LMFDB - Embedded newform 322.2.i.d.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	322.29
Dual form			322.2.i.d.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.195887 - 0.0575176i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.56656 + 1.00676i) q^{5} +(-0.133694 + 0.154291i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.48870 - 1.59939i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.195887 - 0.0575176i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.56656 + 1.00676i) q^{5} +(-0.133694 + 0.154291i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.48870 - 1.59939i) q^{9} +(0.265014 + 1.84322i) q^{10} +(-2.33445 - 5.11174i) q^{11} +(0.0848097 + 0.185707i) q^{12} +(-0.665208 - 4.62662i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(0.364774 - 0.107107i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(2.86765 - 3.30944i) q^{17} +(-2.48870 + 1.59939i) q^{18} +(3.79419 + 4.37873i) q^{19} +(1.78674 + 0.524634i) q^{20} +(-0.0848097 + 0.185707i) q^{21} -5.61956 q^{22} +(-4.17877 + 2.35328i) q^{23} +0.204157 q^{24} +(-0.636551 + 1.39385i) q^{25} +(-4.48486 - 1.31687i) q^{26} +(0.796593 + 0.919317i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-0.269649 + 0.311192i) q^{29} +(0.0541044 - 0.376305i) q^{30} +(0.252528 - 0.0741489i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.163274 + 1.13559i) q^{33} +(-1.81911 - 3.98330i) q^{34} +(0.773573 + 1.69389i) q^{35} +(0.421013 + 2.92821i) q^{36} +(7.85944 + 5.05095i) q^{37} +(5.55920 - 1.63233i) q^{38} +(-0.135807 + 0.944555i) q^{39} +(1.21946 - 1.40733i) q^{40} +(4.44678 - 2.85777i) q^{41} +(0.133694 + 0.154291i) q^{42} +(-6.06085 - 1.77963i) q^{43} +(-2.33445 + 5.11174i) q^{44} +5.50889 q^{45} +(0.404696 + 4.77873i) q^{46} +0.945275 q^{47} +(0.0848097 - 0.185707i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(1.00346 + 1.15805i) q^{50} +(-0.752086 + 0.483336i) q^{51} +(-3.06095 + 3.53252i) q^{52} +(0.751725 - 5.22836i) q^{53} +(1.16716 - 0.342708i) q^{54} +(8.80337 + 5.65758i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-0.491378 - 1.07597i) q^{57} +(0.171054 + 0.374555i) q^{58} +(-1.34939 - 9.38523i) q^{59} +(-0.319823 - 0.205538i) q^{60} +(-4.55760 + 1.33823i) q^{61} +(0.0374557 - 0.260510i) q^{62} +(-1.93729 + 2.23575i) q^{63} +(0.841254 - 0.540641i) q^{64} +(5.70000 + 6.57816i) q^{65} +(1.10080 + 0.323224i) q^{66} +(5.30094 - 11.6074i) q^{67} -4.37902 q^{68} +(0.953920 - 0.220624i) q^{69} +1.86217 q^{70} +(-3.10738 + 6.80422i) q^{71} +(2.83849 + 0.833455i) q^{72} +(7.28226 + 8.40417i) q^{73} +(7.85944 - 5.05095i) q^{74} +(0.204863 - 0.236424i) q^{75} +(0.824557 - 5.73492i) q^{76} +(-5.39193 + 1.58321i) q^{77} +(0.802782 + 0.515916i) q^{78} +(-1.93891 - 13.4854i) q^{79} +(-0.773573 - 1.69389i) q^{80} +(3.58363 + 7.84705i) q^{81} +(-0.752262 - 5.23210i) q^{82} +(-9.76304 - 6.27433i) q^{83} +(0.195887 - 0.0575176i) q^{84} +(-1.16050 + 8.07148i) q^{85} +(-4.13658 + 4.77386i) q^{86} +(0.0707198 - 0.0454488i) q^{87} +(3.68003 + 4.24698i) q^{88} +(4.75641 + 1.39661i) q^{89} +(2.28848 - 5.01107i) q^{90} -4.67420 q^{91} +(4.51500 + 1.61703i) q^{92} -0.0537318 q^{93} +(0.392682 - 0.859853i) q^{94} +(-10.3522 - 3.03967i) q^{95} +(-0.133694 - 0.154291i) q^{96} +(14.1786 - 9.11202i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-2.36591 + 16.4553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−0.195887	−	0.0575176i	−0.113095	−	0.0332078i	0.224695	−	0.974429i	$-0.427861\pi$
$3$	−0.195887	−	0.0575176i	−0.113095	−	0.0332078i	−0.337791	+	0.941221i	$0.609680\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−1.56656	+	1.00676i	−0.700585	+	0.450239i	−0.841835	−	0.539735i	$-0.818524\pi$
$5$	−1.56656	+	1.00676i	−0.700585	+	0.450239i	0.141249	+	0.989974i	$0.454888\pi$
$6$	−0.133694	+	0.154291i	−0.0545804	+	0.0629892i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−2.48870	−	1.59939i	−0.829566	−	0.533130i
$10$	0.265014	+	1.84322i	0.0838049	+	0.582876i
$11$	−2.33445	−	5.11174i	−0.703864	−	1.54125i	−0.835223	−	0.549912i	$-0.814661\pi$
$11$	−2.33445	−	5.11174i	−0.703864	−	1.54125i	0.131359	−	0.991335i	$-0.458066\pi$
$12$	0.0848097	+	0.185707i	0.0244825	+	0.0536091i
$13$	−0.665208	−	4.62662i	−0.184495	−	1.28319i	−0.845972	−	0.533228i	$-0.820979\pi$
$13$	−0.665208	−	4.62662i	−0.184495	−	1.28319i	0.661476	−	0.749966i	$-0.269930\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	0.364774	−	0.107107i	0.0941844	−	0.0276550i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	2.86765	−	3.30944i	0.695507	−	0.802658i	−0.292631	−	0.956225i	$-0.594531\pi$
$17$	2.86765	−	3.30944i	0.695507	−	0.802658i	0.988138	+	0.153567i	$0.0490762\pi$
$18$	−2.48870	+	1.59939i	−0.586592	+	0.376980i
$19$	3.79419	+	4.37873i	0.870447	+	1.00455i	0.999916	+	0.0129661i	$0.00412737\pi$
$19$	3.79419	+	4.37873i	0.870447	+	1.00455i	−0.129469	+	0.991584i	$0.541327\pi$
$20$	1.78674	+	0.524634i	0.399527	+	0.117312i
$21$	−0.0848097	+	0.185707i	−0.0185070	+	0.0405247i
$22$	−5.61956			−1.19810
$23$	−4.17877	+	2.35328i	−0.871333	+	0.490693i
$23$	−4.17877	+	2.35328i	−0.871333	+	0.490693i
$24$	0.204157			0.0416733
$25$	−0.636551	+	1.39385i	−0.127310	+	0.278770i
$26$	−4.48486	−	1.31687i	−0.879553	−	0.258260i
$27$	0.796593	+	0.919317i	0.153304	+	0.176923i
$28$	−0.841254	+	0.540641i	−0.158982	+	0.102172i
$29$	−0.269649	+	0.311192i	−0.0500726	+	0.0577869i	−0.780233	−	0.625489i	$-0.784900\pi$
$29$	−0.269649	+	0.311192i	−0.0500726	+	0.0577869i	0.730161	+	0.683275i	$0.239445\pi$
$30$	0.0541044	−	0.376305i	0.00987807	−	0.0687035i
$31$	0.252528	−	0.0741489i	0.0453554	−	0.0133175i	−0.258976	−	0.965884i	$-0.583385\pi$
$31$	0.252528	−	0.0741489i	0.0453554	−	0.0133175i	0.304332	+	0.952566i	$0.401567\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	0.163274	+	1.13559i	0.0284223	+	0.197682i
$34$	−1.81911	−	3.98330i	−0.311975	−	0.683130i
$35$	0.773573	+	1.69389i	0.130758	+	0.286319i
$36$	0.421013	+	2.92821i	0.0701688	+	0.488035i
$37$	7.85944	+	5.05095i	1.29208	+	0.830372i	0.992327	−	0.123644i	$-0.0394580\pi$
$37$	7.85944	+	5.05095i	1.29208	+	0.830372i	0.299757	+	0.954016i	$0.403094\pi$
$38$	5.55920	−	1.63233i	0.901821	−	0.264799i
$39$	−0.135807	+	0.944555i	−0.0217465	+	0.151250i
$40$	1.21946	−	1.40733i	0.192814	−	0.222519i
$41$	4.44678	−	2.85777i	0.694471	−	0.446309i	−0.145202	−	0.989402i	$-0.546383\pi$
$41$	4.44678	−	2.85777i	0.694471	−	0.446309i	0.839673	+	0.543093i	$0.182747\pi$
$42$	0.133694	+	0.154291i	0.0206295	+	0.0238077i
$43$	−6.06085	−	1.77963i	−0.924271	−	0.271391i	−0.215235	−	0.976562i	$-0.569052\pi$
$43$	−6.06085	−	1.77963i	−0.924271	−	0.271391i	−0.709037	+	0.705172i	$0.750870\pi$
$44$	−2.33445	+	5.11174i	−0.351932	+	0.770623i
$45$	5.50889			0.821217
$46$	0.404696	+	4.77873i	0.0596692	+	0.704585i
$47$	0.945275			0.137883			0.0689413	−	0.997621i	$-0.478038\pi$
$47$	0.945275			0.137883			0.0689413	+	0.997621i	$0.478038\pi$
$48$	0.0848097	−	0.185707i	0.0122412	−	0.0268046i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	1.00346	+	1.15805i	0.141911	+	0.163774i
$51$	−0.752086	+	0.483336i	−0.105313	+	0.0676806i
$52$	−3.06095	+	3.53252i	−0.424477	+	0.489873i
$53$	0.751725	−	5.22836i	0.103257	−	0.718171i	−0.870762	−	0.491705i	$-0.836374\pi$
$53$	0.751725	−	5.22836i	0.103257	−	0.718171i	0.974019	−	0.226466i	$-0.0727171\pi$
$54$	1.16716	−	0.342708i	0.158830	−	0.0466367i
$55$	8.80337	+	5.65758i	1.18705	+	0.762868i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	−0.491378	−	1.07597i	−0.0650846	−	0.142515i
$58$	0.171054	+	0.374555i	0.0224605	+	0.0491815i
$59$	−1.34939	−	9.38523i	−0.175676	−	1.22185i	−0.866629	−	0.498953i	$-0.833718\pi$
$59$	−1.34939	−	9.38523i	−0.175676	−	1.22185i	0.690953	−	0.722900i	$-0.257191\pi$
$60$	−0.319823	−	0.205538i	−0.0412890	−	0.0265348i
$61$	−4.55760	+	1.33823i	−0.583541	+	0.171343i	−0.560161	−	0.828383i	$-0.689261\pi$
$61$	−4.55760	+	1.33823i	−0.583541	+	0.171343i	−0.0233799	+	0.999727i	$0.507443\pi$
$62$	0.0374557	−	0.260510i	0.00475688	−	0.0330848i
$63$	−1.93729	+	2.23575i	−0.244075	+	0.281678i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	5.70000	+	6.57816i	0.706999	+	0.815920i
$66$	1.10080	+	0.323224i	0.135499	+	0.0397861i
$67$	5.30094	−	11.6074i	0.647613	−	1.41807i	−0.246015	−	0.969266i	$-0.579121\pi$
$67$	5.30094	−	11.6074i	0.647613	−	1.41807i	0.893628	−	0.448808i	$-0.148151\pi$
$68$	−4.37902			−0.531034
$69$	0.953920	−	0.220624i	0.114838	−	0.0265600i
$70$	1.86217			0.222572
$71$	−3.10738	+	6.80422i	−0.368779	+	0.807513i	0.630725	+	0.776007i	$0.282758\pi$
$71$	−3.10738	+	6.80422i	−0.368779	+	0.807513i	−0.999504	+	0.0315061i	$0.989970\pi$
$72$	2.83849	+	0.833455i	0.334519	+	0.0982236i
$73$	7.28226	+	8.40417i	0.852324	+	0.983634i	0.999985	−	0.00540371i	$-0.00172006\pi$
$73$	7.28226	+	8.40417i	0.852324	+	0.983634i	−0.147661	+	0.989038i	$0.547175\pi$
$74$	7.85944	−	5.05095i	0.913641	−	0.587162i
$75$	0.204863	−	0.236424i	0.0236555	−	0.0272999i
$76$	0.824557	−	5.73492i	0.0945831	−	0.657840i
$77$	−5.39193	+	1.58321i	−0.614468	+	0.180424i
$78$	0.802782	+	0.515916i	0.0908971	+	0.0584160i
$79$	−1.93891	−	13.4854i	−0.218144	−	1.51723i	−0.744880	−	0.667198i	$-0.767493\pi$
$79$	−1.93891	−	13.4854i	−0.218144	−	1.51723i	0.526736	−	0.850029i	$-0.323416\pi$
