.4165	+	9.51834i	1.67846	+	0.492841i	0.702666	+	0.711520i	$0.251993\pi$
$374$	−5.50574	+	12.0559i	−0.284695	+	0.623395i
$375$	1.74833	−	2.01768i	0.0902834	−	0.104193i
$376$	2.05779	−	14.3123i	0.106123	−	0.738099i
$377$	17.4952	−	5.13706i	0.901050	−	0.264572i
$378$	2.19617	+	2.53452i	0.112959	+	0.130362i
$379$	−19.0364	+	12.2340i	−0.977836	+	0.628417i	−0.928879	−	0.370384i	$-0.879226\pi$
$379$	−19.0364	+	12.2340i	−0.977836	+	0.628417i	−0.0489570	+	0.998801i	$0.515590\pi$
$380$	−5.03338	+	3.23476i	−0.258207	+	0.165939i
$381$	37.1025	+	42.8185i	1.90082	+	2.19366i
$382$	−8.97498	+	2.63529i	−0.459200	+	0.134833i
$383$	1.95053	−	13.5662i	0.0996673	−	0.693201i	−0.877320	−	0.479905i	$-0.840671\pi$
$383$	1.95053	−	13.5662i	0.0996673	−	0.693201i	0.976988	−	0.213296i	$-0.0684199\pi$
$384$	−2.07866	+	2.39890i	−0.106076	+	0.122419i
$385$	−1.19479	+	2.61622i	−0.0608920	+	0.133335i
$386$	−23.9877	−	7.04343i	−1.22094	−	0.358501i
$387$	−0.647541	−	1.41792i	−0.0329164	−	0.0720768i
$388$	0.498068	+	3.46414i	0.0252856	+	0.175865i
$389$	−6.52288	−	4.19200i	−0.330723	−	0.212543i	0.364732	−	0.931113i	$-0.381161\pi$
$389$	−6.52288	−	4.19200i	−0.330723	−	0.212543i	−0.695455	+	0.718570i	$0.744797\pi$
$390$	5.49946			0.278476
$391$	6.67112	−	18.6846i	0.337373	−	0.944921i
$392$	3.07351			0.155236
$393$	−10.2594	−	6.59330i	−0.517517	−	0.332588i
$394$	3.59803	+	25.0249i	0.181266	+	1.26074i
$395$	−1.18993	−	2.60558i	−0.0598718	−	0.131101i
$396$	8.64792	+	2.53926i	0.434574	+	0.127603i
$397$	−2.41494	+	5.28798i	−0.121202	+	0.265396i	−0.960502	−	0.278273i	$-0.910238\pi$
$397$	−2.41494	+	5.28798i	−0.121202	+	0.265396i	0.839300	+	0.543669i	$0.182965\pi$
$398$	−15.7100	+	18.1303i	−0.787471	+	0.908790i
$399$	−2.99435	+	20.8262i	−0.149905	+	1.04261i
$400$	1.82805	−	0.536765i	0.0914027	−	0.0268382i
$401$	−0.621058	−	0.716739i	−0.0310142	−	0.0357922i	0.740031	−	0.672573i	$-0.234811\pi$
$401$	−0.621058	−	0.716739i	−0.0310142	−	0.0357922i	−0.771045	+	0.636781i	$0.780266\pi$
$402$	31.2415	−	20.0777i	1.55819	−	1.00138i
$403$	7.04085	−	4.52488i	0.350730	−	0.225400i
$404$	−0.0657053	−	0.0758280i	−0.00326896	−	0.00377258i
$405$	4.16921	−	1.22419i	0.207170	−	0.0608305i
$406$	1.56310	−	10.8716i	0.0775751	−	0.539547i
$407$	18.3535	−	21.1810i	0.909748	−	1.04990i
$408$	−14.1015	+	30.8779i	−0.698127	+	1.52869i
$409$	−14.1669	−	4.15977i	−0.700507	−	0.205687i	−0.0879626	−	0.996124i	$-0.528036\pi$
$409$	−14.1669	−	4.15977i	−0.700507	−	0.205687i	−0.612544	+	0.790436i	$0.709854\pi$
$410$	−4.32621	−	9.47307i	−0.213656	−	0.467842i
$411$	−5.80888	−	40.4017i	−0.286531	−	1.99287i
$412$	−6.18815	−	3.97688i	−0.304868	−	0.195927i
$413$	1.73975			0.0856075
$414$	21.6106	+	4.38365i	1.06210	+	0.215445i
$415$	−2.94659			−0.144642
$416$	−6.26124	−	4.02385i	−0.306982	−	0.197286i
$417$	0.105054	+	0.730666i	0.00514451	+	0.0357809i
$418$	−10.4887	−	22.9670i	−0.513018	−	1.12335i
$419$	−7.65511	−	2.24774i	−0.373977	−	0.109810i	0.0893424	−	0.996001i	$-0.471523\pi$
$419$	−7.65511	−	2.24774i	−0.373977	−	0.109810i	−0.463319	+	0.886191i	$0.653342\pi$
$420$	−0.841998	+	1.84372i	−0.0410853	+	0.0899642i
$421$	−1.09160	+	1.25977i	−0.0532012	+	0.0613975i	−0.781726	−	0.623622i	$-0.785661\pi$
$421$	−1.09160	+	1.25977i	−0.0532012	+	0.0613975i	0.728525	+	0.685019i	$0.240206\pi$
$422$	−0.841629	+	5.85366i	−0.0409698	+	0.284951i
$423$	18.6323	−	5.47095i	0.905935	−	0.266006i
$424$	4.06933	+	4.69626i	0.197624	+	0.228071i
$425$	3.48017	−	2.23657i	0.168813	−	0.108490i
$426$	34.4905	−	22.1657i	1.67107	−	1.07393i
$427$	8.56548	+	9.88509i	0.414513	+	0.478373i
$428$	−0.755598	+	0.221864i	−0.0365232	+	0.0107242i
$429$	2.02082	−	14.0551i	0.0975659	−	0.678586i
$430$	−0.275472	+	0.317912i	−0.0132845	+	0.0153311i
$431$	−6.90939	+	15.1295i	−0.332814	+	0.728760i	−0.999868	−	0.0162488i	$-0.994828\pi$
$431$	−6.90939	+	15.1295i	−0.332814	+	0.728760i	0.667054	+	0.745009i	$0.267555\pi$
$432$	−5.50370	−	1.61603i	−0.264797	−	0.0777514i
$433$	0.411857	+	0.901842i	0.0197926	+	0.0433398i	0.919270	−	0.393627i	$-0.128780\pi$
$433$	0.411857	+	0.901842i	0.0197926	+	0.0433398i	−0.899478	+	0.436967i	$0.856053\pi$
$434$	−0.717473	−	4.99014i	−0.0344398	−	0.239534i
$435$	22.1455	+	14.2320i	1.06179	+	0.682374i
$436$	−11.4159			−0.546722
$437$	18.5784	+	32.9144i	0.888726	+	1.57451i
$438$	38.9018			1.85880
$439$	5.51411	+	3.54371i	0.263174	+	0.169132i	0.665573	−	0.746333i	$-0.268187\pi$
$439$	5.51411	+	3.54371i	0.263174	+	0.169132i	−0.402399	+	0.915464i	$0.631824\pi$
$440$	−1.25803	−	8.74982i	−0.0599744	−	0.417131i
$441$	1.71471	+	3.75468i	0.0816527	+	0.178794i
$442$	8.17638	+	2.40080i	0.388911	+	0.114195i
$443$	2.56092	−	5.60762i	0.121673	−	0.266426i	−0.838988	−	0.544149i	$-0.816852\pi$
$443$	2.56092	−	5.60762i	0.121673	−	0.266426i	0.960661	+	0.277723i	$0.0895798\pi$
$444$	12.9342	−	14.9268i	0.613829	−	0.708396i
$445$	−1.06004	+	7.37274i	−0.0502507	+	0.349502i
$446$	22.6996	−	6.66522i	1.07486	−	0.315607i
$447$	−4.02832	−	4.64893i	−0.190533	−	0.219887i
$448$	−6.97709	+	4.48390i	−0.329637	+	0.211845i
$449$	13.5080	−	8.68107i	0.637482	−	0.409685i	−0.181591	−	0.983374i	$-0.558125\pi$
$449$	13.5080	−	8.68107i	0.637482	−	0.409685i	0.819073	+	0.573689i	$0.194488\pi$
$450$	3.01098	+	3.47486i	0.141939	+	0.163806i
$451$	−25.8002	+	7.57563i	−1.21488	+	0.356722i
$452$	−0.256727	+	1.78558i	−0.0120754	+	0.0839865i
$453$	12.8739	−	14.8572i	0.604867	−	0.698054i
$454$	4.48801	−	9.82736i	0.210633	−	0.461221i
$455$	1.77434	+	0.520992i	0.0831821	+	0.0244245i
