LMFDB - Embedded newform 855.2.ci.a.182.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(182,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 8]))

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

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

chi := DirichletCharacter("855.182");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.ci (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			182.2
Character	$\chi$	$=$	855.182
Dual form			855.2.ci.a.653.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64907 - 0.709817i) q^{2} +(-1.67832 + 0.428065i) q^{3} +(4.78169 + 2.76071i) q^{4} +(1.47253 - 1.68275i) q^{5} +(4.74984 + 0.0573243i) q^{6} +(3.03796 - 0.814018i) q^{7} +(-6.82893 - 6.82893i) q^{8} +(2.63352 - 1.43686i) q^{9} +O(q^{10})$	\(q+(-2.64907 - 0.709817i) q^{2} +(-1.67832 + 0.428065i) q^{3} +(4.78169 + 2.76071i) q^{4} +(1.47253 - 1.68275i) q^{5} +(4.74984 + 0.0573243i) q^{6} +(3.03796 - 0.814018i) q^{7} +(-6.82893 - 6.82893i) q^{8} +(2.63352 - 1.43686i) q^{9} +(-5.09528 + 3.41250i) q^{10} +(-1.77399 - 1.02421i) q^{11} +(-9.20697 - 2.58648i) q^{12} +(-1.12363 - 4.19343i) q^{13} -8.62557 q^{14} +(-1.75105 + 3.45454i) q^{15} +(7.72161 + 13.3742i) q^{16} +(-1.42132 - 5.30444i) q^{17} +(-7.99629 + 1.93703i) q^{18} +(-4.14005 + 1.36380i) q^{19} +(11.6868 - 3.98117i) q^{20} +(-4.75021 + 2.66663i) q^{21} +(3.97242 + 3.97242i) q^{22} +(-4.15693 + 1.11385i) q^{23} +(14.3844 + 8.53790i) q^{24} +(-0.663308 - 4.95581i) q^{25} +11.9063i q^{26} +(-3.80482 + 3.53883i) q^{27} +(16.7738 + 4.49453i) q^{28} +6.22149 q^{29} +(7.09075 - 7.90839i) q^{30} +(-2.74897 - 4.76136i) q^{31} +(-5.96273 - 22.2532i) q^{32} +(3.41575 + 0.959574i) q^{33} +15.0607i q^{34} +(3.10369 - 6.31079i) q^{35} +(16.5594 + 0.399759i) q^{36} +(0.509969 + 0.509969i) q^{37} +(11.9353 - 0.674123i) q^{38} +(3.68087 + 6.55693i) q^{39} +(-21.5472 + 1.43559i) q^{40} -0.412405i q^{41} +(14.4765 - 3.69231i) q^{42} +(5.39773 + 1.44632i) q^{43} +(-5.65510 - 9.79493i) q^{44} +(1.46006 - 6.54738i) q^{45} +11.8026 q^{46} +(-7.59819 + 7.59819i) q^{47} +(-18.6844 - 19.1409i) q^{48} +(2.50438 - 1.44590i) q^{49} +(-1.76056 + 13.5991i) q^{50} +(4.65608 + 8.29413i) q^{51} +(6.20401 - 23.1537i) q^{52} +(-1.36931 + 5.11032i) q^{53} +(12.5912 - 6.67390i) q^{54} +(-4.33575 + 1.47700i) q^{55} +(-26.3049 - 15.1871i) q^{56} +(6.36454 - 4.06111i) q^{57} +(-16.4812 - 4.41612i) q^{58} +3.15625 q^{59} +(-17.9099 + 11.6844i) q^{60} -8.03628 q^{61} +(3.90253 + 14.5644i) q^{62} +(6.83089 - 6.50886i) q^{63} +32.2964i q^{64} +(-8.71108 - 4.28417i) q^{65} +(-8.36744 - 4.96654i) q^{66} +(-4.55998 + 1.22184i) q^{67} +(7.84770 - 29.2880i) q^{68} +(6.49986 - 3.64883i) q^{69} +(-12.7014 + 14.5147i) q^{70} +(-0.487998 - 0.281746i) q^{71} +(-27.7963 - 8.17190i) q^{72} +(1.00714 + 3.75870i) q^{73} +(-0.988961 - 1.71293i) q^{74} +(3.23465 + 8.03349i) q^{75} +(-23.5615 - 4.90822i) q^{76} +(-6.22303 - 1.66745i) q^{77} +(-5.09666 - 19.9825i) q^{78} +(-0.240647 + 0.138937i) q^{79} +(33.8758 + 6.70040i) q^{80} +(4.87086 - 7.56801i) q^{81} +(-0.292732 + 1.09249i) q^{82} +(3.92282 - 1.05112i) q^{83} +(-30.0758 - 0.362975i) q^{84} +(-11.0190 - 5.41922i) q^{85} +(-13.2723 - 7.66279i) q^{86} +(-10.4417 + 2.66320i) q^{87} +(5.12016 + 19.1087i) q^{88} +(-1.22481 - 2.12143i) q^{89} +(-8.51524 + 16.3081i) q^{90} +(-6.82706 - 11.8248i) q^{91} +(-22.9522 - 6.15001i) q^{92} +(6.65183 + 6.81435i) q^{93} +(25.5215 - 14.7348i) q^{94} +(-3.80142 + 8.97492i) q^{95} +(19.5332 + 34.7956i) q^{96} +(-4.86899 + 18.1713i) q^{97} +(-7.66060 + 2.05265i) q^{98} +(-6.14348 - 0.148309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7}+O(q^{10}) $ 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7	$ 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7} - 4 q^{10} - 24 q^{11} + 2 q^{12} + 2 q^{13} + 10 q^{15} + 212 q^{16} + 18 q^{17} - 24 q^{18} - 12 q^{20} - 4 q^{21} - 20 q^{22} + 18 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{28} + 2 q^{30} - 8 q^{31} - 30 q^{32} + 10 q^{33} - 68 q^{36} - 16 q^{37} + 30 q^{38} - 36 q^{40} - 14 q^{42} + 2 q^{43} + 6 q^{45} - 56 q^{46} + 42 q^{48} - 108 q^{50} + 12 q^{51} - 34 q^{52} - 14 q^{55} - 24 q^{56} - 78 q^{57} - 12 q^{58} - 42 q^{60} - 8 q^{61} - 12 q^{62} + 92 q^{63} - 84 q^{65} - 52 q^{66} + 2 q^{67} - 60 q^{68} - 84 q^{70} - 118 q^{72} - 4 q^{73} + 98 q^{75} - 60 q^{76} - 12 q^{77} + 92 q^{78} + 120 q^{80} - 12 q^{81} + 4 q^{82} - 12 q^{83} + 2 q^{85} - 264 q^{86} + 102 q^{87} + 48 q^{88} - 34 q^{90} - 8 q^{91} + 54 q^{92} - 52 q^{93} - 36 q^{95} + 96 q^{96} + 2 q^{97} + 42 q^{98}+O(q^{100}) $ 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7 - 4 * q^10 - 24 * q^11 + 2 * q^12 + 2 * q^13 + 10 * q^15 + 212 * q^16 + 18 * q^17 - 24 * q^18 - 12 * q^20 - 4 * q^21 - 20 * q^22 + 18 * q^23 - 4 * q^25 - 2 * q^27 - 20 * q^28 + 2 * q^30 - 8 * q^31 - 30 * q^32 + 10 * q^33 - 68 * q^36 - 16 * q^37 + 30 * q^38 - 36 * q^40 - 14 * q^42 + 2 * q^43 + 6 * q^45 - 56 * q^46 + 42 * q^48 - 108 * q^50 + 12 * q^51 - 34 * q^52 - 14 * q^55 - 24 * q^56 - 78 * q^57 - 12 * q^58 - 42 * q^60 - 8 * q^61 - 12 * q^62 + 92 * q^63 - 84 * q^65 - 52 * q^66 + 2 * q^67 - 60 * q^68 - 84 * q^70 - 118 * q^72 - 4 * q^73 + 98 * q^75 - 60 * q^76 - 12 * q^77 + 92 * q^78 + 120 * q^80 - 12 * q^81 + 4 * q^82 - 12 * q^83 + 2 * q^85 - 264 * q^86 + 102 * q^87 + 48 * q^88 - 34 * q^90 - 8 * q^91 + 54 * q^92 - 52 * q^93 - 36 * q^95 + 96 * q^96 + 2 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.64907	−	0.709817i	−1.87318	−	0.501916i	−0.999892	−	0.0147053i	$-0.995319\pi$