$80$	−0.773573	−	1.69389i	−0.0864881	−	0.189383i
$81$	3.58363	+	7.84705i	0.398181	+	0.871894i
$82$	−0.752262	−	5.23210i	−0.0830735	−	0.577789i
$83$	−9.76304	−	6.27433i	−1.07163	−	0.688697i	−0.119023	−	0.992891i	$-0.537976\pi$
$83$	−9.76304	−	6.27433i	−1.07163	−	0.688697i	−0.952610	+	0.304195i	$0.901613\pi$
$84$	0.195887	−	0.0575176i	0.0213730	−	0.00627568i
$85$	−1.16050	+	8.07148i	−0.125874	+	0.875475i
$86$	−4.13658	+	4.77386i	−0.446058	+	0.514779i
$87$	0.0707198	−	0.0454488i	0.00758195	−	0.00487263i
$88$	3.68003	+	4.24698i	0.392293	+	0.452730i
$89$	4.75641	+	1.39661i	0.504179	+	0.148040i	0.523924	−	0.851765i	$-0.324467\pi$
$89$	4.75641	+	1.39661i	0.504179	+	0.148040i	−0.0197456	+	0.999805i	$0.506286\pi$
$90$	2.28848	−	5.01107i	0.241227	−	0.528213i
$91$	−4.67420			−0.489989
$92$	4.51500	+	1.61703i	0.470721	+	0.168587i
$93$	−0.0537318			−0.00557173
$94$	0.392682	−	0.859853i	0.0405020	−	0.0886870i
$95$	−10.3522	−	3.03967i	−1.06211	−	0.311864i
$96$	−0.133694	−	0.154291i	−0.0136451	−	0.0157473i
$97$	14.1786	−	9.11202i	1.43962	−	0.925186i	0.439987	−	0.898004i	$-0.354983\pi$
$97$	14.1786	−	9.11202i	1.43962	−	0.925186i	0.999631	−	0.0271816i	$-0.00865322\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	−2.36591	+	16.4553i	−0.237783	+	1.65382i
$100$	1.47026	−	0.431706i	0.147026	−	0.0431706i
$101$	3.16166	+	2.03187i	0.314597	+	0.202179i	0.688404	−	0.725327i	$-0.258312\pi$
$101$	3.16166	+	2.03187i	0.314597	+	0.202179i	−0.373808	+	0.927506i	$0.621948\pi$
$102$	0.127230	+	0.884907i	0.0125977	+	0.0876188i
$103$	6.88689	+	15.0802i	0.678585	+	1.48589i	0.864135	+	0.503260i	$0.167866\pi$
$103$	6.88689	+	15.0802i	0.678585	+	1.48589i	−0.185550	+	0.982635i	$0.559407\pi$
$104$	1.94173	+	4.25180i	0.190402	+	0.416923i
$105$	−0.0541044	−	0.376305i	−0.00528005	−	0.0367236i
$106$	−4.44361	−	2.85573i	−0.431601	−	0.277373i
$107$	−6.81280	+	2.00042i	−0.658618	+	0.193388i	−0.593929	−	0.804518i	$-0.702424\pi$
$107$	−6.81280	+	2.00042i	−0.658618	+	0.193388i	−0.0646894	+	0.997905i	$0.520606\pi$
$108$	0.173116	−	1.20405i	0.0166581	−	0.115860i
$109$	7.89944	−	9.11644i	0.756629	−	0.873196i	−0.238564	−	0.971127i	$-0.576677\pi$
$109$	7.89944	−	9.11644i	0.756629	−	0.873196i	0.995193	+	0.0979304i	$0.0312223\pi$
$110$	8.80337	−	5.65758i	0.839368	−	0.539429i
$111$	−1.24904	−	1.44147i	−0.118554	−	0.136818i
$112$	0.959493	+	0.281733i	0.0906636	+	0.0266212i
$113$	2.80742	−	6.14739i	0.264100	−	0.578298i	−0.730402	−	0.683018i	$-0.760667\pi$
$113$	2.80742	−	6.14739i	0.264100	−	0.578298i	0.994502	+	0.104719i	$0.0333945\pi$
$114$	−1.18286			−0.110785
$115$	4.17707	−	7.89358i	0.389514	−	0.736080i
$116$	0.411766			0.0382315
$117$	−5.74426	+	12.5782i	−0.531057	+	1.16285i
$118$	−9.09766	−	2.67131i	−0.837508	−	0.245914i
$119$	−2.86765	−	3.30944i	−0.262877	−	0.303376i
$120$	−0.319823	+	0.205538i	−0.0291957	+	0.0187629i
$121$	−13.4767	+	15.5530i	−1.22516	+	1.41391i
$122$	−0.675997	+	4.70166i	−0.0612019	+	0.425669i
$123$	−1.03544	+	0.304032i	−0.0933624	+	0.0274137i
$124$	−0.221409	−	0.142291i	−0.0198831	−	0.0127781i
$125$	−1.73116	−	12.0405i	−0.154840	−	1.07693i
$126$	1.22893	+	2.69098i	0.109482	+	0.239732i
$127$	−4.27130	−	9.35285i	−0.379017	−	0.829932i	−0.998974	−	0.0452954i	$-0.985577\pi$
$127$	−4.27130	−	9.35285i	−0.379017	−	0.829932i	0.619957	−	0.784636i	$-0.287150\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	1.08488	+	0.697211i	0.0955185	+	0.0613860i
$130$	8.35157	−	2.45224i	0.732481	−	0.215076i
$131$	0.909435	−	6.32526i	0.0794577	−	0.552641i	−0.910741	−	0.412977i	$-0.864489\pi$
$131$	0.909435	−	6.32526i	0.0794577	−	0.552641i	0.990199	−	0.139663i	$-0.0446020\pi$
$132$	0.751303	−	0.867050i	0.0653925	−	0.0754670i
$133$	4.87413	−	3.13241i	0.422641	−	0.271615i
$134$	−8.35641	−	9.64381i	−0.721884	−	0.833098i
$135$	−2.17344	−	0.638180i	−0.187060	−	0.0549258i
$136$	−1.81911	+	3.98330i	−0.155988	+	0.341565i
$137$	−1.02164			−0.0872846			−0.0436423	−	0.999047i	$-0.513896\pi$
$137$	−1.02164			−0.0872846			−0.0436423	+	0.999047i	$0.513896\pi$
$138$	0.195586	−	0.959367i	0.0166494	−	0.0816667i
$139$	5.53847			0.469767			0.234883	−	0.972024i	$-0.424529\pi$
$139$	5.53847			0.469767			0.234883	+	0.972024i	$0.424529\pi$
$140$	0.773573	−	1.69389i	0.0653789	−	0.143160i
$141$	−0.185167	−	0.0543699i	−0.0155939	−	0.00457878i
$142$	4.89848	+	5.65315i	0.411072	+	0.474402i
$143$	−22.0972	+	14.2010i	−1.84786	+	1.18755i
$144$	1.93729	−	2.23575i	0.161441	−	0.186312i
$145$	0.109124	−	0.758973i	0.00906225	−	0.0630293i
$146$	10.6699	−	3.13296i	0.883044	−	0.259285i
$147$	0.171747	+	0.110375i	0.0141655	+	0.00910361i
$148$	−1.32958	−	9.24744i	−0.109291	−	0.760135i
$149$	−7.39709	−	16.1974i	−0.605993	−	1.32694i	−0.925281	−	0.379282i	$-0.876171\pi$
$149$	−7.39709	−	16.1974i	−0.605993	−	1.32694i	0.319288	−	0.947658i	$-0.396556\pi$
$150$	−0.129956	−	0.284564i	−0.0106109	−	0.0232346i
$151$	1.04606	+	7.27551i	0.0851272	+	0.592072i	0.987079	+	0.160235i	$0.0512253\pi$
$151$	1.04606	+	7.27551i	0.0851272	+	0.592072i	−0.901952	+	0.431837i	$0.857866\pi$
$152$	−4.87413	−	3.13241i	−0.395344	−	0.254072i
$153$	−12.4298	+	3.64972i	−1.00489	+	0.295062i
$154$	−0.799747	+	5.56237i	−0.0644455	+	0.448228i
$155$	−0.320949	+	0.370395i	−0.0257792	+	0.0297508i
$156$	0.802782	−	0.515916i	0.0642740	−	0.0413064i
$157$	3.76199	+	4.34157i	0.300239	+	0.346495i	0.885744	−	0.464174i	$-0.153649\pi$
$157$	3.76199	+	4.34157i	0.300239	+	0.346495i	−0.585504	+	0.810669i	$0.699103\pi$
$158$	−13.0722	−	3.83835i	−1.03997	−	0.305362i
$159$	−0.447976	+	0.980930i	−0.0355268	+	0.0777928i
$160$	−1.86217			−0.147217
$161$	1.73463	+	4.47114i	0.136708	+	0.352375i
$162$	8.62662			0.677771
$163$	−2.90333	+	6.35740i	−0.227406	+	0.497950i	−0.988598	−	0.150576i	$-0.951887\pi$
$163$	−2.90333	+	6.35740i	−0.227406	+	0.497950i	0.761192	+	0.648526i	$0.224614\pi$
$164$	−5.07179	−	1.48921i	−0.396040	−	0.116288i
$165$	−1.39905	−	1.61459i	−0.108916	−	0.125696i
$166$	−9.76304	+	6.27433i	−0.757759	+	0.486982i
$167$	−10.7802	+	12.4410i	−0.834195	+	0.962713i	−0.999724	−	0.0234924i	$-0.992521\pi$
$167$	−10.7802	+	12.4410i	−0.834195	+	0.962713i	0.165529	+	0.986205i	$0.447067\pi$
$168$	0.0290545	−	0.202079i	0.00224160	−	0.0155907i
$169$	−8.48971	+	2.49280i	−0.653055	+	0.191754i
$170$	6.85999	+	4.40864i	0.526137	+	0.338128i
$171$	−2.43930	−	16.9657i	−0.186538	−	1.29740i
$172$	2.62406	+	5.74590i	0.200083	+	0.438120i
$173$	−0.0660115	−	0.144545i	−0.00501876	−	0.0109895i	0.907106	−	0.420902i	$-0.138286\pi$
$173$	−0.0660115	−	0.144545i	−0.00501876	−	0.0109895i	−0.912125	+	0.409913i	$0.865559\pi$
$174$	−0.0119637	−	0.0832091i	−0.000906963	−	0.00630806i
$175$	1.28907	+	0.828438i	0.0974448	+	0.0626240i
$176$	5.39193	−	1.58321i	0.406432	−	0.119339i
$177$	−0.275487	+	1.91606i	−0.0207069	+	0.144020i
$178$	3.24629	−	3.74641i	0.243319	−	0.280806i
$179$	1.27888	−	0.821887i	0.0955880	−	0.0614307i	−0.491974	−	0.870610i	$-0.663724\pi$
$179$	1.27888	−	0.821887i	0.0955880	−	0.0614307i	0.587562	+	0.809179i	$0.300088\pi$
$180$	−3.60756	−	4.16334i	−0.268891	−	0.310317i
$181$	24.7693	+	7.27291i	1.84108	+	0.540591i	1.00000		0.000312548i	$-9.94873e-5\pi$
$181$	24.7693	+	7.27291i	1.84108	+	0.540591i	0.841085	+	0.540904i	$0.181918\pi$
$182$	−1.94173	+	4.25180i	−0.143931	+	0.315164i
$183$	0.969747			0.0716857
$184$	3.34650	−	3.43525i	0.246707	−	0.253250i
$185$	−17.3974			−1.27908
$186$	−0.0223210	+	0.0488762i	−0.00163665	+	0.00358377i
$187$	−23.6114	−	6.93293i	−1.72664	−	0.506986i
$188$	−0.619024	−	0.714391i	−0.0451469	−	0.0521024i
$189$	1.02333	−	0.657652i	0.0744360	−	0.0478371i
$190$	−7.06543	+	8.15394i	−0.512580	+	0.591549i
$191$	0.487170	−	3.38834i	0.0352504	−	0.245172i	−0.964576	−	0.263805i	$-0.915022\pi$
$191$	0.487170	−	3.38834i	0.0352504	−	0.245172i	0.999826	+	0.0186333i	$0.00593152\pi$
$192$	−0.195887	+	0.0575176i	−0.0141369	+	0.00415097i
$193$	−6.75310	−	4.33995i	−0.486098	−	0.312396i	0.274536	−	0.961577i	$-0.411476\pi$
$193$	−6.75310	−	4.33995i	−0.486098	−	0.312396i	−0.760635	+	0.649180i	$0.775112\pi$
$194$	−2.39859	−	16.6826i	−0.172209	−	1.19774i
$195$	−0.738196	−	1.61642i	−0.0528633	−	0.115755i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	3.14382	+	21.8658i	0.223988	+	1.55787i	0.722736	+	0.691124i	$0.242884\pi$
$197$	3.14382	+	21.8658i	0.223988	+	1.55787i	−0.498748	+	0.866747i	$0.666207\pi$
$198$	13.9854	+	8.98787i	0.993899	+	0.638740i
$199$	0.414096	−	0.121590i	0.0293545	−	0.00861925i	−0.267022	−	0.963690i	$-0.586040\pi$
$199$	0.414096	−	0.121590i	0.0293545	−	0.00861925i	0.296377	+	0.955071i	$0.404222\pi$
$200$	0.218073	−	1.51673i	0.0154201	−	0.107249i
$201$	−1.70602	+	1.96885i	−0.120333	+	0.138872i
$202$	3.16166	−	2.03187i	0.222453	−	0.142962i
$203$	0.269649	+	0.311192i	0.0189257	+	0.0218414i
$204$	0.857793	+	0.251871i	0.0600575	+	0.0176345i
$205$	−4.08903	+	8.95373i	−0.285590	+	0.625356i
$206$	16.5783			1.15507
$207$	14.1635	+	0.826871i	0.984431	+	0.0574715i
$208$	4.67420			0.324097
$209$	13.5256	−	29.6168i	0.935582	−	2.04864i
$210$	−0.364774	−	0.107107i	−0.0251718	−	0.00739112i
$211$	−8.67161	−	10.0076i	−0.596979	−	0.688950i	0.374188	−	0.927353i	$-0.377922\pi$
$211$	−8.67161	−	10.0076i	−0.596979	−	0.688950i	−0.971166	+	0.238403i	$0.923376\pi$