$456$	−26.8639	−	58.8238i	−1.25802	−	2.75468i
$457$	2.62803	+	18.2784i	0.122934	+	0.855025i	0.954204	+	0.299156i	$0.0967052\pi$
$457$	2.62803	+	18.2784i	0.122934	+	0.855025i	−0.831270	+	0.555869i	$0.812386\pi$
$458$	−26.4118	−	16.9738i	−1.23414	−	0.793135i
$459$	−12.4549			−0.581345
$460$	0.823917	+	3.54653i	0.0384153	+	0.165358i
$461$	13.9612			0.650237			0.325118	−	0.945673i	$-0.394596\pi$
$461$	13.9612			0.650237			0.325118	+	0.945673i	$0.394596\pi$
$462$	−7.19550	−	4.62427i	−0.334765	−	0.215140i
$463$	−1.83618	−	12.7709i	−0.0853346	−	0.593515i	−0.986956	−	0.160989i	$-0.948532\pi$
$463$	−1.83618	−	12.7709i	−0.0853346	−	0.593515i	0.901622	−	0.432526i	$-0.142378\pi$
$464$	7.80392	+	17.0882i	0.362288	+	0.793300i
$465$	11.5937	+	3.40420i	0.537643	+	0.157866i
$466$	−3.23876	+	7.09190i	−0.150033	+	0.328526i
$467$	2.90431	−	3.35175i	0.134395	−	0.155101i	−0.684562	−	0.728954i	$-0.740007\pi$
$467$	2.90431	−	3.35175i	0.134395	−	0.155101i	0.818958	+	0.573854i	$0.194552\pi$
$468$	0.824719	−	5.73605i	0.0381226	−	0.265149i
$469$	11.9818	−	3.51816i	0.553267	−	0.162454i
$470$	−3.43177	−	3.96047i	−0.158296	−	0.182683i
$471$	−42.2745	+	27.1682i	−1.94791	+	1.25184i
$472$	−4.49830	+	2.89088i	−0.207051	+	0.133064i
$473$	0.711270	+	0.820850i	0.0327042	+	0.0377427i
$474$	8.17347	−	2.39995i	0.375420	−	0.110233i
$475$	−1.12158	+	7.80073i	−0.0514614	+	0.357922i
$476$	−2.05673	+	2.37359i	−0.0942700	+	0.108793i
$477$	−3.46681	+	7.59125i	−0.158734	+	0.347580i
$478$	21.1140	+	6.19962i	0.965730	+	0.283564i
$479$	1.45190	+	3.17921i	0.0663389	+	0.145262i	0.939897	−	0.341458i	$-0.110921\pi$
$479$	1.45190	+	3.17921i	0.0663389	+	0.145262i	−0.873558	+	0.486720i	$0.838193\pi$
$480$	−1.52920	−	10.6358i	−0.0697981	−	0.485456i
$481$	−15.1594	−	9.74236i	−0.691209	−	0.444213i
$482$	12.0199			0.547489
$483$	11.3228	+	5.97751i	0.515206	+	0.271986i
$484$	2.07101			0.0941366
$485$	3.87803	+	2.49226i	0.176092	+	0.113168i
$486$	3.27085	+	22.7493i	0.148369	+	1.03193i
$487$	−17.2754	−	37.8279i	−0.782823	−	1.71414i	−0.696138	−	0.717908i	$-0.745100\pi$
$487$	−17.2754	−	37.8279i	−0.782823	−	1.71414i	−0.0866859	−	0.996236i	$-0.527628\pi$
$488$	−38.5726	−	11.3259i	−1.74610	−	0.512701i
$489$	12.5389	−	27.4564i	0.567029	−	1.24162i
$490$	0.729458	−	0.841840i	0.0329536	−	0.0380304i
$491$	−2.05781	+	14.3124i	−0.0928676	+	0.645908i	0.889219	+	0.457481i	$0.151248\pi$
$491$	−2.05781	+	14.3124i	−0.0928676	+	0.645908i	−0.982087	+	0.188428i	$0.939661\pi$
$492$	−18.1821	+	5.33874i	−0.819712	+	0.240689i
$493$	26.7120	+	30.8273i	1.20305	+	1.38839i
$494$	−13.6569	+	8.77673i	−0.614451	+	0.394884i
$495$	9.98717	−	6.41837i	0.448890	−	0.288484i
$496$	5.64677	+	6.51672i	0.253547	+	0.292609i
$497$	13.2278	−	3.88404i	0.593350	−	0.174223i
$498$	1.24708	−	8.67366i	0.0558831	−	0.388676i
$499$	−7.51862	+	8.67694i	−0.336579	+	0.388433i	−0.898658	−	0.438651i	$-0.855457\pi$
$499$	−7.51862	+	8.67694i	−0.336579	+	0.388433i	0.562078	+	0.827084i	$0.310002\pi$
$500$	−0.315382	+	0.690589i	−0.0141043	+	0.0308841i
$501$	−28.1364	−	8.26159i	−1.25704	−	0.369101i
$502$	13.1823	+	28.8652i	0.588354	+	1.28832i
$503$	−3.77777	−	26.2750i	−0.168443	−	1.17154i	−0.882105	−	0.471054i	$-0.843874\pi$
$503$	−3.77777	−	26.2750i	−0.168443	−	1.17154i	0.713662	−	0.700490i	$-0.247035\pi$
$504$	−10.6726	−	6.85884i	−0.475394	−	0.305517i
$505$	−0.132159			−0.00588101
$506$	−15.3086	+	1.31159i	−0.680550	+	0.0583071i
$507$	25.5772			1.13593
$508$	−13.5538	−	8.71048i	−0.601351	−	0.386465i
$509$	−4.43689	−	30.8593i	−0.196662	−	1.36781i	−0.813885	−	0.581026i	$-0.802652\pi$
$509$	−4.43689	−	30.8593i	−0.196662	−	1.36781i	0.617223	−	0.786788i	$-0.288257\pi$
$510$	5.11072	+	11.1909i	0.226307	+	0.495542i
$511$	12.5512	+	3.68536i	0.555232	+	0.163031i
$512$	8.05055	−	17.6282i	0.355787	−	0.779066i
$513$	15.5379	−	17.9317i	0.686017	−	0.791706i
$514$	−1.43127	+	9.95469i	−0.0631305	+	0.439082i
$515$	−9.29655	+	2.72971i	−0.409655	+	0.120285i
$516$	0.501251	+	0.578474i	0.0220663	+	0.0254659i
$517$	−11.3829	+	7.31534i	−0.500619	+	0.321728i
$518$	−9.13145	+	5.86842i	−0.401213	+	0.257844i
$519$	22.2329	+	25.6582i	0.975917	+	1.12627i
$520$	−5.45343	+	1.60127i	−0.239149	+	0.0702204i
$521$	−1.61395	+	11.2253i	−0.0707084	+	0.491788i	0.923438	+	0.383747i	$0.125367\pi$
$521$	−1.61395	+	11.2253i	−0.0707084	+	0.491788i	−0.994146	+	0.108040i	$0.965542\pi$
$522$	−29.6887	+	34.2626i	−1.29944	+	1.49964i
$523$	−12.5615	+	27.5059i	−0.549276	+	1.20275i	0.407843	+	0.913052i	$0.366281\pi$
$523$	−12.5615	+	27.5059i	−0.549276	+	1.20275i	−0.957119	+	0.289695i	$0.906446\pi$
$524$	3.32748	+	0.977036i	0.145362	+	0.0426820i
$525$	1.10906	+	2.42851i	0.0484035	+	0.105989i
$526$	−0.389949	−	2.71216i	−0.0170026	−	0.118256i
$527$	15.7509	+	10.1225i	0.686119	+	0.440942i
$528$	14.6295			0.636667
$529$	22.6648	−	3.91240i	0.985426	−	0.170104i
$530$	2.25212			0.0978259
$531$	−6.04118	−	3.88243i	−0.262165	−	0.168483i
$532$	−0.851496	−	5.92229i	−0.0369171	−	0.256764i
$533$	7.18207	+	15.7265i	0.311090	+	0.681192i
$534$	−21.2540	−	6.24073i	−0.919749	−	0.270063i
$535$	−0.430900	+	0.943540i	−0.0186295	+	0.0407928i
$536$	−25.1340	+	29.0062i	−1.08562	+	1.25288i
$537$	−0.351182	+	2.44253i	−0.0151546	+	0.105403i
$538$	−2.37742	+	0.698074i	−0.102498	+	0.0300961i
$539$	−1.88346	−	2.17363i	−0.0811265	−	0.0936250i
$540$	1.92286	−	1.23575i	0.0827466	−	0.0531780i
$541$	2.37074	−	1.52358i	0.101926	−	0.0655039i	−0.488685	−	0.872460i	$-0.662523\pi$
$541$	2.37074	−	1.52358i	0.101926	−	0.0655039i	0.590611	+	0.806956i	$0.298887\pi$
$542$	−8.29528	−	9.57326i	−0.356313	−	0.411207i
$543$	37.7515	−	11.0848i	1.62007	−	0.475696i
$544$	2.36954	−	16.4805i	0.101593	−	0.706595i
$545$	−9.84702	+	11.3641i	−0.421800	+	0.486783i
$546$	−2.28456	+	5.00249i	−0.0977701	+	0.214087i
$547$	−6.10627	−	1.79296i	−0.261085	−	0.0766615i	0.148570	−	0.988902i	$-0.452533\pi$
$547$	−6.10627	−	1.79296i	−0.261085	−	0.0766615i	−0.409655	+	0.912240i	$0.634351\pi$
$548$	4.82174	+	10.5581i	0.205975	+	0.451022i
$549$	−7.68353	−	53.4401i	−0.327925	−	2.28077i
$550$	−2.69517	−	1.73208i	−0.114923	−	0.0738562i
$551$	−77.7074			−3.31045
$552$	−39.2089	+	3.35928i	−1.66884	+	0.142980i
$553$	2.86443			0.121808
$554$	2.75355	+	1.76960i	0.116987	+	0.0751832i
$555$	−3.70242	−	25.7509i	−0.157159	−	1.09307i
$556$	−0.0872015	−	0.190945i	−0.00369817	−	0.00809786i
$557$	−20.9482	−	6.15096i	−0.887606	−	0.260625i	−0.194019	−	0.980998i	$-0.562152\pi$
$557$	−20.9482	−	6.15096i	−0.887606	−	0.260625i	−0.693587	+	0.720373i	$0.743971\pi$
$558$	−8.64461	+	18.9291i	−0.365955	+	0.801331i
$559$	0.457320	−	0.527776i	0.0193426	−	0.0223225i
$560$	−0.271142	+	1.88584i	−0.0114579	+	0.0796911i
$561$	30.4788	−	8.94939i	1.28682	−	0.377844i
$562$	13.1865	+	15.2180i	0.556237	+	0.641932i
$563$	−6.55846	+	4.21487i	−0.276406	+	0.177636i	−0.671498	−	0.741006i	$-0.734349\pi$
$563$	−6.55846	+	4.21487i	−0.276406	+	0.177636i	0.395092	+	0.918641i	$0.370713\pi$
$564$	−8.02183	+	5.15532i	−0.337780	+	0.217078i
$565$	1.55603	+	1.79575i	0.0654625	+	0.0755477i
$566$	15.9328	−	4.67830i	0.669706	−	0.196644i
$567$	−0.618389	+	4.30099i	−0.0259699	+	0.180625i
$568$	−27.7479	+	32.0228i	−1.16428	+	1.34365i
$569$	−0.473784	+	1.03744i	−0.0198620	+	0.0434918i	−0.919303	−	0.393550i	$-0.871247\pi$
$569$	−0.473784	+	1.03744i	−0.0198620	+	0.0434918i	0.899441	+	0.437042i	$0.143974\pi$
$570$	−22.4878	−	6.60301i	−0.941909	−	0.276569i
$571$	1.13666	+	2.48893i	0.0475676	+	0.104158i	0.931924	−	0.362654i	$-0.118129\pi$
$571$	1.13666	+	2.48893i	0.0475676	+	0.104158i	−0.884356	+	0.466813i	$0.845402\pi$
$572$	0.574654	+	3.99681i	0.0240275	+	0.167115i
$573$	18.8600	+	12.1206i	0.787888	+	0.506345i
$574$	10.4142			0.434679
$575$	4.24112	+	2.23896i	0.176867	+	0.0933710i
$576$	34.2338			1.42641
$577$	−21.3708	−	13.7342i	−0.889678	−	0.571762i	0.0140341	−	0.999902i	$-0.495533\pi$
$577$	−21.3708	−	13.7342i	−0.889678	−	0.571762i	−0.903712	+	0.428140i	$0.859169\pi$
$578$	0.0180485	+	0.125530i	0.000750720	+	0.00522137i
$579$	24.8916	+	54.5050i	1.03446	+	2.26515i
$580$	−7.18257	−	2.10899i	−0.298240	−	0.0875711i
$581$	1.22406	−	2.68031i	0.0507824	−	0.111198i
$582$	−8.97757	+	10.3607i	−0.372132	+	0.429464i
$583$	0.827558	−	5.75579i	0.0342739	−	0.238381i
$584$	−38.5762	+	11.3270i	−1.59629	+	0.468714i
$585$	−4.99862	−	5.76872i	−0.206668	−	0.238507i
$586$	−1.78915	+	1.14982i	−0.0739092	+	0.0474985i
$587$	−5.23155	+	3.36211i	−0.215929	+	0.138769i	−0.644135	−	0.764912i	$-0.722782\pi$
$587$	−5.23155	+	3.36211i	−0.215929	+	0.138769i	0.428206	+	0.903681i	$0.359146\pi$
$588$	−1.32733	−	1.53182i	−0.0547380	−	0.0631710i
$589$	−34.2235	+	10.0489i	−1.41015	+	0.414059i
$590$	−0.275797	+	1.91821i	−0.0113544	+	0.0789713i
$591$	39.6814	−	45.7948i	1.63228	−	1.88375i
$592$	7.71241	−	16.8878i	0.316978	−	0.694086i
$593$	8.95210	+	2.62857i	0.367619	+	0.107943i	0.460324	−	0.887751i	$-0.347733\pi$
$593$	8.95210	+	2.62857i	0.367619	+	0.107943i	−0.0927053	+	0.995694i	$0.529551\pi$
$594$	4.00689	+	8.77388i	0.164405	+	0.359996i
$595$	0.588741	+	4.09478i	0.0241360	+	0.167870i
$596$	1.47157	+	0.945722i	0.0602780	+	0.0387383i
$597$	57.4977			2.35322
$598$	2.23550	+	9.62266i	0.0914165	+	0.393500i
$599$	−36.0662			−1.47363			−0.736813	−	0.676096i	$-0.763670\pi$
$599$	−36.0662			−1.47363			−0.736813	+	0.676096i	$0.763670\pi$
$600$	−6.90296	−	4.43627i	−0.281812	−	0.181110i
$601$	−4.50683	−	31.3457i	−0.183837	−	1.27862i	−0.847585	−	0.530660i	$-0.821944\pi$
$601$	−4.50683	−	31.3457i	−0.183837	−	1.27862i	0.663748	−	0.747957i	$-0.268965\pi$
$602$	−0.174748	−	0.382644i	−0.00712218	−	0.0155954i
$603$	−49.4571	−	14.5219i	−2.01405	−	0.591378i
$604$	−2.32232	+	5.08517i	−0.0944938	+	0.206913i
$605$	1.78639	−	2.06160i	0.0726271	−	0.0838161i
$606$	0.0559337	−	0.389028i	0.00227215	−	0.0158032i
$607$	23.1835	−	6.80729i	0.940989	−	0.276299i	0.224958	−	0.974368i	$-0.427775\pi$
$607$	23.1835	−	6.80729i	0.940989	−	0.276299i	0.716030	+	0.698069i	$0.245957\pi$
$608$	20.7714	+	23.9715i	0.842393	+	0.972174i
$609$	−22.1455	+	14.2320i	−0.897381	+	0.576711i
$610$	−12.2569	+	7.87704i	−0.496268	+	0.318932i
$611$	5.69719	+	6.57491i	0.230484	+	0.265992i
$612$	12.4388	−	3.65235i	0.502807	−	0.147638i
$613$	3.57308	−	24.8513i	0.144315	−	1.00374i	−0.780998	−	0.624533i	$-0.785289\pi$
$613$	3.57308	−	24.8513i	0.144315	−	1.00374i	0.925314	−	0.379202i	$-0.123802\pi$
$614$	−9.11364	+	10.5177i	−0.367796	+	0.424460i
$615$	−10.3688	+	22.7046i	−0.418112	+	0.915538i
$616$	8.48172	+	2.49046i	0.341738	+	0.100343i
$617$	−13.1404	−	28.7736i	−0.529014	−	1.15838i	−0.965913	−	0.258869i	$-0.916650\pi$
$617$	−13.1404	−	28.7736i	−0.529014	−	1.15838i	0.436898	−	0.899511i	$-0.356077\pi$
$618$	−4.10068	−	28.5209i	−0.164954	−	1.14728i
$619$	8.26408	+	5.31100i	0.332161	+	0.213467i	0.696081	−	0.717963i	$-0.254925\pi$
$619$	8.26408	+	5.31100i	0.332161	+	0.213467i	−0.363920	+	0.931430i	$0.618562\pi$
$620$	−3.43604			−0.137995
$621$	−7.09735	−	12.5740i	−0.284807	−	0.504577i
$622$	−21.9268			−0.879185