$212$	−4.44361	+	2.85573i	−0.305188	+	0.196133i
$213$	1.00006	−	1.15413i	0.0685228	−	0.0790796i
$214$	−1.01049	+	7.02814i	−0.0690760	+	0.480434i
$215$	11.2863	−	3.31397i	0.769722	−	0.226011i
$216$	−1.02333	−	0.657652i	−0.0696285	−	0.0447475i
$217$	−0.0374557	−	0.260510i	−0.00254266	−	0.0176846i
$218$	−5.01106	−	10.9727i	−0.339392	−	0.743164i
$219$	−0.943111	−	2.06513i	−0.0637295	−	0.139548i
$220$	−1.48927	−	10.3581i	−0.100406	−	0.698341i
$221$	−17.2191	−	11.0661i	−1.15828	−	0.744384i
$222$	−1.83008	+	0.537360i	−0.122827	+	0.0360652i
$223$	−2.63073	+	18.2971i	−0.176167	+	1.22527i	0.689366	+	0.724413i	$0.257889\pi$
$223$	−2.63073	+	18.2971i	−0.176167	+	1.22527i	−0.865533	+	0.500853i	$0.833020\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	3.81349	−	2.45078i	0.254233	−	0.163386i
$226$	−4.42562	−	5.10744i	−0.294388	−	0.339742i
$227$	−6.77804	−	1.99021i	−0.449875	−	0.132095i	0.0489440	−	0.998802i	$-0.484414\pi$
$227$	−6.77804	−	1.99021i	−0.449875	−	0.132095i	−0.498819	+	0.866706i	$0.666233\pi$
$228$	−0.491378	+	1.07597i	−0.0325423	+	0.0712577i
$229$	−3.66143			−0.241954			−0.120977	−	0.992655i	$-0.538603\pi$
$229$	−3.66143			−0.241954			−0.120977	+	0.992655i	$0.538603\pi$
$230$	−5.44503	−	7.07871i	−0.359035	−	0.466756i
$231$	1.14727			0.0754849
$232$	0.171054	−	0.374555i	0.0112302	−	0.0245908i
$233$	−19.5093	−	5.72845i	−1.27810	−	0.375283i	−0.428896	−	0.903354i	$-0.641097\pi$
$233$	−19.5093	−	5.72845i	−1.27810	−	0.375283i	−0.849200	+	0.528071i	$0.822916\pi$
$234$	9.05527	+	10.4503i	0.591961	+	0.683160i
$235$	−1.48083	+	0.951670i	−0.0965985	+	0.0620801i
$236$	−6.20922	+	7.16582i	−0.404186	+	0.466455i
$237$	−0.395841	+	2.75314i	−0.0257126	+	0.178835i
$238$	−4.20164	+	1.23371i	−0.272352	+	0.0799697i
$239$	20.1307	+	12.9372i	1.30215	+	0.836839i	0.993444	−	0.114319i	$-0.0364687\pi$
$239$	20.1307	+	12.9372i	1.30215	+	0.836839i	0.308703	+	0.951158i	$0.400105\pi$
$240$	0.0541044	+	0.376305i	0.00349243	+	0.0242904i
$241$	−9.51907	−	20.8439i	−0.613177	−	1.34267i	−0.920379	−	0.391027i	$-0.872120\pi$
$241$	−9.51907	−	20.8439i	−0.613177	−	1.34267i	0.307202	−	0.951644i	$-0.400607\pi$
$242$	8.54904	+	18.7198i	0.549553	+	1.20335i
$243$	−0.769991	−	5.35540i	−0.0493949	−	0.343549i
$244$	3.99597	+	2.56805i	0.255815	+	0.164403i
$245$	1.78674	−	0.524634i	0.114151	−	0.0335176i
$246$	−0.153579	+	1.06817i	−0.00979186	+	0.0681039i
$247$	17.7348	−	20.4671i	1.12844	−	1.30229i
$248$	−0.221409	+	0.142291i	−0.0140595	+	0.00903547i
$249$	1.55157	+	1.79060i	0.0983266	+	0.113475i
$250$	−11.6716	−	3.42708i	−0.738174	−	0.216747i
$251$	12.7516	−	27.9222i	0.804876	−	1.76243i	0.176856	−	0.984237i	$-0.443407\pi$
$251$	12.7516	−	27.9222i	0.804876	−	1.76243i	0.628021	−	0.778197i	$-0.283865\pi$
$252$	2.95832			0.186357
$253$	21.7845	+	15.8671i	1.36958	+	0.997558i
$254$	−10.2820			−0.645151
$255$	0.691579	−	1.51435i	0.0433084	−	0.0948321i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	16.9023	+	19.5063i	1.05434	+	1.21677i	0.975526	+	0.219882i	$0.0705672\pi$
$257$	16.9023	+	19.5063i	1.05434	+	1.21677i	0.0788120	+	0.996889i	$0.474887\pi$
$258$	1.08488	−	0.697211i	0.0675418	−	0.0434065i
$259$	6.11806	−	7.06062i	0.380158	−	0.438725i
$260$	1.23873	−	8.61555i	0.0768227	−	0.534314i
$261$	1.16879	−	0.343188i	0.0723464	−	0.0212428i
$262$	−5.37587	−	3.45486i	−0.332122	−	0.213442i
$263$	1.73445	+	12.0634i	0.106951	+	0.743861i	0.970762	+	0.240045i	$0.0771620\pi$
$263$	1.73445	+	12.0634i	0.106951	+	0.743861i	−0.863811	+	0.503816i	$0.831929\pi$
$264$	−0.476594	−	1.04359i	−0.0293323	−	0.0642288i
$265$	4.08611	+	8.94734i	0.251008	+	0.549631i
$266$	−0.824557	−	5.73492i	−0.0505568	−	0.351630i
$267$	−0.851389	−	0.547155i	−0.0521042	−	0.0334853i
$268$	−12.2437	+	3.59507i	−0.747903	+	0.219604i
$269$	3.03707	−	21.1233i	0.185173	−	1.28791i	−0.659124	−	0.752035i	$-0.729073\pi$
$269$	3.03707	−	21.1233i	0.185173	−	1.28791i	0.844297	−	0.535875i	$-0.180018\pi$
$270$	−1.48339	+	1.71192i	−0.0902763	+	0.104184i
$271$	−3.65037	+	2.34595i	−0.221744	+	0.142506i	−0.646797	−	0.762662i	$-0.723892\pi$
$271$	−3.65037	+	2.34595i	−0.221744	+	0.142506i	0.425053	+	0.905169i	$0.360256\pi$
$272$	2.86765	+	3.30944i	0.173877	+	0.200664i
$273$	0.915614	+	0.268848i	0.0554155	+	0.0162715i
$274$	−0.424405	+	0.929317i	−0.0256392	+	0.0561421i
$275$	8.61100			0.519263
$276$	−0.791421	−	0.576447i	−0.0476380	−	0.0346980i
$277$	11.0293			0.662685			0.331343	−	0.943510i	$-0.392498\pi$
$277$	11.0293			0.662685			0.331343	+	0.943510i	$0.392498\pi$
$278$	2.30076	−	5.03797i	0.137991	−	0.302157i
$279$	−0.747059	−	0.219356i	−0.0447252	−	0.0131325i
$280$	−1.21946	−	1.40733i	−0.0728768	−	0.0841043i
$281$	6.69297	−	4.30131i	0.399269	−	0.256595i	−0.325563	−	0.945520i	$-0.605554\pi$
$281$	6.69297	−	4.30131i	0.399269	−	0.256595i	0.724832	+	0.688926i	$0.241917\pi$
$282$	−0.126378	+	0.145848i	−0.00752569	+	0.00868511i
$283$	−3.03234	+	21.0904i	−0.180254	+	1.25369i	0.675908	+	0.736986i	$0.263752\pi$
$283$	−3.03234	+	21.0904i	−0.180254	+	1.25369i	−0.856162	+	0.516707i	$0.827158\pi$
$284$	7.17719	−	2.10741i	0.425888	−	0.125052i
$285$	1.85302	+	1.19086i	0.109763	+	0.0705406i
$286$	3.73818	+	25.9996i	0.221043	+	1.53739i
$287$	−2.19584	−	4.80823i	−0.129617	−	0.283821i
$288$	−1.22893	−	2.69098i	−0.0724154	−	0.158568i
$289$	−0.309653	−	2.15368i	−0.0182149	−	0.126687i
$290$	−0.645055	−	0.414551i	−0.0378789	−	0.0243433i
$291$	−3.30150	+	0.969408i	−0.193537	+	0.0568277i
$292$	1.58259	−	11.0071i	0.0926138	−	0.644143i
$293$	−9.06104	+	10.4570i	−0.529352	+	0.610904i	−0.955947	−	0.293538i	$-0.905167\pi$
$293$	−9.06104	+	10.4570i	−0.529352	+	0.610904i	0.426596	+	0.904442i	$0.359713\pi$
$294$	0.171747	−	0.110375i	0.0100165	−	0.00643722i
$295$	11.5626	+	13.3440i	0.673202	+	0.776916i
$296$	−8.96409	−	2.63210i	−0.521027	−	0.152987i
$297$	2.83970	−	6.21807i	0.164776	−	0.360809i
$298$	−17.8065			−1.03150
$299$	13.6675	+	17.7681i	0.790411	+	1.02756i
$300$	−0.312834			−0.0180615
$301$	−2.62406	+	5.74590i	−0.151248	+	0.331188i
$302$	7.05258	+	2.07083i	0.405831	+	0.119163i
$303$	−0.502459	−	0.579868i	−0.0288655	−	0.0333126i
$304$	−4.87413	+	3.13241i	−0.279551	+	0.179656i
$305$	5.79246	−	6.68485i	0.331675	−	0.382774i
$306$	−1.84362	+	12.8227i	−0.105393	+	0.733024i
$307$	−23.8797	+	7.01170i	−1.36288	+	0.400179i	−0.879779	−	0.475384i	$-0.842309\pi$
$307$	−23.8797	+	7.01170i	−1.36288	+	0.400179i	−0.483105	+	0.875562i	$0.660491\pi$
$308$	4.72748	+	3.03817i	0.269373	+	0.173116i
$309$	−0.481676	−	3.35013i	−0.0274016	−	0.190582i
$310$	0.203596	+	0.445813i	0.0115635	+	0.0253205i
$311$	6.50398	+	14.2417i	0.368807	+	0.807575i	0.999502	+	0.0315443i	$0.0100425\pi$
$311$	6.50398	+	14.2417i	0.368807	+	0.807575i	−0.630695	+	0.776031i	$0.717230\pi$
$312$	−0.135807	−	0.944555i	−0.00768853	−	0.0534749i
$313$	29.1992	+	18.7652i	1.65044	+	1.06067i	0.930273	+	0.366867i	$0.119570\pi$
$313$	29.1992	+	18.7652i	1.65044	+	1.06067i	0.720164	+	0.693804i	$0.244067\pi$
$314$	5.51202	−	1.61847i	0.311061	−	0.0913358i
$315$	0.783997	−	5.45282i	0.0441732	−	0.307232i
$316$	−8.92188	+	10.2964i	−0.501895	+	0.579217i
$317$	12.3808	−	7.95665i	0.695374	−	0.446890i	−0.144618	−	0.989488i	$-0.546195\pi$
$317$	12.3808	−	7.95665i	0.695374	−	0.446890i	0.839993	+	0.542597i	$0.182559\pi$
$318$	0.706190	+	0.814986i	0.0396011	+	0.0457022i
$319$	2.22021	+	0.651914i	0.124308	+	0.0365002i
$320$	−0.773573	+	1.69389i	−0.0432441	+	0.0946913i
$321$	1.44960			0.0809086
$322$	4.78768	+	0.279507i	0.266807	+	0.0155763i
$323$	25.3716			1.41171
$324$	3.58363	−	7.84705i	0.199090	−	0.435947i
$325$	6.87226	+	2.01788i	0.381205	+	0.111932i
$326$	4.57681	+	5.28192i	0.253486	+	0.292538i
$327$	−2.07175	+	1.33143i	−0.114568	+	0.0736284i
$328$	−3.46153	+	3.99482i	−0.191131	+	0.220577i
$329$	0.134527	−	0.935654i	0.00741670	−	0.0515843i
$330$	−2.04987	+	0.601897i	−0.112842	+	0.0331334i
$331$	−19.2277	−	12.3569i	−1.05685	−	0.679197i	−0.107753	−	0.994178i	$-0.534366\pi$
$331$	−19.2277	−	12.3569i	−1.05685	−	0.679197i	−0.949098	+	0.314981i	$0.898002\pi$
$332$	1.65161	+	11.4872i	0.0906441	+	0.630443i
$333$	−11.4813	−	25.1406i	−0.629173	−	1.37770i
$334$	6.83847	+	14.9742i	0.374185	+	0.819350i
$335$	3.38174	+	23.5205i	0.184764	+	1.28506i
$336$	−0.171747	−	0.110375i	−0.00936959	−	0.00602147i
$337$	−10.8807	+	3.19487i	−0.592710	+	0.174035i	−0.564313	−	0.825561i	$-0.690859\pi$
$337$	−10.8807	+	3.19487i	−0.592710	+	0.174035i	−0.0283978	+	0.999597i	$0.509041\pi$
$338$	−1.25922	+	8.75806i	−0.0684925	+	0.476376i
$339$	−0.903520	+	1.04272i	−0.0490725	+	0.0566327i
$340$	6.85999	−	4.40864i	0.372035	−	0.239092i
$341$	−0.968544	−	1.11776i	−0.0524496	−	0.0605301i
$342$	−16.4459	−	4.82895i	−0.889292	−	0.261120i
$343$	−0.415415	+	0.909632i	−0.0224303	+	0.0491155i
$344$	6.31672			0.340575
$345$	−1.27225	+	1.30599i	−0.0684958	+	0.0703123i
$346$	−0.158905			−0.00854278
$347$	4.25299	−	9.31275i	0.228313	−	0.499935i	−0.760456	−	0.649389i	$-0.775025\pi$
$347$	4.25299	−	9.31275i	0.228313	−	0.499935i	0.988769	+	0.149455i	$0.0477518\pi$
$348$	−0.0806595	−	0.0236838i	−0.00432380	−	0.00126958i
$349$	10.8407	+	12.5108i	0.580288	+	0.669688i	0.967667	−	0.252233i	$-0.0811648\pi$
$349$	10.8407	+	12.5108i	0.580288	+	0.669688i	−0.387379	+	0.921921i	$0.626619\pi$