$623$	−6.26613	−	4.02700i	−0.251047	−	0.161338i
$624$	−1.33865	−	9.31049i	−0.0535887	−	0.372718i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	9.76933	+	2.86853i	0.390461	+	0.114650i
$627$	−25.1387	+	55.0461i	−1.00394	+	2.19833i
$628$	9.35794	−	10.7996i	0.373423	−	0.430953i
$629$	5.73700	−	39.9017i	0.228749	−	1.59099i
$630$	−4.41165	+	1.29538i	−0.175764	+	0.0516091i
$631$	−11.0829	−	12.7904i	−0.441204	−	0.509176i	0.490975	−	0.871173i	$-0.336640\pi$
$631$	−11.0829	−	12.7904i	−0.441204	−	0.509176i	−0.932179	+	0.361997i	$0.882095\pi$
$632$	−7.40627	+	4.75972i	−0.294606	+	0.189331i
$633$	11.9240	−	7.66306i	0.473935	−	0.304579i
$634$	−17.2395	−	19.8954i	−0.684668	−	0.790149i
$635$	−20.3620	+	5.97883i	−0.808042	+	0.237263i
$636$	0.583202	−	4.05626i	0.0231255	−	0.160841i
$637$	−1.21100	+	1.39756i	−0.0479814	+	0.0553735i
$638$	13.1228	−	28.7349i	0.519536	−	1.13762i
$639$	−54.6005	−	16.0321i	−2.15996	−	0.634222i
$640$	−0.493904	−	1.08150i	−0.0195233	−	0.0427500i
$641$	5.37994	+	37.4183i	0.212495	+	1.47793i	0.764787	+	0.644284i	$0.222844\pi$
$641$	5.37994	+	37.4183i	0.212495	+	1.47793i	−0.552292	+	0.833651i	$0.686247\pi$
$642$	−2.59506	−	1.66775i	−0.102419	−	0.0658206i
$643$	16.8604			0.664911			0.332456	−	0.943119i	$-0.392123\pi$
$643$	16.8604			0.664911			0.332456	+	0.943119i	$0.392123\pi$
$644$	−3.56831	−	0.723820i	−0.140611	−	0.0285225i
$645$	1.00821			0.0396983
$646$	−30.5514	−	19.6342i	−1.20203	−	0.772496i
$647$	3.15192	+	21.9221i	0.123915	+	0.861846i	0.953053	+	0.302803i	$0.0979223\pi$
$647$	3.15192	+	21.9221i	0.123915	+	0.861846i	−0.829139	+	0.559043i	$0.811169\pi$
$648$	−5.54789	−	12.1482i	−0.217942	−	0.477226i
$649$	4.80106	+	1.40972i	0.188458	+	0.0553363i
$650$	−0.855712	+	1.87375i	−0.0335638	+	0.0734945i
$651$	−7.91275	+	9.13180i	−0.310125	+	0.357904i
$652$	−1.22154	+	8.49599i	−0.0478392	+	0.332729i
$653$	−30.2101	+	8.87047i	−1.18221	+	0.347128i	−0.813026	−	0.582227i	$-0.802181\pi$
$653$	−30.2101	+	8.87047i	−1.18221	+	0.347128i	−0.369185	+	0.929356i	$0.620363\pi$
$654$	−29.2840	−	33.7956i	−1.14510	−	1.32151i
$655$	3.84279	−	2.46961i	0.150150	−	0.0964956i
$656$	−14.9847	+	9.63007i	−0.585053	+	0.375991i
$657$	−35.3590	−	40.8065i	−1.37949	−	1.59201i
$658$	5.02818	−	1.47641i	0.196019	−	0.0575564i
$659$	2.94350	−	20.4725i	0.114662	−	0.797495i	−0.848620	−	0.529003i	$-0.822566\pi$
$659$	2.94350	−	20.4725i	0.114662	−	0.797495i	0.963282	−	0.268491i	$-0.0865250\pi$
$660$	−3.81756	+	4.40570i	−0.148598	+	0.171492i
$661$	0.447134	−	0.979087i	0.0173915	−	0.0380821i	−0.900737	−	0.434365i	$-0.856973\pi$
$661$	0.447134	−	0.979087i	0.0173915	−	0.0380821i	0.918128	+	0.396283i	$0.129700\pi$
$662$	23.4408	+	6.88285i	0.911053	+	0.267509i
$663$	−8.48447	−	18.5784i	−0.329509	−	0.721525i
$664$	1.28885	+	8.96417i	0.0500172	+	0.347877i
$665$	−6.62988	−	4.26076i	−0.257096	−	0.165225i
$666$	44.8044			1.73613
$667$	−15.9004	+	44.5342i	−0.615667	+	1.72437i
$668$	8.33885			0.322640
$669$	−47.7010	−	30.6555i	−1.84423	−	1.18521i
$670$	1.97962	+	13.7685i	0.0764792	+	0.531925i
$671$	15.6276	+	34.2197i	0.603298	+	1.32104i
$672$	10.3099	+	3.02727i	0.397714	+	0.116779i
$673$	−13.9612	+	30.5708i	−0.538166	+	1.17842i	0.423926	+	0.905697i	$0.360651\pi$
$673$	−13.9612	+	30.5708i	−0.538166	+	1.17842i	−0.962093	+	0.272723i	$0.912076\pi$
$674$	11.0076	−	12.7034i	0.423997	−	0.489318i
$675$	0.428466	−	2.98005i	0.0164917	−	0.114702i
$676$	−6.97871	+	2.04913i	−0.268412	+	0.0788128i
$677$	−5.95927	−	6.87737i	−0.229033	−	0.264319i	0.629588	−	0.776929i	$-0.283224\pi$
$677$	−5.95927	−	6.87737i	−0.229033	−	0.264319i	−0.858621	+	0.512611i	$0.828678\pi$
$678$	−5.94457	+	3.82034i	−0.228300	+	0.146719i
$679$	−3.87803	+	2.49226i	−0.148825	+	0.0956440i
$680$	−8.32639	−	9.60917i	−0.319303	−	0.368495i
$681$	−24.8448	+	7.29510i	−0.952056	+	0.279549i
$682$	2.06354	−	14.3523i	0.0790172	−	0.549577i
$683$	25.6498	−	29.6014i	0.981461	−	1.13267i	−0.00969404	−	0.999953i	$-0.503086\pi$
$683$	25.6498	−	29.6014i	0.981461	−	1.13267i	0.991155	−	0.132713i	$-0.0423688\pi$
$684$	−10.2594	+	22.4650i	−0.392278	+	0.858970i
$685$	14.6693	+	4.30730i	0.560485	+	0.164573i
$686$	0.462736	+	1.01325i	0.0176674	+	0.0386861i
$687$	10.7089	+	74.4819i	0.408569	+	2.84166i
$688$	0.605273	+	0.388985i	0.0230758	+	0.0148299i
$689$	−3.73882			−0.142438
$690$	−8.38563	+	11.5367i	−0.319235	+	0.439194i
$691$	−8.33809			−0.317196			−0.158598	−	0.987343i	$-0.550697\pi$
$691$	−8.33809			−0.317196			−0.158598	+	0.987343i	$0.550697\pi$
$692$	−8.12183	−	5.21958i	−0.308746	−	0.198419i
$693$	1.68953	+	11.7509i	0.0641799	+	0.446381i
$694$	−1.25049	−	2.73819i	−0.0474680	−	0.103940i
$695$	−0.265295	−	0.0778977i	−0.0100632	−	0.00295483i
$696$	33.6105	−	73.5967i	1.27400	−	2.78968i
$697$	−25.3277	+	29.2298i	−0.959356	+	1.10716i
$698$	4.47265	−	31.1080i	0.169292	−	1.17745i
$699$	17.9292	−	5.26450i	0.678146	−	0.199122i
$700$	−0.497168	−	0.573762i	−0.0187912	−	0.0216862i
$701$	30.3805	−	19.5243i	1.14745	−	0.737424i	0.178324	−	0.983972i	$-0.442933\pi$
$701$	30.3805	−	19.5243i	1.14745	−	0.737424i	0.969131	+	0.246548i	$0.0792963\pi$
$702$	5.21721	−	3.35290i	0.196911	−	0.126547i
$703$	50.2908	+	58.0387i	1.89675	+	2.18897i
$704$	−22.8874	+	6.72036i	−0.862603	+	0.253283i
$705$	−1.78749	+	12.4322i	−0.0673206	+	0.468225i
$706$	6.25939	−	7.22372i	0.235575	−	0.271868i
$707$	0.0549009	−	0.120216i	0.00206476	−	0.00452120i
$708$	3.38343	+	0.993465i	0.127157	+	0.0373367i
$709$	−18.4157	−	40.3247i	−0.691616	−	1.51443i	−0.849849	−	0.527026i	$-0.823307\pi$
$709$	−18.4157	−	40.3247i	−0.691616	−	1.51443i	0.158234	−	0.987402i	$-0.449420\pi$
$710$	2.18549	+	15.2004i	0.0820200	+	0.570461i
$711$	−9.94656	−	6.39227i	−0.373025	−	0.239729i
$712$	22.8932			0.857959
$713$	−1.24373	+	21.6697i	−0.0465781	+	0.811538i
$714$	−12.3027			−0.460416
$715$	4.47434	+	2.87548i	0.167331	+	0.107537i
$716$	−0.0998647	−	0.694575i	−0.00373212	−	0.0259575i
$717$	−21.9095	−	47.9752i	−0.818226	−	1.79167i
$718$	−18.5797	−	5.45549i	−0.693388	−	0.203597i
$719$	−7.09840	+	15.5433i	−0.264726	+	0.579668i	−0.994585	−	0.103929i	$-0.966858\pi$
$719$	−7.09840	+	15.5433i	−0.264726	+	0.579668i	0.729859	+	0.683598i	$0.239586\pi$
$720$	5.14996	−	5.94337i	0.191928	−	0.221496i
$721$	1.37889	−	9.59040i	0.0513526	−	0.357165i
$722$	46.0750	−	13.5288i	1.71473	−	0.503491i
$723$	−18.8656	−	21.7721i	−0.701620	−	0.809713i
$724$	−9.41237	+	6.04897i	−0.349808	+	0.224808i
$725$	−8.29489	+	5.33080i	−0.308065	+	0.197981i
$726$	5.31254	+	6.13100i	0.197167	+	0.227543i
$727$	−10.5861	+	3.10836i	−0.392617	+	0.115283i	−0.472082	−	0.881555i	$-0.656497\pi$
$727$	−10.5861	+	3.10836i	−0.392617	+	0.115283i	0.0794642	+	0.996838i	$0.474679\pi$
$728$	0.808869	−	5.62581i	0.0299787	−	0.208506i
$729$	27.5365	−	31.7788i	1.01987	−	1.17699i
$730$	−6.05309	+	13.2544i	−0.224035	+	0.490568i
$731$	1.49897	+	0.440138i	0.0554414	+	0.0162791i
$732$	11.0132	+	24.1156i	0.407060	+	0.891336i
$733$	−1.94325	−	13.5156i	−0.0717754	−	0.499209i	−0.993721	−	0.111889i	$-0.964310\pi$
$733$	−1.94325	−	13.5156i	−0.0717754	−	0.499209i	0.921945	−	0.387320i	$-0.126599\pi$
$734$	26.4680	+	17.0100i	0.976953	+	0.627849i
$735$	−2.66977			−0.0984761
$736$	17.9884	−	6.99911i	0.663060	−	0.257991i
$737$	35.9159			1.32298
$738$	−36.1626	−	23.2403i	−1.33116	−	0.855487i
$739$	−2.18631	−	15.2061i	−0.0804249	−	0.559367i	−0.989698	−	0.143168i	$-0.954271\pi$
$739$	−2.18631	−	15.2061i	−0.0804249	−	0.559367i	0.909274	−	0.416199i	$-0.136638\pi$
$740$	3.07325	+	6.72947i	0.112975	+	0.247380i
$741$	37.3327	+	10.9619i	1.37145	+	0.402694i
$742$	−0.935565	+	2.04860i	−0.0343457	+	0.0752065i
$743$	10.4052	−	12.0082i	0.381729	−	0.440539i	−0.532073	−	0.846698i	$-0.678587\pi$
$743$	10.4052	−	12.0082i	0.381729	−	0.440539i	0.913802	+	0.406160i	$0.133132\pi$
$744$	5.28522	−	36.7595i	0.193765	−	1.34767i
$745$	2.21076	−	0.649139i	0.0809961	−	0.0237826i
$746$	−24.6448	−	28.4416i	−0.902309	−	1.04132i
$747$	−10.2318	+	6.57560i	−0.374363	+	0.240589i
$748$	−7.59911	+	4.88365i	−0.277851	+	0.178564i
$749$	−0.679272	−	0.783922i	−0.0248201	−	0.0286439i
$750$	−2.85343	+	0.837844i	−0.104193	+	0.0305937i
$751$	1.90938	−	13.2800i	0.0696742	−	0.484595i	−0.924870	−	0.380283i	$-0.875827\pi$
$751$	1.90938	−	13.2800i	0.0696742	−	0.484595i	0.994545	−	0.104312i	$-0.0332642\pi$
$752$	−5.86967	+	6.77396i	−0.214045	+	0.247021i
$753$	31.5947	−	69.1826i	1.15137	−	2.52116i
$754$	−19.4882	−	5.72224i	−0.709717	−	0.208392i
$755$	3.05892	+	6.69809i	0.111325	+	0.243769i
$756$	0.325290	+	2.26244i	0.0118307	+	0.0822842i
$757$	21.9822	+	14.1271i	0.798955	+	0.513457i	0.875275	−	0.483626i	$-0.160681\pi$
$757$	21.9822	+	14.1271i	0.798955	+	0.513457i	−0.0763195	+	0.997083i	$0.524317\pi$
$758$	25.2064			0.915536
$759$	26.4032	+	25.6706i	0.958374	+	0.931782i
$760$	24.2221			0.878630
$761$	0.214391	+	0.137780i	0.00777165	+	0.00499454i	0.544521	−	0.838747i	$-0.316712\pi$
$761$	0.214391	+	0.137780i	0.00777165	+	0.00499454i	−0.536749	+	0.843742i	$0.680348\pi$
$762$	−8.98164	−	62.4686i	−0.325370	−	2.26300i
$763$	−6.24652	−	13.6780i	−0.226139	−	0.495176i
$764$	−6.11697	−	1.79610i	−0.221304	−	0.0649808i
$765$	7.09355	−	15.5327i	0.256468	−	0.561586i
$766$	−9.99775	+	11.5380i	−0.361234	+	0.416886i
$767$	0.457858	−	3.18448i	0.0165323	−	0.114985i
$768$	−39.0981	+	11.4802i	−1.41083	+	0.414258i
$769$	−2.18591	−	2.52267i	−0.0788258	−	0.0909698i	0.714967	−	0.699159i	$-0.246442\pi$
$769$	−2.18591	−	2.52267i	−0.0788258	−	0.0909698i	−0.793792	+	0.608189i	$0.791896\pi$
$770$	2.69517	−	1.73208i	0.0971273	−	0.0624199i
$771$	20.2778	−	13.0317i	0.730287	−	0.469327i
$772$	−11.1583	−	12.8774i	−0.401597	−	0.463467i
$773$	39.2268	−	11.5180i	1.41089	−	0.414275i	0.514481	−	0.857502i	$-0.327985\pi$
$773$	39.2268	−	11.5180i	1.41089	−	0.414275i	0.896409	+	0.443227i	$0.146166\pi$
$774$	−0.247108	+	1.71867i	−0.00888212	+	0.0617765i
$775$	−2.96383	+	3.42044i	−0.106464	+	0.122866i
$776$	5.88573	−	12.8880i	0.211285	−	0.462650i
$777$	24.9619	+	7.32947i	0.895503	+	0.262943i
$778$	3.58795	+	7.85651i	0.128634	+	0.281669i
$779$	−10.4858	−	72.9304i	−0.375693	−	2.61300i
$780$	3.15319	+	2.02643i	0.112902	+	0.0725578i
$781$	39.6511			1.41883
$782$	−17.5038	+	13.4915i	−0.625934	+	0.482456i
$783$	29.6859			1.06089
$784$	−1.60278	−	1.03004i	−0.0572421	−	0.0367873i
$785$	−2.67872	−	18.6309i	−0.0956077	−	0.664966i
$786$	5.64323	+	12.3569i	0.201287	+	0.440758i
$787$	1.09524	+	0.321590i	0.0390409	+	0.0114635i	0.301195	−	0.953563i	$-0.402615\pi$
$787$	1.09524	+	0.321590i	0.0390409	+	0.0114635i	−0.262154	+	0.965026i	$0.584433\pi$
$788$	−7.15814	+	15.6741i	−0.254998	+	0.558368i
$789$	−4.30061	+	4.96317i	−0.153106	+	0.176694i
$790$	−0.454088	+	3.15825i	−0.0161557	+	0.112366i
$791$	−2.27987	+	0.669429i	−0.0810627	+	0.0238022i
$792$	−23.8945	−	27.5758i	−0.849056	−	0.979862i
$793$	20.3481	−	13.0769i	0.722582	−	0.464375i
$794$	5.44757	−	3.50094i	0.193327	−	0.124244i
$795$	−3.53479	−	4.07936i	−0.125366	−	0.144680i
$796$	−15.6881	+	4.60645i	−0.556051	+	0.163271i