$350$	1.28907	−	0.828438i	0.0689039	−	0.0442818i
$351$	3.72343	−	4.29707i	0.198742	−	0.229361i
$352$	0.799747	−	5.56237i	0.0426267	−	0.296475i
$353$	−17.5035	+	5.13948i	−0.931615	+	0.273547i	−0.712113	−	0.702065i	$-0.752262\pi$
$353$	−17.5035	+	5.13948i	−0.931615	+	0.273547i	−0.219503	+	0.975612i	$0.570443\pi$
$354$	1.62846	+	1.04655i	0.0865519	+	0.0556236i
$355$	−1.98236	−	13.7876i	−0.105213	−	0.731770i
$356$	−2.05930	−	4.50924i	−0.109143	−	0.238989i
$357$	0.371384	+	0.813217i	0.0196557	+	0.0430400i
$358$	−0.216348	−	1.50474i	−0.0114344	−	0.0795277i
$359$	9.28583	+	5.96764i	0.490088	+	0.314960i	0.762241	−	0.647294i	$-0.224099\pi$
$359$	9.28583	+	5.96764i	0.490088	+	0.314960i	−0.272153	+	0.962254i	$0.587736\pi$
$360$	−5.28574	+	1.55203i	−0.278583	+	0.0817994i
$361$	−2.07341	+	14.4209i	−0.109127	+	0.758993i
$362$	16.9052	−	19.5096i	0.888517	−	1.02540i
$363$	3.53448	−	2.27147i	0.185512	−	0.119221i
$364$	3.06095	+	3.53252i	0.160437	+	0.185155i
$365$	−19.8691	−	5.83409i	−1.04000	−	0.305370i
$366$	0.402847	−	0.882113i	0.0210572	−	0.0461088i
$367$	7.44631			0.388694			0.194347	−	0.980933i	$-0.437741\pi$
$367$	7.44631			0.388694			0.194347	+	0.980933i	$0.437741\pi$
$368$	−1.73463	−	4.47114i	−0.0904236	−	0.233074i
$369$	−15.6374			−0.814050
$370$	−7.22713	+	15.8252i	−0.375721	+	0.822714i
$371$	−5.06816	−	1.48815i	−0.263126	−	0.0772608i
$372$	0.0351868	+	0.0406078i	0.00182435	+	0.00210542i
$373$	16.8093	−	10.8027i	0.870355	−	0.559343i	−0.0275062	−	0.999622i	$-0.508757\pi$
$373$	16.8093	−	10.8027i	0.870355	−	0.559343i	0.897861	+	0.440278i	$0.145120\pi$
$374$	−16.1149	+	18.5976i	−0.833284	+	0.961661i
$375$	−0.353428	+	2.45814i	−0.0182509	+	0.126938i
$376$	−0.906985	+	0.266315i	−0.0467742	+	0.0137341i
$377$	1.61914	+	1.04056i	0.0833900	+	0.0535915i
$378$	−0.173116	−	1.20405i	−0.00890413	−	0.0619296i
$379$	−9.13244	−	19.9973i	−0.469102	−	1.02719i	−0.985318	−	0.170732i	$-0.945387\pi$
$379$	−9.13244	−	19.9973i	−0.469102	−	1.02719i	0.516216	−	0.856459i	$-0.327340\pi$
$380$	4.48200	+	9.81421i	0.229922	+	0.503458i
$381$	0.298739	+	2.07778i	0.0153049	+	0.106448i
$382$	−2.87977	−	1.85071i	−0.147342	−	0.0946907i
$383$	3.89603	−	1.14398i	0.199078	−	0.0584546i	−0.180673	−	0.983543i	$-0.557828\pi$
$383$	3.89603	−	1.14398i	0.199078	−	0.0584546i	0.379751	+	0.925089i	$0.376010\pi$
$384$	−0.0290545	+	0.202079i	−0.00148268	+	0.0103123i
$385$	6.85284	−	7.90860i	0.349253	−	0.403060i
$386$	−6.75310	+	4.33995i	−0.343723	+	0.220898i
$387$	12.2373	+	14.1226i	0.622058	+	0.717893i
$388$	−16.1714	−	4.74835i	−0.820979	−	0.241061i
$389$	−2.31512	+	5.06940i	−0.117381	+	0.257029i	−0.959198	−	0.282734i	$-0.908759\pi$
$389$	−2.31512	+	5.06940i	−0.117381	+	0.257029i	0.841817	+	0.539762i	$0.181486\pi$
$390$	−1.77701			−0.0899824
$391$	−4.19519	+	20.5778i	−0.212160	+	1.04066i
$392$	1.00000			0.0505076
$393$	−0.541960	+	1.18673i	−0.0273383	+	0.0598625i
$394$	21.1958	+	6.22364i	1.06783	+	0.313543i
$395$	16.6140	+	19.1736i	0.835943	+	0.964730i
$396$	13.9854	−	8.98787i	0.702793	−	0.451657i
$397$	−7.68429	+	8.86814i	−0.385663	+	0.445079i	−0.915074	−	0.403287i	$-0.867868\pi$
$397$	−7.68429	+	8.86814i	−0.385663	+	0.445079i	0.529410	+	0.848366i	$0.322413\pi$
$398$	0.0614199	−	0.427185i	0.00307870	−	0.0214128i
$399$	−1.13495	+	0.333250i	−0.0568184	+	0.0166834i
$400$	−1.28907	−	0.828438i	−0.0644537	−	0.0414219i
$401$	−1.62830	−	11.3251i	−0.0813136	−	0.565549i	−0.989227	−	0.146390i	$-0.953234\pi$
$401$	−1.62830	−	11.3251i	−0.0813136	−	0.565549i	0.907913	−	0.419158i	$-0.137675\pi$
$402$	1.08222	+	2.36974i	0.0539763	+	0.118192i
$403$	−0.511043	−	1.11903i	−0.0254568	−	0.0557427i
$404$	−0.534857	−	3.72002i	−0.0266102	−	0.185078i
$405$	−13.5141	−	8.68498i	−0.671520	−	0.431560i
$406$	0.395087	−	0.116008i	0.0196078	−	0.00575737i
$407$	7.47167	−	51.9666i	0.370357	−	2.57589i
$408$	0.585450	−	0.675645i	0.0289841	−	0.0334494i
$409$	19.6385	−	12.6209i	0.971060	−	0.624063i	0.0440225	−	0.999031i	$-0.485983\pi$
$409$	19.6385	−	12.6209i	0.971060	−	0.624063i	0.927038	+	0.374968i	$0.122346\pi$
$410$	6.44595	+	7.43903i	0.318343	+	0.367387i
$411$	0.200126	+	0.0587623i	0.00987148	+	0.00289853i
$412$	6.88689	−	15.0802i	0.339293	−	0.742947i
$413$	−9.48174			−0.466566
$414$	6.63587	−	12.5401i	0.326135	−	0.616311i
$415$	21.6111			1.06085
$416$	1.94173	−	4.25180i	0.0952012	−	0.208462i
$417$	−1.08491	−	0.318559i	−0.0531284	−	0.0155999i
$418$	−21.3217	−	24.6066i	−1.04288	−	1.20355i
$419$	−22.8098	+	14.6590i	−1.11433	+	0.716138i	−0.962233	−	0.272227i	$-0.912240\pi$
$419$	−22.8098	+	14.6590i	−1.11433	+	0.716138i	−0.152100	+	0.988365i	$0.548603\pi$
$420$	−0.248961	+	0.287317i	−0.0121481	+	0.0140196i
$421$	0.724015	−	5.03563i	0.0352863	−	0.245422i	−0.964542	−	0.263928i	$-0.914982\pi$
$421$	0.724015	−	5.03563i	0.0352863	−	0.245422i	0.999829	+	0.0185061i	$0.00589102\pi$
$422$	−12.7055	+	3.73068i	−0.618496	+	0.181607i
$423$	−2.35250	−	1.51186i	−0.114383	−	0.0735093i
$424$	0.751725	+	5.22836i	0.0365070	+	0.253912i
$425$	2.78747	+	6.10371i	0.135212	+	0.296073i
$426$	−0.634393	−	1.38913i	−0.0307364	−	0.0673034i
$427$	0.675997	+	4.70166i	0.0327138	+	0.227530i
$428$	5.97325	+	3.83877i	0.288728	+	0.185554i
$429$	5.14535	−	1.51081i	0.248420	−	0.0729427i
$430$	1.67402	−	11.6431i	0.0807285	−	0.561479i
$431$	−9.49075	+	10.9529i	−0.457153	+	0.527583i	−0.936794	−	0.349882i	$-0.886222\pi$
$431$	−9.49075	+	10.9529i	−0.457153	+	0.527583i	0.479640	+	0.877465i	$0.340767\pi$
$432$	−1.02333	+	0.657652i	−0.0492348	+	0.0316413i
$433$	−8.05014	−	9.29036i	−0.386865	−	0.446466i	0.528595	−	0.848874i	$-0.322719\pi$
$433$	−8.05014	−	9.29036i	−0.386865	−	0.446466i	−0.915461	+	0.402408i	$0.868173\pi$
$434$	−0.252528	−	0.0741489i	−0.0121217	−	0.00355926i
$435$	−0.0650302	+	0.142396i	−0.00311796	+	0.00682738i
$436$	−12.0628			−0.577702
$437$	−26.1594	−	9.36890i	−1.25137	−	0.448175i
$438$	−2.27029			−0.108478
$439$	11.1665	−	24.4512i	0.532946	−	1.16699i	−0.431355	−	0.902182i	$-0.641964\pi$
$439$	11.1665	−	24.4512i	0.532946	−	1.16699i	0.964301	−	0.264808i	$-0.0853084\pi$
$440$	−10.0407	−	2.94821i	−0.478671	−	0.140551i
$441$	1.93729	+	2.23575i	0.0922518	+	0.106464i
$442$	−17.2191	+	11.0661i	−0.819030	+	0.526359i
$443$	3.32136	−	3.83305i	0.157803	−	0.182114i	−0.671343	−	0.741147i	$-0.734282\pi$
$443$	3.32136	−	3.83305i	0.157803	−	0.182114i	0.829145	+	0.559033i	$0.188828\pi$
$444$	−0.271443	+	1.88793i	−0.0128821	+	0.0895970i
$445$	−8.85725	+	2.60072i	−0.419874	+	0.123286i
$446$	15.5508	+	9.99390i	0.736352	+	0.473225i
$447$	0.517359	+	3.59831i	0.0244702	+	0.170194i
$448$	−0.415415	−	0.909632i	−0.0196265	−	0.0429761i
$449$	−0.959394	−	2.10078i	−0.0452766	−	0.0991419i	0.885642	−	0.464369i	$-0.153719\pi$
$449$	−0.959394	−	2.10078i	−0.0452766	−	0.0991419i	−0.930919	+	0.365227i	$0.880991\pi$
$450$	−0.645129	−	4.48697i	−0.0304117	−	0.211518i
$451$	−24.9890	−	16.0594i	−1.17669	−	0.756210i
$452$	−6.48436	+	1.90398i	−0.304999	+	0.0895557i
$453$	0.213560	−	1.48534i	0.0100339	−	0.0697875i
$454$	−4.62606	+	5.33876i	−0.217112	+	0.250560i
$455$	7.32240	−	4.70582i	0.343279	−	0.220612i
$456$	0.774609	+	0.893947i	0.0362744	+	0.0418629i
$457$	−10.8832	−	3.19559i	−0.509093	−	0.149483i	0.0170908	−	0.999854i	$-0.494560\pi$
$457$	−10.8832	−	3.19559i	−0.509093	−	0.149483i	−0.526184	+	0.850371i	$0.676378\pi$
$458$	−1.52101	+	3.33055i	−0.0710722	+	0.155627i
$459$	5.32678			0.248633
$460$	−8.70097	+	2.01237i	−0.405685	+	0.0938274i
$461$	−28.0768			−1.30767			−0.653834	−	0.756638i	$-0.726841\pi$
$461$	−28.0768			−1.30767			−0.653834	+	0.756638i	$0.726841\pi$
$462$	0.476594	−	1.04359i	0.0221731	−	0.0485524i
$463$	−24.3348	−	7.14534i	−1.13093	−	0.332072i	−0.337859	−	0.941197i	$-0.609703\pi$
$463$	−24.3348	−	7.14534i	−1.13093	−	0.332072i	−0.793074	+	0.609125i	$0.791521\pi$
$464$	−0.269649	−	0.311192i	−0.0125182	−	0.0144467i
$465$	0.0841739	−	0.0540953i	0.00390347	−	0.00250861i
$466$	−13.3152	+	15.3666i	−0.616816	+	0.711844i
$467$	1.81517	−	12.6248i	0.0839959	−	0.584204i	−0.903741	−	0.428079i	$-0.859191\pi$
$467$	1.81517	−	12.6248i	0.0839959	−	0.584204i	0.987737	−	0.156125i	$-0.0499003\pi$
$468$	13.2677	−	3.89573i	0.613297	−	0.180080i
$469$	−10.7349	−	6.89890i	−0.495691	−	0.318561i
$470$	0.250512	+	1.74235i	0.0115552	+	0.0803684i
$471$	−0.487208	−	1.06684i	−0.0224494	−	0.0491572i
$472$	3.93886	+	8.62489i	0.181301	+	0.396993i
$473$	5.05178	+	35.1359i	0.232281	+	1.61555i
$474$	2.33990	+	1.50376i	0.107475	+	0.0690701i
$475$	−8.51850	+	2.50126i	−0.390855	+	0.114766i
$476$	−0.623200	+	4.33445i	−0.0285643	+	0.198669i
$477$	−10.2330	+	11.8095i	−0.468537	+	0.540720i
$478$	20.1307	−	12.9372i	0.920757	−	0.591735i
$479$	19.3459	+	22.3264i	0.883938	+	1.02012i	0.999640	+	0.0268352i	$0.00854294\pi$
$479$	19.3459	+	22.3264i	0.883938	+	1.02012i	−0.115702	+	0.993284i	$0.536912\pi$
$480$	0.364774	+	0.107107i	0.0166496	+	0.00488876i
$481$	18.1407	−	39.7226i	0.827144	−	1.81119i
$482$	−22.9146			−1.04373
$483$	−0.0826214	−	0.975609i	−0.00375940	−	0.0443917i
$484$	20.5795			0.935432
$485$	−13.0379	+	28.5490i	−0.592020	+	1.29634i
$486$	−5.19131	−	1.52431i	−0.235483	−	0.0691439i
$487$	17.7238	+	20.4544i	0.803144	+	0.926877i	0.998549	−	0.0538454i	$-0.0171478\pi$