$797$	1.44630	−	10.0592i	0.0512304	−	0.356315i	−0.948041	−	0.318148i	$-0.896939\pi$
$797$	1.44630	−	10.0592i	0.0512304	−	0.356315i	0.999271	−	0.0381670i	$-0.0121519\pi$
$798$	15.3481	−	17.7126i	0.543316	−	0.627020i
$799$	−8.08488	+	17.7034i	−0.286023	+	0.626302i
$800$	3.86172	+	1.13390i	0.136533	+	0.0400896i
$801$	12.7721	+	27.9670i	0.451280	+	0.988165i
$802$	0.150344	+	1.04566i	0.00530882	+	0.0369236i
$803$	31.6503	+	20.3404i	1.11692	+	0.717798i
$804$	25.3109			0.892647
$805$	−3.79845	+	2.92776i	−0.133878	+	0.103190i
$806$	−9.32287			−0.328384
$807$	4.99591	+	3.21067i	0.175864	+	0.113021i
$808$	0.0578072	+	0.402058i	0.00203365	+	0.0141443i
$809$	16.7742	+	36.7303i	0.589748	+	1.29137i	0.935594	+	0.353077i	$0.114865\pi$
$809$	16.7742	+	36.7303i	0.589748	+	1.29137i	−0.345846	+	0.938291i	$0.612408\pi$
$810$	−4.64414	−	1.36364i	−0.163178	−	0.0479135i
$811$	−19.6157	+	42.9523i	−0.688799	+	1.50826i	0.164245	+	0.986420i	$0.447481\pi$
$811$	−19.6157	+	42.9523i	−0.688799	+	1.50826i	−0.853044	+	0.521840i	$0.825246\pi$
$812$	4.90215	−	5.65739i	0.172032	−	0.198535i
$813$	−4.32071	+	30.0512i	−0.151534	+	1.05394i
$814$	−29.9545	+	8.79544i	−1.04991	+	0.308280i
$815$	7.40375	+	8.54439i	0.259342	+	0.299297i
$816$	17.7020	−	11.3764i	0.619694	−	0.398253i
$817$	−2.50370	+	1.60903i	−0.0875935	+	0.0562929i
$818$	10.7704	+	12.4297i	0.376579	+	0.434595i
$819$	7.32392	−	2.15050i	0.255918	−	0.0751444i
$820$	1.01013	−	7.02562i	0.0352753	−	0.245345i
$821$	0.0389532	−	0.0449544i	0.00135948	−	0.00156892i	−0.755069	−	0.655645i	$-0.772397\pi$
$821$	0.0389532	−	0.0449544i	0.00135948	−	0.00156892i	0.756429	+	0.654076i	$0.226942\pi$
$822$	−18.8876	+	41.3580i	−0.658780	+	1.44253i
$823$	31.0960	+	9.13061i	1.08394	+	0.318273i	0.774453	−	0.632631i	$-0.218025\pi$
$823$	31.0960	+	9.13061i	1.08394	+	0.318273i	0.309485	+	0.950904i	$0.399843\pi$
$824$	12.3708	+	27.0882i	0.430956	+	0.943661i
$825$	1.09278	+	7.60045i	0.0380457	+	0.264614i
$826$	−1.63029	−	1.04773i	−0.0567251	−	0.0364550i
$827$	−22.4685			−0.781307			−0.390654	−	0.920538i	$-0.627751\pi$
$827$	−22.4685			−0.781307			−0.390654	+	0.920538i	$0.627751\pi$
$828$	10.7754	+	10.4765i	0.374472	+	0.364082i
$829$	21.1156			0.733375			0.366687	−	0.930344i	$-0.380492\pi$
$829$	21.1156			0.733375			0.366687	+	0.930344i	$0.380492\pi$
$830$	2.76120	+	1.77451i	0.0958426	+	0.0615943i
$831$	−1.11645	−	7.76509i	−0.0387293	−	0.269368i
$832$	6.37124	+	13.9511i	0.220883	+	0.483666i
$833$	−3.96932	−	1.16550i	−0.137529	−	0.0403821i
$834$	0.341583	−	0.747962i	0.0118280	−	0.0258998i
$835$	7.19285	−	8.30100i	0.248919	−	0.287268i
$836$	2.44901	−	17.0333i	0.0847009	−	0.589107i
$837$	13.0741	−	3.83890i	0.451907	−	0.132692i
$838$	5.81983	+	6.71644i	0.201043	+	0.232016i
$839$	−47.4600	+	30.5007i	−1.63850	+	1.05300i	−0.696408	+	0.717646i	$0.745220\pi$
$839$	−47.4600	+	30.5007i	−1.63850	+	1.05300i	−0.942092	+	0.335354i	$0.891144\pi$
$840$	6.90296	−	4.43627i	0.238175	−	0.153066i
$841$	−44.6764	−	51.5593i	−1.54056	−	1.77791i
$842$	1.78159	−	0.523121i	0.0613975	−	0.0180279i
$843$	6.86835	−	47.7704i	0.236559	−	1.64530i
$844$	−2.63950	+	3.04615i	−0.0908554	+	0.104853i
$845$	−3.97980	+	8.71455i	−0.136909	+	0.299790i
$846$	−20.7548	−	6.09416i	−0.713565	−	0.209522i
$847$	1.13321	+	2.48138i	0.0389375	+	0.0852612i
$848$	−0.548198	−	3.81280i	−0.0188252	−	0.130932i
$849$	−33.4812	−	21.5170i	−1.14907	−	0.738463i
$850$	−4.60814			−0.158058
$851$	43.5525	−	16.9459i	1.49296	−	0.580898i
$852$	27.9432			0.957317
$853$	−18.4717	−	11.8711i	−0.632460	−	0.406458i	0.184759	−	0.982784i	$-0.440849\pi$
$853$	−18.4717	−	11.8711i	−0.632460	−	0.406458i	−0.817220	+	0.576326i	$0.804486\pi$
$854$	−2.07350	−	14.4215i	−0.0709538	−	0.493494i
$855$	13.5135	+	29.5905i	0.462152	+	1.01197i
$856$	3.05894	+	0.898185i	0.104552	+	0.0306993i
$857$	−13.8418	+	30.3093i	−0.472827	+	1.03535i	0.511547	+	0.859255i	$0.329072\pi$
$857$	−13.8418	+	30.3093i	−0.472827	+	1.03535i	−0.984374	+	0.176091i	$0.943655\pi$
$858$	−10.3580	+	11.9538i	−0.353617	+	0.408096i
$859$	0.923800	−	6.42517i	0.0315196	−	0.219224i	−0.967974	−	0.251052i	$-0.919224\pi$
$859$	0.923800	−	6.42517i	0.0315196	−	0.219224i	0.999493	+	0.0318276i	$0.0101327\pi$
$860$	−0.275089	+	0.0807735i	−0.00938046	+	0.00275435i
$861$	−16.3455	−	18.8637i	−0.557052	−	0.642872i
$862$	15.5861	−	10.0165i	0.530863	−	0.341165i
$863$	43.4357	−	27.9144i	1.47857	−	0.950218i	0.481285	−	0.876564i	$-0.340170\pi$
$863$	43.4357	−	27.9144i	1.47857	−	0.950218i	0.997284	−	0.0736538i	$-0.0234660\pi$
$864$	−7.93514	−	9.15764i	−0.269959	−	0.311549i
$865$	−12.2015	+	3.58270i	−0.414865	+	0.121815i
$866$	0.157169	−	1.09313i	0.00534082	−	0.0371462i
$867$	0.199051	−	0.229717i	0.00676011	−	0.00780159i
$868$	1.42738	−	3.12553i	0.0484485	−	0.106087i
$869$	7.90475	+	2.32104i	0.268150	+	0.0787361i
$870$	−12.1813	−	26.6732i	−0.412983	−	0.904307i
$871$	−3.28642	−	22.8576i	−0.111356	−	0.774499i
$872$	38.8792	+	24.9861i	1.31661	+	0.846137i
$873$	19.0279			0.643998
$874$	2.41242	−	42.0320i	0.0816013	−	1.42175i
$875$	−1.00000			−0.0338062
$876$	22.3048	+	14.3344i	0.753610	+	0.484316i
$877$	−4.45911	−	31.0138i	−0.150574	−	1.04726i	−0.915261	−	0.402861i	$-0.868016\pi$
$877$	−4.45911	−	31.0138i	−0.150574	−	1.04726i	0.764688	−	0.644401i	$-0.222893\pi$
$878$	−3.03307	−	6.64150i	−0.102361	−	0.224140i
$879$	4.89086	+	1.43609i	0.164965	+	0.0484380i
$880$	−2.27634	+	4.98449i	−0.0767354	+	0.168027i
$881$	−31.6685	+	36.5474i	−1.06694	+	1.23131i	−0.0951478	+	0.995463i	$0.530332\pi$
$881$	−31.6685	+	36.5474i	−1.06694	+	1.23131i	−0.971790	+	0.235848i	$0.924213\pi$
$882$	0.654349	−	4.55110i	0.0220331	−	0.153243i
$883$	4.16680	−	1.22348i	0.140224	−	0.0411734i	−0.210867	−	0.977515i	$-0.567629\pi$
$883$	4.16680	−	1.22348i	0.140224	−	0.0411734i	0.351091	+	0.936341i	$0.385811\pi$
$884$	3.80339	+	4.38935i	0.127922	+	0.147630i
$885$	3.90741	−	2.51114i	0.131346	−	0.0844109i
$886$	−5.77686	+	3.71256i	−0.194077	+	0.124726i
$887$	−13.3848	−	15.4469i	−0.449417	−	0.518655i	0.485156	−	0.874428i	$-0.338763\pi$
$887$	−13.3848	−	15.4469i	−0.449417	−	0.518655i	−0.934572	+	0.355773i	$0.884218\pi$
$888$	−76.7205	+	22.5272i	−2.57457	+	0.755963i
$889$	3.02016	−	21.0056i	0.101293	−	0.704507i
$890$	5.43341	−	6.27049i	0.182128	−	0.210187i
$891$	−5.19161	+	11.3680i	−0.173925	+	0.380844i
$892$	15.4711	+	4.54273i	0.518011	+	0.152102i
$893$	−15.4020	−	33.7258i	−0.515410	−	1.12859i
$894$	0.975162	+	6.78240i	0.0326143	+	0.226837i
$895$	−0.777562	−	0.499709i	−0.0259910	−	0.0167034i
$896$	1.18894			0.0397197
$897$	13.9212	−	19.1524i	0.464817	−	0.639480i
$898$	−17.8861			−0.596867
$899$	−37.5418	−	24.1266i	−1.25209	−	0.804668i
$900$	0.445976	+	3.10183i	0.0148659	+	0.103394i
$901$	−3.47453	−	7.60816i	−0.115753	−	0.253465i
$902$	28.7392	+	8.43859i	0.956911	+	0.280974i
$903$	−0.418827	+	0.917102i	−0.0139377	+	0.0305193i
$904$	4.78245	−	5.51925i	0.159062	−	0.183567i
$905$	−2.09734	+	14.5873i	−0.0697179	+	0.484898i
$906$	−21.0113	+	6.16948i	−0.698054	+	0.204967i
$907$	−19.6348	−	22.6598i	−0.651962	−	0.752405i	0.329480	−	0.944163i	$-0.393127\pi$
$907$	−19.6348	−	22.6598i	−0.651962	−	0.752405i	−0.981442	+	0.191758i	$0.938581\pi$
$908$	6.19442	−	3.98091i	0.205569	−	0.132111i
$909$	−0.458915	+	0.294927i	−0.0152212	+	0.00978210i
$910$	−1.34895	−	1.55677i	−0.0447171	−	0.0516063i
$911$	21.6686	−	6.36247i	0.717912	−	0.210798i	0.0976815	−	0.995218i	$-0.468857\pi$
$911$	21.6686	−	6.36247i	0.717912	−	0.210798i	0.620230	+	0.784420i	$0.287039\pi$
$912$	−5.70493	+	39.6787i	−0.188909	+	1.31389i
$913$	5.54979	−	6.40479i	0.183671	−	0.211968i
$914$	8.54504	−	18.7110i	0.282645	−	0.618905i
$915$	33.5057	+	9.83817i	1.10767	+	0.325240i
$916$	−8.88906	−	19.4643i	−0.293703	−	0.643119i
$917$	0.650084	+	4.52144i	0.0214677	+	0.149311i
$918$	11.6713	+	7.50068i	0.385210	+	0.247559i
$919$	−24.7465			−0.816311			−0.408156	−	0.912912i	$-0.633828\pi$
$919$	−24.7465			−0.816311			−0.408156	+	0.912912i	$0.633828\pi$
$920$	4.95632	−	13.8818i	0.163405	−	0.457668i
$921$	33.3554			1.09910
$922$	−13.0828	−	8.40780i	−0.430859	−	0.276896i
$923$	−3.62820	−	25.2347i	−0.119424	−	0.830610i
$924$	−2.42169	−	5.30277i	−0.0796678	−	0.174448i
$925$	9.34981	+	2.74535i	0.307420	+	0.0902666i
$926$	−5.97034	+	13.0732i	−0.196198	+	0.429613i
$927$	−26.1901	+	30.2249i	−0.860194	+	0.992717i
$928$	−5.64772	+	39.2808i	−0.185396	+	1.28945i
$929$	3.58969	−	1.05403i	0.117774	−	0.0345816i	−0.222314	−	0.974975i	$-0.571361\pi$
$929$	3.58969	−	1.05403i	0.117774	−	0.0345816i	0.340088	+	0.940393i	$0.389543\pi$
$930$	−8.81412	−	10.1720i	−0.289026	−	0.333554i
$931$	6.62988	−	4.26076i	0.217285	−	0.139641i
$932$	−4.47020	+	2.87282i	−0.146426	+	0.0941024i
$933$	34.4150	+	39.7170i	1.12670	+	1.30028i
$934$	−4.74010	+	1.39182i	−0.155101	+	0.0455417i
$935$	−1.69329	+	11.7771i	−0.0553766	+	0.385153i
$936$	−15.3633	+	17.7302i	−0.502165	+	0.579530i
$937$	−7.77116	+	17.0165i	−0.253873	+	0.555904i	−0.993062	−	0.117594i	$-0.962482\pi$
$937$	−7.77116	+	17.0165i	−0.253873	+	0.555904i	0.739189	+	0.673498i	$0.235209\pi$
$938$	−13.3467	−	3.91893i	−0.435784	−	0.127958i
$939$	−10.1374	−	22.1979i	−0.330823	−	0.724401i
$940$	−0.508302	−	3.53532i	−0.0165790	−	0.115309i
$941$	33.0634	+	21.2486i	1.07784	+	0.692684i	0.954057	−	0.299626i	$-0.0968618\pi$
$941$	33.0634	+	21.2486i	1.07784	+	0.692684i	0.123780	+	0.992310i	$0.460498\pi$
$942$	55.9762			1.82380
$943$	−43.9422	−	8.91354i	−1.43095	−	0.290265i
$944$	3.31462			0.107882
$945$	2.53275	+	1.62770i	0.0823905	+	0.0529492i
$946$	−0.172182	−	1.19755i	−0.00559811	−	0.0389357i
$947$	−15.4073	−	33.7373i	−0.500670	−	1.09632i	−0.976251	−	0.216643i	$-0.930489\pi$
$947$	−15.4073	−	33.7373i	−0.500670	−	1.09632i	0.475580	−	0.879672i	$-0.342238\pi$
$948$	5.57069	+	1.63570i	0.180928	+	0.0531251i
$949$	10.0489	−	22.0041i	0.326202	−	0.714283i
$950$	5.74882	−	6.63450i	0.186516	−	0.215251i
$951$	−8.97943	+	62.4533i	−0.291178	+	2.02519i
$952$	12.1997	−	3.58216i	0.395395	−	0.116098i
$953$	−20.1335	−	23.2353i	−0.652189	−	0.752666i	0.329292	−	0.944228i	$-0.393190\pi$
$953$	−20.1335	−	23.2353i	−0.652189	−	0.752666i	−0.981480	+	0.191562i	$0.938645\pi$
$954$	7.82035	−	5.02583i	0.253193	−	0.162717i
$955$	−7.06427	+	4.53993i	−0.228594	+	0.146909i
$956$	9.82153	+	11.3347i	0.317651	+	0.366589i
$957$	−72.6454	+	21.3306i	−2.34829	+	0.689521i
$958$	0.554059	−	3.85356i	0.0179008	−	0.124503i
$959$	−10.0119	+	11.5544i	−0.323301	+	0.373110i
$960$	−9.19823	+	20.1413i	−0.296872	+	0.650058i
$961$	10.0903	+	2.96279i	0.325495	+	0.0955738i
$962$	8.33852	+	18.2588i	0.268845	+	0.588688i
$963$	0.609330	+	4.23798i	0.0196354	+	0.136567i
$964$	6.89174	+	4.42905i	0.221968	+	0.142650i
$965$	−22.4438			−0.722490
$966$	−7.01062	−	12.4203i	−0.225563	−	0.399618i
$967$	2.96069			0.0952094			0.0476047	−	0.998866i	$-0.484841\pi$
$967$	2.96069			0.0952094			0.0476047	+	0.998866i	$0.484841\pi$
$968$	−7.05323	−	4.53284i	−0.226700	−	0.145691i
$969$	12.3873	+	86.1557i	0.397938	+	2.76772i
$970$	−2.13313	−	4.67091i	−0.0684907	−	0.149974i