$487$	17.7238	+	20.4544i	0.803144	+	0.926877i	−0.195406	+	0.980722i	$0.562602\pi$
$488$	3.99597	−	2.56805i	0.180889	−	0.116250i
$489$	0.934386	−	1.07834i	0.0422544	−	0.0487642i
$490$	0.265014	−	1.84322i	0.0119721	−	0.0832680i
$491$	24.9447	−	7.32444i	1.12574	−	0.330547i	0.334708	−	0.942322i	$-0.391362\pi$
$491$	24.9447	−	7.32444i	1.12574	−	0.330547i	0.791032	+	0.611774i	$0.209544\pi$
$492$	0.907840	+	0.583434i	0.0409286	+	0.0263032i
$493$	0.256612	+	1.78478i	0.0115572	+	0.0803824i
$494$	−11.2502	−	24.6345i	−0.506170	−	1.10836i
$495$	−12.8602	−	28.1600i	−0.578025	−	1.26570i
$496$	0.0374557	+	0.260510i	0.00168181	+	0.0116973i
$497$	6.29274	+	4.04410i	0.282268	+	0.181403i
$498$	2.27334	−	0.667512i	0.101871	−	0.0299119i
$499$	3.06940	−	21.3482i	0.137405	−	0.955675i	−0.798141	−	0.602471i	$-0.794183\pi$
$499$	3.06940	−	21.3482i	0.137405	−	0.955675i	0.935546	−	0.353204i	$-0.114908\pi$
$500$	−7.96592	+	9.19316i	−0.356247	+	0.411131i
$501$	2.82727	−	1.81698i	0.126313	−	0.0811765i
$502$	−20.1017	−	23.1986i	−0.897183	−	1.03540i
$503$	−4.88355	−	1.43394i	−0.217747	−	0.0639362i	0.171040	−	0.985264i	$-0.445287\pi$
$503$	−4.88355	−	1.43394i	−0.217747	−	0.0639362i	−0.388786	+	0.921328i	$0.627106\pi$
$504$	1.22893	−	2.69098i	0.0547409	−	0.119866i
$505$	−6.99853			−0.311431
$506$	23.4828	−	13.2244i	1.04394	−	0.587896i
$507$	1.80640			0.0802252
$508$	−4.27130	+	9.35285i	−0.189509	+	0.414966i
$509$	−1.39818	−	0.410542i	−0.0619731	−	0.0181969i	0.250599	−	0.968091i	$-0.419372\pi$
$509$	−1.39818	−	0.410542i	−0.0619731	−	0.0181969i	−0.312572	+	0.949894i	$0.601191\pi$
$510$	−1.09021	−	1.25817i	−0.0482751	−	0.0557125i
$511$	9.35501	−	6.01210i	0.413841	−	0.265960i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−1.00302	+	6.97613i	−0.0442842	+	0.308004i
$514$	24.7651	−	7.27168i	1.09234	−	0.320740i
$515$	−25.9709	−	16.6905i	−1.14441	−	0.735471i
$516$	−0.183529	−	1.27647i	−0.00807943	−	0.0561937i
$517$	−2.20670	−	4.83200i	−0.0970505	−	0.212511i
$518$	−3.88103	−	8.49827i	−0.170523	−	0.373392i
$519$	0.00461690	+	0.0321113i	0.000202660	+	0.00140953i
$520$	−7.32240	−	4.70582i	−0.321108	−	0.206364i
$521$	−0.838839	+	0.246305i	−0.0367502	+	0.0107908i	−0.300056	−	0.953922i	$-0.597005\pi$
$521$	−0.838839	+	0.246305i	−0.0367502	+	0.0107908i	0.263306	+	0.964712i	$0.415187\pi$
$522$	0.173359	−	1.20574i	0.00758771	−	0.0527737i
$523$	−3.16602	+	3.65378i	−0.138440	+	0.159769i	−0.820736	−	0.571308i	$-0.806436\pi$
$523$	−3.16602	+	3.65378i	−0.138440	+	0.159769i	0.682296	+	0.731076i	$0.260982\pi$
$524$	−5.37587	+	3.45486i	−0.234846	+	0.150926i
$525$	−0.204863	−	0.236424i	−0.00894095	−	0.0103184i
$526$	11.6938	+	3.43360i	0.509872	+	0.149712i
$527$	0.478770	−	1.04836i	0.0208556	−	0.0456673i
$528$	−1.14727			−0.0499286
$529$	11.9242	−	19.6676i	0.518442	−	0.855113i
$530$	9.83622			0.427258
$531$	−11.6524	+	25.5152i	−0.505671	+	1.10727i
$532$	−5.55920	−	1.63233i	−0.241022	−	0.0707704i
$533$	−16.1799	−	18.6726i	−0.700828	−	0.808799i
$534$	−0.851389	+	0.547155i	−0.0368432	+	0.0236777i
$535$	8.65868	−	9.99265i	0.374347	−	0.432020i
$536$	−1.81602	+	12.6307i	−0.0784402	+	0.545563i
$537$	−0.297789	+	0.0874387i	−0.0128505	+	0.00377326i
$538$	−17.9528	−	11.5376i	−0.773999	−	0.497419i
$539$	0.799747	+	5.56237i	0.0344476	+	0.239588i
$540$	0.940998	+	2.06050i	0.0404941	+	0.0886697i
$541$	−7.57835	−	16.5943i	−0.325819	−	0.713444i	0.673858	−	0.738861i	$-0.264636\pi$
$541$	−7.57835	−	16.5943i	−0.325819	−	0.713444i	−0.999677	+	0.0254172i	$0.991909\pi$
$542$	0.617533	+	4.29504i	0.0265253	+	0.184488i
$543$	−4.43365	−	2.84933i	−0.190266	−	0.122277i
$544$	4.20164	−	1.23371i	0.180144	−	0.0528950i
$545$	−3.19681	+	22.2343i	−0.136936	+	0.952412i
$546$	0.624913	−	0.721188i	0.0267438	−	0.0308640i
$547$	3.37000	−	2.16577i	0.144091	−	0.0926015i	−0.466609	−	0.884464i	$-0.654525\pi$
$547$	3.37000	−	2.16577i	0.144091	−	0.0926015i	0.610700	+	0.791862i	$0.290888\pi$
$548$	0.669032	+	0.772104i	0.0285796	+	0.0329827i
$549$	13.4829	+	3.95892i	0.575434	+	0.168963i
$550$	3.57714	−	7.83284i	0.152530	−	0.333993i
$551$	−2.38573			−0.101635
$552$	−0.853123	+	0.480437i	−0.0363113	+	0.0204488i
$553$	−13.6241			−0.579355
$554$	4.58173	−	10.0326i	0.194659	−	0.426244i
$555$	3.40792	+	1.00065i	0.144658	+	0.0424754i
$556$	−3.62693	−	4.18570i	−0.153816	−	0.177513i
$557$	−23.3465	+	15.0039i	−0.989224	+	0.635736i	−0.931936	−	0.362622i	$-0.881882\pi$
$557$	−23.3465	+	15.0039i	−0.989224	+	0.635736i	−0.0572881	+	0.998358i	$0.518245\pi$
$558$	−0.509873	+	0.588425i	−0.0215846	+	0.0249100i
$559$	−4.20193	+	29.2251i	−0.177723	+	1.23609i
$560$	−1.78674	+	0.524634i	−0.0755035	+	0.0221698i
$561$	4.22640	+	2.71614i	0.178439	+	0.114676i
$562$	−1.13225	−	7.87496i	−0.0477610	−	0.332185i
$563$	5.78926	+	12.6767i	0.243988	+	0.534260i	0.991518	−	0.129968i	$-0.0414876\pi$
$563$	5.78926	+	12.6767i	0.243988	+	0.534260i	−0.747530	+	0.664228i	$0.768760\pi$
$564$	0.0801685	+	0.175545i	0.00337570	+	0.00739176i
$565$	1.79100	+	12.4567i	0.0753478	+	0.524055i
$566$	17.9248	+	11.5196i	0.753436	+	0.484204i
$567$	8.27718	−	2.43040i	0.347609	−	0.102067i
$568$	1.06454	−	7.40406i	0.0446672	−	0.310667i
$569$	9.13489	−	10.5422i	0.382955	−	0.441953i	−0.531244	−	0.847219i	$-0.678275\pi$
$569$	9.13489	−	10.5422i	0.382955	−	0.441953i	0.914199	+	0.405265i	$0.132821\pi$
$570$	1.85302	−	1.19086i	0.0776144	−	0.0498798i
$571$	−0.0217521	−	0.0251033i	−0.000910299	−	0.00105054i	0.755294	−	0.655386i	$-0.227494\pi$
$571$	−0.0217521	−	0.0251033i	−0.000910299	−	0.00105054i	−0.756205	+	0.654335i	$0.772949\pi$
$572$	25.2030	+	7.40026i	1.05379	+	0.309420i
$573$	−0.290319	+	0.635711i	−0.0121283	+	0.0265572i
$574$	−5.28590			−0.220629
$575$	−0.620126	−	7.32256i	−0.0258610	−	0.305372i
$576$	−2.95832			−0.123263
$577$	−13.0581	+	28.5932i	−0.543615	+	1.19035i	0.416086	+	0.909325i	$0.363402\pi$
$577$	−13.0581	+	28.5932i	−0.543615	+	1.19035i	−0.959701	+	0.281025i	$0.909326\pi$
$578$	−2.08769	−	0.613002i	−0.0868366	−	0.0254975i
$579$	1.07322	+	1.23856i	0.0446015	+	0.0514728i
$580$	−0.645055	+	0.414551i	−0.0267844	+	0.0172133i
$581$	−7.59989	+	8.77074i	−0.315297	+	0.363872i
$582$	−0.489688	+	3.40586i	−0.0202982	+	0.141177i
$583$	−28.4809	+	8.36274i	−1.17956	+	0.346349i
$584$	−9.35501	−	6.01210i	−0.387113	−	0.248782i
$585$	−3.66456	−	25.4876i	−0.151511	−	1.05378i
$586$	5.74793	+	12.5862i	0.237445	+	0.519931i
$587$	7.75055	+	16.9713i	0.319899	+	0.700482i	0.999451	−	0.0331464i	$-0.0105527\pi$
$587$	7.75055	+	16.9713i	0.319899	+	0.700482i	−0.679551	+	0.733628i	$0.737825\pi$
$588$	−0.0290545	−	0.202079i	−0.00119819	−	0.00833358i
$589$	1.28282	+	0.824417i	0.0528576	+	0.0339695i
$590$	16.9414	−	4.97444i	0.697466	−	0.204794i
$591$	0.641832	−	4.46404i	0.0264014	−	0.183626i
$592$	−6.11806	+	7.06062i	−0.251451	+	0.290190i
$593$	−5.94613	+	3.82135i	−0.244178	+	0.156924i	−0.657006	−	0.753885i	$-0.728178\pi$
$593$	−5.94613	+	3.82135i	−0.244178	+	0.156924i	0.412828	+	0.910809i	$0.364541\pi$
$594$	−4.47650	−	5.16616i	−0.183673	−	0.211970i
$595$	7.82417	+	2.29738i	0.320760	+	0.0941835i
$596$	−7.39709	+	16.1974i	−0.302996	+	0.663470i
$597$	−0.0881095			−0.00360608
$598$	21.8401	−	5.05122i	0.893110	−	0.206560i
$599$	−19.8213			−0.809878			−0.404939	−	0.914344i	$-0.632707\pi$
$599$	−19.8213			−0.809878			−0.404939	+	0.914344i	$0.632707\pi$
$600$	−0.129956	+	0.284564i	−0.00530543	+	0.0116173i
$601$	−36.3010	−	10.6589i	−1.48075	−	0.434788i	−0.561174	−	0.827698i	$-0.689650\pi$
$601$	−36.3010	−	10.6589i	−1.48075	−	0.434788i	−0.919577	+	0.392911i	$0.871468\pi$
$602$	4.13658	+	4.77386i	0.168594	+	0.194568i
$603$	−31.7572	+	20.4091i	−1.29325	+	0.831124i
$604$	4.81344	−	5.55500i	0.195856	−	0.226030i
$605$	5.45387	−	37.9325i	0.221731	−	1.54217i
$606$	−0.736195	+	0.216166i	−0.0299059	+	0.00878116i
$607$	16.5430	+	10.6316i	0.671461	+	0.431522i	0.831452	−	0.555597i	$-0.187510\pi$
$607$	16.5430	+	10.6316i	0.671461	+	0.431522i	−0.159991	+	0.987118i	$0.551146\pi$
$608$	0.824557	+	5.73492i	0.0334402	+	0.232582i
$609$	−0.0349218	−	0.0764680i	−0.00141510	−	0.00309864i
$610$	−3.67448	−	8.04599i	−0.148775	−	0.325773i
$611$	−0.628804	−	4.37343i	−0.0254387	−	0.176930i
$612$	10.8981	+	7.00376i	0.440528	+	0.283110i
$613$	−25.3021	+	7.42938i	−1.02194	+	0.300070i	−0.749431	−	0.662082i	$-0.769673\pi$
$613$	−25.3021	+	7.42938i	−1.02194	+	0.300070i	−0.272513	+	0.962152i	$0.587855\pi$
$614$	−3.54190	+	24.6345i	−0.142939	+	0.994166i
$615$	1.31598	−	1.51873i	0.0530656	−	0.0612410i
$616$	4.72748	−	3.03817i	0.190476	−	0.122411i
$617$	19.8584	+	22.9178i	0.799470	+	0.922637i	0.998352	−	0.0573862i	$-0.0182766\pi$
$617$	19.8584	+	22.9178i	0.799470	+	0.922637i	−0.198882	+	0.980023i	$0.563731\pi$
$618$	−3.24748	−	0.953546i	−0.130633	−	0.0383572i
$619$	5.00702	−	10.9639i	0.201249	−	0.440675i	−0.781918	−	0.623381i	$-0.785759\pi$
$619$	5.00702	−	10.9639i	0.201249	−	0.440675i	0.983167	+	0.182707i	$0.0584858\pi$
$620$	0.490103			0.0196830
$621$	−5.49218	−	1.96700i	−0.220394	−	0.0789332i
$622$	15.6566			0.627772
$623$	2.05930	−	4.50924i	0.0825042	−	0.180659i
$624$	−0.915614	−	0.268848i	−0.0366539	−	0.0107626i
$625$	9.81659	+	11.3290i	0.392664	+	0.453158i
$626$	29.1992	−	18.7652i	1.16704	−	0.750008i
$627$	−4.35297	+	5.02359i	−0.173841	+	0.200623i
$628$	0.817558	−	5.68624i	0.0326241	−	0.226906i
$629$	39.2540	−	11.5260i	1.56516	−	0.459572i
$630$	−4.63438	−	2.97833i	−0.184638	−	0.118660i
$631$	−0.0386950	−	0.269129i	−0.00154042	−	0.0107139i	0.989037	−	0.147670i	$-0.0471773\pi$
$631$	−0.0386950	−	0.269129i	−0.00154042	−	0.0107139i	−0.990577	+	0.136956i	$0.956268\pi$
$632$	5.65965	+	12.3929i	0.225129	+	0.492963i
$633$	1.12304	+	2.45912i	0.0446370	+	0.0977414i
$634$	−2.09446	−	14.5673i	−0.0831816	−	0.578540i
$635$	16.1074	+	10.3516i	0.639201	+	0.410790i
$636$	1.03470	−	0.303815i	0.0410285	−	0.0120471i
$637$	−0.665208	+	4.62662i	−0.0263565	+	0.183313i
$638$	1.51531	−	1.74876i	0.0599918	−	0.0692342i
$639$	18.6159	−	11.9637i	0.736435	−	0.473278i
$640$	1.21946	+	1.40733i	0.0482035	+	0.0556297i
$641$	32.3465	+	9.49778i	1.27761	+	0.375140i	0.849020	−	0.528360i	$-0.177193\pi$
$641$	32.3465	+	9.49778i	1.27761	+	0.375140i	0.428588	+	0.903500i	$0.359011\pi$
$642$	0.602184	−	1.31860i	0.0237663	−	0.0520410i
$643$	17.8065			0.702221			0.351110	−	0.936334i	$-0.385804\pi$
$643$	17.8065			0.702221			0.351110	+	0.936334i	$0.385804\pi$
$644$	2.24312	−	4.23892i	0.0883914	−	0.167037i
$645$	−2.40146			−0.0945572
$646$	10.5397	−	23.0788i	0.414680	−	0.908023i
$647$	27.3026	+	8.01675i	1.07337	+	0.315171i	0.770225	−	0.637772i	$-0.220144\pi$
$647$	27.3026	+	8.01675i	1.07337	+	0.315171i	0.303149	+	0.952943i	$0.401962\pi$
$648$	−5.64923	−	6.51956i	−0.221923	−	0.256113i
$649$	−44.8247	+	28.8071i	−1.75952	+	1.13078i
$650$	4.69037	−	5.41297i	0.183971	−	0.212314i
$651$	−0.00764683	+	0.0531849i	−0.000299703	+	0.00208448i
$652$	6.70588	−	1.96902i	0.262622	−	0.0771129i
$653$	30.4098	+	19.5432i	1.19003	+	0.764783i	0.977203	−	0.212308i	$-0.0680979\pi$
$653$	30.4098	+	19.5432i	1.19003	+	0.764783i	0.212823	+	0.977091i	$0.431734\pi$
$654$	0.350478	+	2.43763i	0.0137048	+	0.0953188i
$655$	4.94337	+	10.8245i	0.193153	+	0.422947i
$656$	2.19584	+	4.80823i	0.0857333	+	0.187730i
$657$	−4.68180	−	32.5626i	−0.182654	−	1.27039i
$658$	−0.795216	−	0.511054i	−0.0310008	−	0.0199230i
$659$	10.4629	−	3.07219i	0.407577	−	0.119676i	−0.0715160	−	0.997439i	$-0.522784\pi$
$659$	10.4629	−	3.07219i	0.407577	−	0.119676i	0.479093	+	0.877764i	$0.340966\pi$
$660$	−0.304043	+	2.11467i	−0.0118349	+	0.0823133i
$661$	−24.2382	+	27.9724i	−0.942757	+	1.08800i	0.0532375	+	0.998582i	$0.483046\pi$
$661$	−24.2382	+	27.9724i	−0.942757	+	1.08800i	−0.995994	+	0.0894174i	$0.971499\pi$
$662$	−19.2277	+	12.3569i	−0.747306	+	0.480265i
$663$	2.73651	+	3.15810i	0.106277	+	0.122650i
$664$	11.1353	+	3.26961i	0.432132	+	0.126885i
$665$	−4.48200	+	9.81421i	−0.173804	+	0.380579i
$666$	−27.6382			−1.07096
$667$	0.394480	−	1.93496i	0.0152743	−	0.0749219i
$668$	16.4618			0.636926
$669$	1.56773	−	3.43285i	0.0606120	−	0.132722i
$670$	22.7998	+	6.69464i	0.880834	+	0.258636i
$671$	17.4802	+	20.1732i	0.674816	+	0.778779i
$672$	−0.171747	+	0.110375i	−0.00662530	+	0.00425782i
$673$	4.67580	−	5.39616i	0.180239	−	0.208007i	−0.658440	−	0.752634i	$-0.728783\pi$
$673$	4.67580	−	5.39616i	0.180239	−	0.208007i	0.838679	+	0.544627i	$0.183329\pi$
$674$	−1.61386	+	11.2246i	−0.0621636	+	0.432357i
$675$	−1.78846	+	0.525140i	−0.0688380	+	0.0202127i
$676$	7.44352	+	4.78366i	0.286289	+	0.183987i
$677$	−2.80791	−	19.5294i	−0.107917	−	0.750577i	−0.969876	−	0.243599i	$-0.921672\pi$
$677$	−2.80791	−	19.5294i	−0.107917	−	0.750577i	0.861959	−	0.506977i	$-0.169237\pi$
$678$	0.573154	+	1.25503i	0.0220118	+	0.0481992i
$679$	−7.00145	−	15.3310i	−0.268691	−	0.588351i
$680$	−1.16050	−	8.07148i	−0.0445033	−	0.309527i
$681$	1.21326	+	0.779713i	0.0464921	+	0.0298787i
$682$	−1.41910	+	0.416685i	−0.0543401	+	0.0159557i
$683$	−4.78749	+	33.2977i	−0.183188	+	1.27410i	0.665976	+	0.745973i	$0.268015\pi$
$683$	−4.78749	+	33.2977i	−0.183188	+	1.27410i	−0.849164	+	0.528129i	$0.822894\pi$
$684$	−11.2244	+	12.9537i	−0.429177	+	0.495297i
$685$	1.60046	−	1.02855i	0.0611503	−	0.0392989i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	0.717226	+	0.210596i	0.0273639	+	0.00803476i
$688$	2.62406	−	5.74590i	0.100041	−	0.219060i
$689$	−24.6897			−0.940603
$690$	0.659460	+	1.69981i	0.0251052	+	0.0647107i
$691$	10.7443			0.408733			0.204366	−	0.978894i	$-0.434487\pi$
$691$	10.7443			0.408733			0.204366	+	0.978894i	$0.434487\pi$
$692$	−0.0660115	+	0.144545i	−0.00250938	+	0.00549477i
$693$	15.9511	+	4.68365i	0.605931	+	0.177917i
$694$	−6.70442	−	7.73732i	−0.254496	−	0.293704i
$695$	−8.67633	+	5.57594i	−0.329112	+	0.211507i
$696$	−0.0550507	+	0.0635319i	−0.00208669	+	0.00240817i
$697$	3.29417	−	22.9115i	0.124776	−	0.867834i
$698$	15.8836	−	4.66385i	0.601203	−	0.176529i
$699$	3.49213	+	2.24425i	0.132084	+	0.0848855i
$700$	−0.218073	−	1.51673i	−0.00824237	−	0.0573269i
$701$	9.86512	+	21.6016i	0.372600	+	0.815881i	0.999328	+	0.0366429i	$0.0116664\pi$
$701$	9.86512	+	21.6016i	0.372600	+	0.815881i	−0.626728	+	0.779238i	$0.715606\pi$
$702$	−2.36198	−	5.17202i	−0.0891473	−	0.195205i
$703$	7.70345	+	53.5787i	0.290541	+	2.02076i
$704$	−4.72748	−	3.03817i	−0.178174	−	0.114505i
$705$	0.344812	−	0.101246i	0.0129864	−	0.00381315i
$706$	−2.59617	+	18.0567i	−0.0977080	+	0.679574i
$707$	2.46114	−	2.84031i	0.0925608	−	0.106821i
$708$	1.62846	−	1.04655i	0.0612015	−	0.0393318i
$709$	14.0807	+	16.2500i	0.528813	+	0.610283i	0.955815	−	0.293968i	$-0.0949758\pi$
$709$	14.0807	+	16.2500i	0.528813	+	0.610283i	−0.427002	+	0.904251i	$0.640430\pi$
$710$	−13.3651	−	3.92436i	−0.501585	−	0.147279i
$711$	−16.7430	+	36.6622i	−0.627913	+	1.37494i
$712$	−4.95722			−0.185780
$713$	−0.880762	+	0.904120i	−0.0329848	+	0.0338596i
$714$	0.894006			0.0334573
$715$	20.3194	−	44.4933i	0.759903	−	1.66396i
$716$	−1.45863	−	0.428292i	−0.0545115	−	0.0160060i
$717$	−3.19922	−	3.69210i	−0.119477	−	0.137884i
$718$	9.28583	−	5.96764i	0.346544	−	0.222710i
$719$	−7.87029	+	9.08280i	−0.293512	+	0.338731i	−0.883284	−	0.468839i	$-0.844672\pi$
$719$	−7.87029	+	9.08280i	−0.293512	+	0.338731i	0.589771	+	0.807570i	$0.299218\pi$
$720$	−0.783997	+	5.45282i	−0.0292179	+	0.203215i
$721$	15.9068	−	4.67066i	0.592400	−	0.173944i
$722$	12.2564	+	7.87669i	0.456135	+	0.293140i
$723$	0.665773	+	4.63055i	0.0247604	+	0.172212i
$724$	−10.7239	−	23.4821i	−0.398551	−	0.872705i
$725$	−0.262110	−	0.573941i	−0.00973452	−	0.0213156i
$726$	−0.597928	−	4.15868i	−0.0221912	−	0.154343i
$727$	−29.7955	−	19.1484i	−1.10506	−	0.710176i	−0.144845	−	0.989454i	$-0.546268\pi$
$727$	−29.7955	−	19.1484i	−1.10506	−	0.710176i	−0.960210	+	0.279278i	$0.909905\pi$
$728$	4.48486	−	1.31687i	0.166220	−	0.0488066i
$729$	3.52589	−	24.5231i	0.130588	−	0.908263i
$730$	−13.5608	+	15.6500i	−0.501908	+	0.579232i
$731$	−23.2700	+	14.9547i	−0.860671	+	0.553120i
$732$	−0.635049	−	0.732886i	−0.0234721	−	0.0270882i
$733$	−29.9371	−	8.79032i	−1.10575	−	0.324678i	−0.322616	−	0.946530i	$-0.604562\pi$
$733$	−29.9371	−	8.79032i	−1.10575	−	0.324678i	−0.783135	+	0.621852i	$0.786381\pi$
$734$	3.09331	−	6.77340i	0.114176	−	0.250011i
$735$	−0.380174			−0.0140229
$736$	−4.78768	−	0.279507i	−0.176476	−	0.0103028i
$737$	−71.7090			−2.64143
$738$	−6.49601	+	14.2243i	−0.239121	+	0.523603i
$739$	5.77023	+	1.69429i	0.212261	+	0.0623256i	0.386134	−	0.922443i	$-0.373810\pi$
$739$	5.77023	+	1.69429i	0.212261	+	0.0623256i	−0.173873	+	0.984768i	$0.555628\pi$
$740$	11.3929	+	13.1481i	0.418810	+	0.483332i
$741$	−4.65123	+	2.98916i	−0.170867	+	0.109810i
$742$	−3.45906	+	3.99197i	−0.126986	+	0.146550i
$743$	−1.69328	+	11.7771i	−0.0621206	+	0.432058i	0.934899	+	0.354913i	$0.115490\pi$
$743$	−1.69328	+	11.7771i	−0.0621206	+	0.432058i	−0.997020	+	0.0771451i	$0.975420\pi$
$744$	0.0515553	−	0.0151380i	0.00189011	−	0.000554986i
$745$	27.8949	+	17.9270i	1.02199	+	0.656793i
$746$	−2.84364	−	19.7779i	−0.104113	−	0.724121i
$747$	14.2622	+	31.2298i	0.521826	+	1.14264i
$748$	10.2226	+	22.3844i	0.373776	+	0.818455i
$749$	1.01049	+	7.02814i	0.0369227	+	0.256803i
$750$	2.08919	+	1.34264i	0.0762863	+	0.0490262i
$751$	37.2368	−	10.9337i	1.35879	−	0.398977i	0.480454	−	0.877020i	$-0.340472\pi$
$751$	37.2368	−	10.9337i	1.35879	−	0.398977i	0.878337	+	0.478043i	$0.158654\pi$
$752$	−0.134527	+	0.935654i	−0.00490568	+	0.0341198i
$753$	−4.10390	+	4.73615i	−0.149554	+	0.172595i
$754$	1.61914	−	1.04056i	0.0589656	−	0.0378949i
$755$	−8.96344	−	10.3444i	−0.326213	−	0.376470i
$756$	−1.16716	−	0.342708i	−0.0424491	−	0.0124642i
$757$	11.3689	−	24.8945i	0.413210	−	0.904805i	−0.582548	−	0.812796i	$-0.697944\pi$
$757$	11.3689	−	24.8945i	0.413210	−	0.904805i	0.995758	−	0.0920081i	$-0.0293286\pi$
$758$	−21.9839			−0.798491
$759$	−3.35465	−	4.36115i	−0.121766	−	0.158300i
$760$	10.7892			0.391366
$761$	15.2166	−	33.3198i	0.551603	−	1.20784i	−0.404427	−	0.914570i	$-0.632529\pi$
$761$	15.2166	−	33.3198i	0.551603	−	1.20784i	0.956029	−	0.293271i	$-0.0947437\pi$
$762$	2.01411	+	0.591397i	0.0729636	+	0.0214240i
$763$	−7.89944	−	9.11644i	−0.285979	−	0.330037i
$764$	−2.87977	+	1.85071i	−0.104186	+	0.0669565i
$765$	15.7976	−	18.2314i	0.571162	−	0.659157i
$766$	0.577871	−	4.01918i	0.0208793	−	0.145219i
$767$	−42.5243	+	12.4863i	−1.53546	+	0.450852i
$768$	0.171747	+	0.110375i	0.00619740	+	0.00398283i
$769$	−3.85515	−	26.8132i	−0.139020	−	0.966907i	−0.933234	−	0.359269i	$-0.883026\pi$