$971$	20.7995	+	6.10729i	0.667488	+	0.195992i	0.597884	−	0.801582i	$-0.296008\pi$
$971$	20.7995	+	6.10729i	0.667488	+	0.195992i	0.0696040	+	0.997575i	$0.477826\pi$
$972$	−6.50721	+	14.2488i	−0.208719	+	0.457031i
$973$	0.181066	−	0.208961i	0.00580471	−	0.00669899i
$974$	−6.59246	+	45.8516i	−0.211236	+	1.46918i
$975$	4.73708	−	1.39093i	0.151708	−	0.0445454i
$976$	16.3192	+	18.8334i	0.522365	+	0.602841i
$977$	−1.13174	+	0.727328i	−0.0362077	+	0.0232693i	−0.558619	−	0.829424i	$-0.688669\pi$
$977$	−1.13174	+	0.727328i	−0.0362077	+	0.0232693i	0.522412	+	0.852693i	$0.325032\pi$
$978$	−28.2850	+	18.1777i	−0.904454	+	0.581257i
$979$	−14.0291	−	16.1904i	−0.448371	−	0.517448i
$980$	0.728444	−	0.213890i	0.0232693	−	0.00683248i
$981$	−8.83311	+	61.4356i	−0.282019	+	1.96149i
$982$	10.5476	−	12.1726i	0.336589	−	0.388444i
$983$	15.7205	−	34.4231i	0.501407	−	1.09793i	−0.474603	−	0.880200i	$-0.657408\pi$
$983$	15.7205	−	34.4231i	0.501407	−	1.09793i	0.976010	−	0.217728i	$-0.0698644\pi$
$984$	73.6078	+	21.6132i	2.34653	+	0.689004i
$985$	9.42857	+	20.6457i	0.300419	+	0.657826i
$986$	−6.46635	−	44.9745i	−0.205931	−	1.43228i
$987$	−10.5662	−	6.79049i	−0.336326	−	0.216144i
$988$	−11.0644			−0.352004
$989$	0.409833	+	1.76412i	0.0130319	+	0.0560956i
$990$	−13.2241			−0.420291
$991$	51.7190	+	33.2378i	1.64291	+	1.05583i	0.938058	+	0.346477i	$0.112622\pi$
$991$	51.7190	+	33.2378i	1.64291	+	1.05583i	0.704850	+	0.709356i	$0.251014\pi$
$992$	2.59235	+	18.0302i	0.0823072	+	0.572459i
$993$	−24.3241	−	53.2623i	−0.771901	−	1.69023i
$994$	−14.7347	−	4.32649i	−0.467355	−	0.137228i
$995$	−8.94660	+	19.5903i	−0.283626	+	0.621055i
$996$	3.91108	−	4.51363i	0.123927	−	0.143020i
$997$	8.16290	−	56.7742i	0.258522	−	1.79806i	−0.284858	−	0.958570i	$-0.591947\pi$
$997$	8.16290	−	56.7742i	0.258522	−	1.79806i	0.543380	−	0.839487i	$-0.317144\pi$
$998$	12.2711	−	3.60311i	0.388434	−	0.114054i
$999$	−19.2122	−	22.1720i	−0.607846	−	0.701492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.71.5	✓	130
23.12	even	11	inner	805.2.u.d.771.5	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.71.5	✓	130	1.1	even	1	trivial
805.2.u.d.771.5	yes	130	23.12	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.937084 - 0.602227i) q^{2} +(0.379948 + 2.64260i) q^{3} +(-0.315382 - 0.690589i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(1.23540 - 2.70515i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.437406 + 3.04222i) q^{8} +(-3.96049 + 1.16291i) q^{9} +O(q^{10})\)	\(q+(-0.937084 - 0.602227i) q^{2} +(0.379948 + 2.64260i) q^{3} +(-0.315382 - 0.690589i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(1.23540 - 2.70515i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.437406 + 3.04222i) q^{8} +(-3.96049 + 1.16291i) q^{9} +(0.729458 + 0.841840i) q^{10} +(2.41955 - 1.55495i) q^{11} +(1.70512 - 1.09582i) q^{12} +(-1.21100 - 1.39756i) q^{13} +(-1.06879 + 0.313826i) q^{14} +(0.379948 - 2.64260i) q^{15} +(1.24766 - 1.43988i) q^{16} +(1.71853 - 3.76305i) q^{17} +(4.41165 + 1.29538i) q^{18} +(3.27386 + 7.16876i) q^{19} +(0.108045 + 0.751469i) q^{20} +(2.24596 + 1.44339i) q^{21} -3.20376 q^{22} +(4.77833 - 0.409390i) q^{23} -8.20557 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.293154 + 2.03893i) q^{26} +(-1.25069 - 2.73862i) q^{27} +(-0.728444 - 0.213890i) q^{28} +(-4.09606 + 8.96911i) q^{29} +(-1.94749 + 2.24752i) q^{30} +(-0.644101 + 4.47982i) q^{31} +(3.86172 - 1.13390i) q^{32} +(5.02842 + 5.80311i) q^{33} +(-3.87661 + 2.49135i) q^{34} +(-0.841254 + 0.540641i) q^{35} +(2.05216 + 2.36832i) q^{36} +(9.34981 - 2.74535i) q^{37} +(1.24934 - 8.68934i) q^{38} +(3.23309 - 3.73118i) q^{39} +(1.27678 - 2.79576i) q^{40} +(-8.97047 - 2.63397i) q^{41} +(-1.23540 - 2.70515i) q^{42} +(0.0537437 + 0.373796i) q^{43} +(-1.83692 - 1.18051i) q^{44} +4.12769 q^{45} +(-4.72424 - 2.49401i) q^{46} -4.70455 q^{47} +(4.27906 + 2.74999i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.462736 - 1.01325i) q^{50} +(10.5972 + 3.11161i) q^{51} +(-0.583217 + 1.27707i) q^{52} +(1.32400 - 1.52798i) q^{53} +(-0.477274 + 3.31951i) q^{54} +(-2.75962 + 0.810299i) q^{55} +(2.01272 + 2.32280i) q^{56} +(-17.7003 + 11.3753i) q^{57} +(9.23979 - 5.93805i) q^{58} +(1.13929 + 1.31482i) q^{59} +(-1.94478 + 0.571039i) q^{60} +(-1.86146 + 12.9467i) q^{61} +(3.30145 - 3.81007i) q^{62} +(-1.71471 + 3.75468i) q^{63} +(-7.95773 - 2.33660i) q^{64} +(0.768203 + 1.68213i) q^{65} +(-1.21726 - 8.46625i) q^{66} +(10.5052 + 6.75131i) q^{67} -3.14071 q^{68} +(2.89737 + 12.4717i) q^{69} +1.11391 q^{70} +(11.5978 + 7.45342i) q^{71} +(-1.80548 - 12.5574i) q^{72} +(5.43407 + 11.8990i) q^{73} +(-10.4149 - 3.05809i) q^{74} +(-1.10906 + 2.42851i) q^{75} +(3.91815 - 4.52179i) q^{76} +(0.409316 - 2.84685i) q^{77} +(-5.27669 + 1.54938i) q^{78} +(1.87580 + 2.16479i) q^{79} +(-1.60278 + 1.03004i) q^{80} +(-3.65543 + 2.34920i) q^{81} +(6.81984 + 7.87051i) q^{82} +(2.82723 - 0.830149i) q^{83} +(0.288456 - 2.00625i) q^{84} +(-2.70909 + 3.12645i) q^{85} +(0.174748 - 0.382644i) q^{86} +(-25.2581 - 7.41644i) q^{87} +(3.67218 + 8.04096i) q^{88} +(-1.06004 - 7.37274i) q^{89} +(-3.86800 - 2.48581i) q^{90} -1.84924 q^{91} +(-1.78972 - 3.17075i) q^{92} -12.0831 q^{93} +(4.40855 + 2.83321i) q^{94} +(-1.12158 - 7.80073i) q^{95} +(4.46371 + 9.77416i) q^{96} +(-4.42309 - 1.29874i) q^{97} +(-0.462736 + 1.01325i) q^{98} +(-7.77436 + 8.97209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

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