$769$	−3.85515	−	26.8132i	−0.139020	−	0.966907i	0.794214	−	0.607638i	$-0.207883\pi$
$770$	−4.34714	−	9.51892i	−0.156660	−	0.343038i
$771$	−2.18899	−	4.79321i	−0.0788345	−	0.172623i
$772$	1.14242	+	7.94571i	0.0411166	+	0.285972i
$773$	14.2990	+	9.18940i	0.514299	+	0.330520i	0.771913	−	0.635728i	$-0.219300\pi$
$773$	14.2990	+	9.18940i	0.514299	+	0.330520i	−0.257614	+	0.966248i	$0.582936\pi$
$774$	17.9299	−	5.26471i	0.644479	−	0.189236i
$775$	−0.0573943	+	0.399186i	−0.00206167	+	0.0143392i
$776$	−11.0371	+	12.7375i	−0.396209	+	0.457249i
$777$	−1.60456	+	1.03119i	−0.0575631	+	0.0369936i
$778$	3.64955	+	4.21181i	0.130843	+	0.151001i
$779$	29.3854	+	8.62832i	1.05284	+	0.309142i
$780$	−0.738196	+	1.61642i	−0.0264317	+	0.0578773i
$781$	42.0354			1.50415
$782$	16.9755	+	12.3644i	0.607041	+	0.442150i
$783$	−0.500885			−0.0179002
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−10.2643	−	3.01387i	−0.366349	−	0.107570i
$786$	0.854347	+	0.985968i	0.0304735	+	0.0351683i
$787$	39.5472	−	25.4154i	1.40971	−	0.905963i	0.409725	−	0.912209i	$-0.365625\pi$
$787$	39.5472	−	25.4154i	1.40971	−	0.905963i	0.999980	+	0.00624663i	$0.00198838\pi$
$788$	14.4663	−	16.6950i	0.515340	−	0.594734i
$789$	0.354100	−	2.46282i	0.0126063	−	0.0876788i
$790$	24.3427	−	7.14765i	0.866073	−	0.254302i
$791$	−5.68529	−	3.65371i	−0.202145	−	0.129911i
$792$	−2.36591	−	16.4553i	−0.0840689	−	0.584712i
$793$	9.22325	+	20.1961i	0.327527	+	0.717185i
$794$	4.87458	+	10.6738i	0.172992	+	0.378800i
$795$	−0.285787	−	1.98769i	−0.0101358	−	0.0704961i
$796$	−0.363066	−	0.233329i	−0.0128685	−	0.00827011i
$797$	−11.6478	+	3.42010i	−0.412586	+	0.121146i	−0.481437	−	0.876481i	$-0.659885\pi$
$797$	−11.6478	+	3.42010i	−0.412586	+	0.121146i	0.0688506	+	0.997627i	$0.478067\pi$
$798$	−0.168339	+	1.17082i	−0.00595913	+	0.0414466i
$799$	2.71072	−	3.12834i	0.0958983	−	0.110673i
$800$	−1.28907	+	0.828438i	−0.0455756	+	0.0292897i
$801$	−9.60355	−	11.0831i	−0.339325	−	0.391602i
$802$	−10.9781	−	3.22346i	−0.387650	−	0.113824i
$803$	25.9598	−	56.8441i	0.916103	−	2.00599i
$804$	2.60516			0.0918769
$805$	−7.21877	−	5.25793i	−0.254428	−	0.185318i
$806$	−1.23020			−0.0433319
$807$	−1.80988	+	3.96309i	−0.0637109	+	0.139507i
$808$	−3.60603	−	1.05883i	−0.126860	−	0.0372494i
$809$	3.16047	+	3.64738i	0.111116	+	0.128235i	0.808583	−	0.588382i	$-0.200235\pi$
$809$	3.16047	+	3.64738i	0.111116	+	0.128235i	−0.697467	+	0.716617i	$0.745689\pi$
$810$	−13.5141	+	8.68498i	−0.474837	+	0.305159i
$811$	11.2012	−	12.9269i	0.393327	−	0.453923i	−0.524201	−	0.851594i	$-0.675636\pi$
$811$	11.2012	−	12.9269i	0.393327	−	0.453923i	0.917528	+	0.397671i	$0.130181\pi$
$812$	0.0586004	−	0.407575i	0.00205647	−	0.0143031i
$813$	0.849993	−	0.249580i	0.0298106	−	0.00875317i
$814$	−44.1666	−	28.3842i	−1.54804	−	0.994865i
$815$	−1.85218	−	12.8822i	−0.0648790	−	0.451244i
$816$	−0.371384	−	0.813217i	−0.0130010	−	0.0284683i
$817$	−15.2035	−	33.2911i	−0.531904	−	1.16471i
$818$	−3.32224	−	23.1067i	−0.116159	−	0.807907i
$819$	11.6327	+	7.47586i	0.406478	+	0.261228i
$820$	9.44452	−	2.77316i	0.329817	−	0.0968430i
$821$	−1.57846	+	10.9784i	−0.0550886	+	0.383150i	0.943561	+	0.331199i	$0.107453\pi$
$821$	−1.57846	+	10.9784i	−0.0550886	+	0.383150i	−0.998650	+	0.0519511i	$0.983456\pi$
$822$	0.136587	−	0.157630i	0.00476403	−	0.00549799i
$823$	37.1033	−	23.8448i	1.29334	−	0.831179i	0.300870	−	0.953665i	$-0.402723\pi$
$823$	37.1033	−	23.8448i	1.29334	−	0.831179i	0.992470	+	0.122486i	$0.0390867\pi$
$824$	−10.8565	−	12.5291i	−0.378204	−	0.436471i
$825$	−1.68678	−	0.495284i	−0.0587262	−	0.0172436i
$826$	−3.93886	+	8.62489i	−0.137050	+	0.300098i
$827$	12.6023			0.438224			0.219112	−	0.975700i	$-0.429684\pi$
$827$	12.6023			0.438224			0.219112	+	0.975700i	$0.429684\pi$
$828$	−8.65021	−	11.2455i	−0.300615	−	0.390809i
$829$	52.7652			1.83261			0.916306	−	0.400479i	$-0.131156\pi$
$829$	52.7652			1.83261			0.916306	+	0.400479i	$0.131156\pi$
$830$	8.97759	−	19.6582i	0.311617	−	0.682345i
$831$	−2.16049	−	0.634377i	−0.0749466	−	0.0220063i
$832$	−3.06095	−	3.53252i	−0.106119	−	0.122468i
$833$	−3.68387	+	2.36748i	−0.127638	+	0.0820282i
$834$	−0.740461	+	0.854538i	−0.0256401	+	0.0295902i
$835$	4.36261	−	30.3426i	0.150974	−	1.05005i
$836$	−31.2403	+	9.17297i	−1.08047	+	0.317254i
$837$	0.269328	+	0.173087i	0.00930935	+	0.00598276i
$838$	3.85874	+	26.8381i	0.133298	+	0.927107i
$839$	6.42074	+	14.0595i	0.221669	+	0.485386i	0.987493	−	0.157663i	$-0.0503961\pi$
$839$	6.42074	+	14.0595i	0.221669	+	0.485386i	−0.765824	+	0.643050i	$0.777669\pi$
$840$	0.157930	+	0.345819i	0.00544911	+	0.0119319i
$841$	4.10300	+	28.5370i	0.141483	+	0.984034i
$842$	−4.27981	−	2.75046i	−0.147492	−	0.0947872i
$843$	−1.55846	+	0.457607i	−0.0536764	+	0.0157608i
$844$	−1.88452	+	13.1071i	−0.0648679	+	0.451166i
$845$	10.7899	−	12.4523i	0.371185	−	0.428371i
$846$	−2.35250	+	1.51186i	−0.0808808	+	0.0519789i
$847$	13.4767	+	15.5530i	0.463065	+	0.534406i
$848$	5.06816	+	1.48815i	0.174041	+	0.0511032i
$849$	1.80706	−	3.95692i	0.0620182	−	0.135801i
$850$	6.71008			0.230154
$851$	−44.7291	−	2.61130i	−1.53329	−	0.0895143i
$852$	−1.52713			−0.0523186
$853$	10.1505	−	22.2264i	0.347545	−	0.761018i	−0.652450	−	0.757832i	$-0.726259\pi$
$853$	10.1505	−	22.2264i	0.347545	−	0.761018i	0.999995	−	0.00318612i	$-0.00101417\pi$
$854$	4.55760	+	1.33823i	0.155958	+	0.0457934i
$855$	20.9018	+	24.1220i	0.714826	+	0.824954i
$856$	5.97325	−	3.83877i	0.204161	−	0.131207i
$857$	4.00039	−	4.61670i	0.136651	−	0.157703i	−0.683299	−	0.730138i	$-0.739456\pi$
$857$	4.00039	−	4.61670i	0.136651	−	0.157703i	0.819950	+	0.572435i	$0.194001\pi$
$858$	0.763174	−	5.30799i	0.0260543	−	0.181212i
$859$	−20.9632	+	6.15534i	−0.715254	+	0.210017i	−0.619058	−	0.785345i	$-0.712486\pi$
$859$	−20.9632	+	6.15534i	−0.715254	+	0.210017i	−0.0961955	+	0.995362i	$0.530667\pi$
$860$	−9.89551	−	6.35946i	−0.337434	−	0.216856i
$861$	0.153579	+	1.06817i	0.00523397	+	0.0364031i
$862$	6.02052	+	13.1831i	0.205060	+	0.449018i
$863$	20.9652	+	45.9073i	0.713662	+	1.56270i	0.822578	+	0.568652i	$0.192535\pi$
$863$	20.9652	+	45.9073i	0.713662	+	1.56270i	−0.108916	+	0.994051i	$0.534738\pi$
$864$	0.173116	+	1.20405i	0.00588953	+	0.0409626i
$865$	0.248933	+	0.159980i	0.00846399	+	0.00543948i
$866$	−11.7950	+	3.46331i	−0.400809	+	0.117688i
$867$	−0.0632177	+	0.439689i	−0.00214699	+	0.0149326i
$868$	−0.172352	+	0.198905i	−0.00585001	+	0.00675128i
$869$	−64.4076	+	41.3922i	−2.18488	+	1.40413i
$870$	0.102514	+	0.118307i	0.00347554	+	0.00401099i
$871$	−57.2295	−	16.8041i	−1.93915	−	0.569385i
$872$	−5.01106	+	10.9727i	−0.169696	+	0.371582i
$873$	−49.8599			−1.68750
$874$	−19.3893	+	19.9035i	−0.655851	+	0.673244i
$875$	−12.1643			−0.411228
$876$	−0.943111	+	2.06513i	−0.0318648	+	0.0697741i
$877$	28.6176	+	8.40288i	0.966348	+	0.283745i	0.726578	−	0.687084i	$-0.241110\pi$
$877$	28.6176	+	8.40288i	0.966348	+	0.283745i	0.239770	+	0.970830i	$0.422928\pi$
$878$	−17.6028	−	20.3148i	−0.594067	−	0.685590i
$879$	2.37640	−	1.52722i	0.0801540	−	0.0515118i
$880$	−6.85284	+	7.90860i	−0.231009	+	0.266599i
$881$	3.11762	−	21.6835i	0.105035	−	0.730535i	−0.867442	−	0.497538i	$-0.834238\pi$
$881$	3.11762	−	21.6835i	0.105035	−	0.730535i	0.972477	−	0.232997i	$-0.0748534\pi$
$882$	2.83849	−	0.833455i	0.0955768	−	0.0280639i
$883$	−21.4622	−	13.7929i	−0.722259	−	0.464168i	0.127163	−	0.991882i	$-0.459413\pi$
$883$	−21.4622	−	13.7929i	−0.722259	−	0.464168i	−0.849422	+	0.527714i	$0.823049\pi$
$884$	2.91296	+	20.2601i	0.0979734	+	0.681420i
$885$	−1.49745	−	3.27896i	−0.0503363	−	0.110221i
$886$	−2.10693	−	4.61352i	−0.0707835	−	0.154994i
$887$	−0.453787	−	3.15616i	−0.0152367	−	0.105973i	0.980784	−	0.195097i	$-0.0625023\pi$
$887$	−0.453787	−	3.15616i	−0.0152367	−	0.105973i	−0.996021	+	0.0891241i	$0.971593\pi$
$888$	1.60456	+	1.03119i	0.0538454	+	0.0346043i
$889$	−9.86552	+	2.89678i	−0.330879	+	0.0971549i
$890$	−1.31373	+	9.13722i	−0.0440364	+	0.306280i
$891$	31.7462	−	36.6371i	1.06354	−	1.22739i
$892$	15.5508	−	9.99390i	0.520679	−	0.334620i
$893$	3.58656	+	4.13911i	0.120020	+	0.138510i
$894$	3.48806	+	1.02419i	0.116658	+	0.0342539i
$895$	−1.17599	+	2.57506i	−0.0393091	+	0.0860749i
$896$	−1.00000			−0.0334077
$897$	−1.65530	−	4.26667i	−0.0552688	−	0.142460i
$898$	−2.30948			−0.0770684
$899$	−0.0450195	+	0.0985789i	−0.00150148	+	0.00328779i
$900$	−4.34949	−	1.27712i	−0.144983	−	0.0425708i
$901$	−15.1473	−	17.4809i	−0.504629	−	0.582373i
$902$	−24.9890	+	16.0594i	−0.832042	+	0.534721i
$903$	0.844509	−	0.974616i	0.0281035	−	0.0324332i
$904$	−0.961780	+	6.68932i	−0.0319883	+	0.222484i
$905$	−46.1246	+	13.5434i	−1.53323	+	0.450198i
$906$	−1.26240	−	0.811295i	−0.0419404	−	0.0269535i
$907$	0.0513153	+	0.356906i	0.00170390	+	0.0118509i	0.990656	−	0.136387i	$-0.0435490\pi$
$907$	0.0513153	+	0.356906i	0.00170390	+	0.0118509i	−0.988952	+	0.148238i	$0.952640\pi$
$908$	2.93457	+	6.42582i	0.0973872	+	0.213248i
$909$	−4.61865	−	10.1134i	−0.153191	−	0.335442i
$910$	−1.23873	−	8.61555i	−0.0410635	−	0.285603i
$911$	16.8208	+	10.8101i	0.557297	+	0.358153i	0.788770	−	0.614688i	$-0.210718\pi$
$911$	16.8208	+	10.8101i	0.557297	+	0.358153i	−0.231473	+	0.972841i	$0.574354\pi$
$912$	1.13495	−	0.333250i	0.0375818	−	0.0110350i
$913$	−9.28135	+	64.5532i	−0.307168	+	2.13640i
$914$	−7.42784	+	8.57219i	−0.245691	+	0.283543i
$915$	−1.51916	+	0.976307i	−0.0502220	+	0.0322757i
$916$	2.39773	+	2.76712i	0.0792231	+	0.0914283i
$917$	−6.13145	−	1.80036i	−0.202478	−	0.0594530i
$918$	2.21282	−	4.84541i	0.0730340	−	0.159922i
$919$	−47.7628			−1.57555			−0.787774	−	0.615964i	$-0.788767\pi$
$919$	−47.7628			−1.57555			−0.787774	+	0.615964i	$0.788767\pi$
$920$	−1.78400	+	8.75065i	−0.0588166	+	0.288500i
$921$	5.08101			0.167425
$922$	−11.6635	+	25.5396i	−0.384118	+	0.841102i
$923$	33.5476	+	9.85047i	1.10423	+	0.324232i
$924$	−0.751303	−	0.867050i	−0.0247161	−	0.0285238i
$925$	−12.0432	+	7.73971i	−0.395979	+	0.254480i
$926$	−16.6087	+	19.1674i	−0.545795	+	0.629880i
$927$	6.97969	−	48.5448i	0.229243	−	1.59442i
$928$	−0.395087	+	0.116008i	−0.0129694	+	0.00380815i
$929$	38.3482	+	24.6449i	1.25816	+	0.808573i	0.988032	−	0.154250i	$-0.0492961\pi$
$929$	38.3482	+	24.6449i	1.25816	+	0.808573i	0.270133	+	0.962823i	$0.412932\pi$
$930$	−0.0142397	−	0.0990393i	−0.000466938	−	0.00324763i
$931$	−2.40687	−	5.27031i	−0.0788820	−	0.172727i
$932$	8.44660	+	18.4955i	0.276678	+	0.605840i
$933$	−0.454895	−	3.16386i	−0.0148926	−	0.103580i
$934$	−10.7298	−	6.89565i	−0.351091	−	0.225632i
$935$	43.9684	−	12.9103i	1.43792	−	0.422212i
$936$	1.96790	−	13.6870i	0.0643227	−	0.447374i
$937$	−2.08896	+	2.41079i	−0.0682435	+	0.0787572i	−0.788845	−	0.614593i	$-0.789320\pi$
$937$	−2.08896	+	2.41079i	−0.0682435	+	0.0787572i	0.720601	+	0.693350i	$0.243866\pi$
$938$	−10.7349	+	6.89890i	−0.350507	+	0.225257i
$939$	−4.64041	−	5.35532i	−0.151434	−	0.174764i
$940$	1.68896	+	0.495923i	0.0550878	+	0.0161752i
$941$	12.5018	−	27.3752i	0.407548	−	0.892406i	−0.588901	−	0.808206i	$-0.700439\pi$
$941$	12.5018	−	27.3752i	0.407548	−	0.892406i	0.996449	−	0.0842007i	$-0.0268337\pi$
$942$	−1.17282			−0.0382126
$943$	−11.8569	+	22.4065i	−0.386115	+	0.729656i
$944$	9.48174			0.308604
$945$	−0.940998	+	2.06050i	−0.0306107	+	0.0670280i
$946$	34.0594	+	10.0007i	1.10737	+	0.325152i
$947$	−27.5521	−	31.7968i	−0.895324	−	1.03326i	−0.999252	−	0.0386737i	$-0.987687\pi$
$947$	−27.5521	−	31.7968i	−0.895324	−	1.03326i	0.103928	−	0.994585i	$-0.466859\pi$
$948$	2.33990	−	1.50376i	0.0759965	−	0.0488400i
$949$	34.0387	−	39.2828i	1.10494	−	1.27517i
$950$	−1.26349	+	8.78776i	−0.0409930	+	0.285113i
$951$	−2.88288	+	0.846490i	−0.0934838	+	0.0274493i
$952$	3.68387	+	2.36748i	0.119395	+	0.0767304i
$953$	1.42431	+	9.90628i	0.0461379	+	0.320896i	0.999800	+	0.0200152i	$0.00637147\pi$
$953$	1.42431	+	9.90628i	0.0461379	+	0.320896i	−0.953662	+	0.300881i	$0.902719\pi$
$954$	6.49137	+	14.2141i	0.210166	+	0.460199i
$955$	2.64808	+	5.79849i	0.0856900	+	0.187635i
$956$	−3.40551	−	23.6858i	−0.110142	−	0.766055i
$957$	−0.397414	−	0.255403i	−0.0128466	−	0.00825600i
$958$	28.3454	−	8.32296i	0.915798	−	0.268903i
$959$	−0.145395	+	1.01124i	−0.00469504	+	0.0326547i
$960$	0.248961	−	0.287317i	0.00803519	−	0.00927310i
$961$	−26.0206	+	16.7224i	−0.839374	+	0.539433i
$962$	−28.5970	−	33.0027i	−0.922005	−	1.06405i
$963$	20.1544	+	5.91788i	0.649468	+	0.190701i
$964$	−9.51907	+	20.8439i	−0.306589	+	0.671336i
$965$	14.9484			0.481207
$966$	−0.921767	−	0.330127i	−0.0296574	−	0.0106217i
$967$	−26.7494			−0.860202			−0.430101	−	0.902781i	$-0.641522\pi$
$967$	−26.7494			−0.860202			−0.430101	+	0.902781i	$0.641522\pi$
$968$	8.54904	−	18.7198i	0.274776	−	0.601677i
$969$	−4.96996	−	1.45931i	−0.159658	−	0.0468798i
$970$	20.5529	+	23.7194i	0.659915	+	0.761583i
$971$	23.3687	−	15.0182i	0.749937	−	0.481956i	−0.108996	−	0.994042i	$-0.534764\pi$
$971$	23.3687	−	15.0182i	0.749937	−	0.481956i	0.858934	+	0.512087i	$0.171127\pi$
$972$	−3.54311	+	4.08896i	−0.113645	+	0.131154i
$973$	0.788206	−	5.48210i	0.0252687	−	0.175748i
$974$	25.9687	−	7.62510i	0.832091	−	0.244324i
$975$	−1.23012	−	0.790552i	−0.0393955	−	0.0253179i
$976$	−0.675997	−	4.70166i	−0.0216381	−	0.150497i
$977$	−23.2604	−	50.9332i	−0.744166	−	1.62950i	−0.776577	−	0.630022i	$-0.783046\pi$
$977$	−23.2604	−	50.9332i	−0.744166	−	1.62950i	0.0324111	−	0.999475i	$-0.489681\pi$
$978$	−0.592734	−	1.29791i	−0.0189535	−	0.0415024i
$979$	−3.96452	−	27.5738i	−0.126707	−	0.881264i
$980$	−1.56656	−	1.00676i	−0.0500418	−	0.0321599i
$981$	−34.2400	+	10.0538i	−1.09320	+	0.320992i
$982$	3.69988	−	25.7332i	0.118068	−	0.821180i
$983$	9.97222	−	11.5086i	0.318064	−	0.367066i	−0.574093	−	0.818790i	$-0.694645\pi$
$983$	9.97222	−	11.5086i	0.318064	−	0.367066i	0.892158	+	0.451724i	$0.149191\pi$
$984$	0.907840	−	0.583434i	0.0289409	−	0.0185992i
$985$	−26.9386	−	31.0889i	−0.858337	−	0.990573i
$986$	1.73009	+	0.508001i	0.0550974	+	0.0161780i
$987$	−0.0801685	+	0.175545i	−0.00255179	+	0.00558765i
$988$	−27.0818			−0.861587
$989$	29.5148	−	6.82623i	0.938517	−	0.217062i
$990$	−30.9576			−0.983897
$991$	−1.96341	+	4.29927i	−0.0623698	+	0.136571i	−0.938250	−	0.345957i	$-0.887554\pi$
$991$	−1.96341	+	4.29927i	−0.0623698	+	0.136571i	0.875880	+	0.482528i	$0.160281\pi$
$992$	0.252528	+	0.0741489i	0.00801777	+	0.00235423i
$993$	3.05572	+	3.52649i	0.0969703	+	0.111910i
$994$	6.29274	−	4.04410i	0.199594	−	0.128271i
$995$	−0.526293	+	0.607374i	−0.0166846	+	0.0192551i
$996$	0.337188	−	2.34519i	0.0106842	−	0.0743103i
$997$	−55.2325	+	16.2177i	−1.74923	+	0.513621i	−0.990468	−	0.137745i	$-0.956015\pi$
$997$	−55.2325	+	16.2177i	−1.74923	+	0.513621i	−0.758764	+	0.651366i	$0.774196\pi$
$998$	−18.1439	−	11.6604i	−0.574335	−	0.369103i
$999$	1.61734	+	11.2489i	0.0511705	+	0.355898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.29.3	✓	40
23.2	even	11		7406.2.a.bu.1.10		20
23.4	even	11	inner	322.2.i.d.211.3	yes	40
23.21	odd	22		7406.2.a.bv.1.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.29.3	✓	40	1.1	even	1	trivial
322.2.i.d.211.3	yes	40	23.4	even	11	inner
7406.2.a.bu.1.10		20	23.2	even	11
7406.2.a.bv.1.10		20	23.21	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.195887 - 0.0575176i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.56656 + 1.00676i) q^{5} +(-0.133694 + 0.154291i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.48870 - 1.59939i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.195887 - 0.0575176i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.56656 + 1.00676i) q^{5} +(-0.133694 + 0.154291i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-2.48870 - 1.59939i) q^{9} +(0.265014 + 1.84322i) q^{10} +(-2.33445 - 5.11174i) q^{11} +(0.0848097 + 0.185707i) q^{12} +(-0.665208 - 4.62662i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(0.364774 - 0.107107i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(2.86765 - 3.30944i) q^{17} +(-2.48870 + 1.59939i) q^{18} +(3.79419 + 4.37873i) q^{19} +(1.78674 + 0.524634i) q^{20} +(-0.0848097 + 0.185707i) q^{21} -5.61956 q^{22} +(-4.17877 + 2.35328i) q^{23} +0.204157 q^{24} +(-0.636551 + 1.39385i) q^{25} +(-4.48486 - 1.31687i) q^{26} +(0.796593 + 0.919317i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-0.269649 + 0.311192i) q^{29} +(0.0541044 - 0.376305i) q^{30} +(0.252528 - 0.0741489i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.163274 + 1.13559i) q^{33} +(-1.81911 - 3.98330i) q^{34} +(0.773573 + 1.69389i) q^{35} +(0.421013 + 2.92821i) q^{36} +(7.85944 + 5.05095i) q^{37} +(5.55920 - 1.63233i) q^{38} +(-0.135807 + 0.944555i) q^{39} +(1.21946 - 1.40733i) q^{40} +(4.44678 - 2.85777i) q^{41} +(0.133694 + 0.154291i) q^{42} +(-6.06085 - 1.77963i) q^{43} +(-2.33445 + 5.11174i) q^{44} +5.50889 q^{45} +(0.404696 + 4.77873i) q^{46} +0.945275 q^{47} +(0.0848097 - 0.185707i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(1.00346 + 1.15805i) q^{50} +(-0.752086 + 0.483336i) q^{51} +(-3.06095 + 3.53252i) q^{52} +(0.751725 - 5.22836i) q^{53} +(1.16716 - 0.342708i) q^{54} +(8.80337 + 5.65758i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-0.491378 - 1.07597i) q^{57} +(0.171054 + 0.374555i) q^{58} +(-1.34939 - 9.38523i) q^{59} +(-0.319823 - 0.205538i) q^{60} +(-4.55760 + 1.33823i) q^{61} +(0.0374557 - 0.260510i) q^{62} +(-1.93729 + 2.23575i) q^{63} +(0.841254 - 0.540641i) q^{64} +(5.70000 + 6.57816i) q^{65} +(1.10080 + 0.323224i) q^{66} +(5.30094 - 11.6074i) q^{67} -4.37902 q^{68} +(0.953920 - 0.220624i) q^{69} +1.86217 q^{70} +(-3.10738 + 6.80422i) q^{71} +(2.83849 + 0.833455i) q^{72} +(7.28226 + 8.40417i) q^{73} +(7.85944 - 5.05095i) q^{74} +(0.204863 - 0.236424i) q^{75} +(0.824557 - 5.73492i) q^{76} +(-5.39193 + 1.58321i) q^{77} +(0.802782 + 0.515916i) q^{78} +(-1.93891 - 13.4854i) q^{79} +(-0.773573 - 1.69389i) q^{80} +(3.58363 + 7.84705i) q^{81} +(-0.752262 - 5.23210i) q^{82} +(-9.76304 - 6.27433i) q^{83} +(0.195887 - 0.0575176i) q^{84} +(-1.16050 + 8.07148i) q^{85} +(-4.13658 + 4.77386i) q^{86} +(0.0707198 - 0.0454488i) q^{87} +(3.68003 + 4.24698i) q^{88} +(4.75641 + 1.39661i) q^{89} +(2.28848 - 5.01107i) q^{90} -4.67420 q^{91} +(4.51500 + 1.61703i) q^{92} -0.0537318 q^{93} +(0.392682 - 0.859853i) q^{94} +(-10.3522 - 3.03967i) q^{95} +(-0.133694 - 0.154291i) q^{96} +(14.1786 - 9.11202i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-2.36591 + 16.4553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

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