$2$	−2.64907	−	0.709817i	−1.87318	−	0.501916i	−0.873284	−	0.487211i	$-0.838014\pi$
$3$	−1.67832	+	0.428065i	−0.968979	+	0.247144i
$3$	−1.67832	+	0.428065i	−0.968979	+	0.247144i
$4$	4.78169	+	2.76071i	2.39084	+	1.38035i
$5$	1.47253	−	1.68275i	0.658536	−	0.752550i
$5$	1.47253	−	1.68275i	0.658536	−	0.752550i
$6$	4.74984	+	0.0573243i	1.93911	+	0.0234025i
$7$	3.03796	−	0.814018i	1.14824	−	0.307670i	0.365980	−	0.930623i	$-0.380734\pi$
$7$	3.03796	−	0.814018i	1.14824	−	0.307670i	0.782259	+	0.622953i	$0.214067\pi$
$8$	−6.82893	−	6.82893i	−2.41439	−	2.41439i
$9$	2.63352	−	1.43686i	0.877840	−	0.478954i
$10$	−5.09528	+	3.41250i	−1.61127	+	1.07913i
$11$	−1.77399	−	1.02421i	−0.534877	−	0.308812i	0.208123	−	0.978103i	$-0.433265\pi$
$11$	−1.77399	−	1.02421i	−0.534877	−	0.308812i	−0.743000	+	0.669291i	$0.766598\pi$
$12$	−9.20697	−	2.58648i	−2.65782	−	0.746653i
$13$	−1.12363	−	4.19343i	−0.311638	−	1.16305i	−0.927079	−	0.374866i	$-0.877689\pi$
$13$	−1.12363	−	4.19343i	−0.311638	−	1.16305i	0.615441	−	0.788183i	$-0.288978\pi$
$14$	−8.62557			−2.30528
$15$	−1.75105	+	3.45454i	−0.452119	+	0.891957i
$16$	7.72161	+	13.3742i	1.93040	+	3.34356i
$17$	−1.42132	−	5.30444i	−0.344721	−	1.28652i	−0.892938	−	0.450180i	$-0.851360\pi$
$17$	−1.42132	−	5.30444i	−0.344721	−	1.28652i	0.548217	−	0.836336i	$-0.315307\pi$
$18$	−7.99629	+	1.93703i	−1.88474	+	0.456563i
$19$	−4.14005	+	1.36380i	−0.949794	+	0.312877i
$19$	−4.14005	+	1.36380i	−0.949794	+	0.312877i
$20$	11.6868	−	3.98117i	2.61324	−	0.890216i
$21$	−4.75021	+	2.66663i	−1.03658	+	0.581906i
$22$	3.97242	+	3.97242i	0.846922	+	0.846922i
$23$	−4.15693	+	1.11385i	−0.866780	+	0.232253i	−0.664695	−	0.747115i	$-0.731438\pi$
$23$	−4.15693	+	1.11385i	−0.866780	+	0.232253i	−0.202085	+	0.979368i	$0.564772\pi$
$24$	14.3844	+	8.53790i	2.93619	+	1.74279i
$25$	−0.663308	−	4.95581i	−0.132662	−	0.991161i
$26$			11.9063i			2.33501i
$27$	−3.80482	+	3.53883i	−0.732238	+	0.681049i
$28$	16.7738	+	4.49453i	3.16996	+	0.849387i
$29$	6.22149			1.15530			0.577651	−	0.816284i	$-0.303970\pi$
$29$	6.22149			1.15530			0.577651	+	0.816284i	$0.303970\pi$
$30$	7.09075	−	7.90839i	1.29459	−	1.44387i
$31$	−2.74897	−	4.76136i	−0.493730	−	0.855166i	0.506244	−	0.862390i	$-0.331034\pi$
$31$	−2.74897	−	4.76136i	−0.493730	−	0.855166i	−0.999974	+	0.00722484i	$0.997700\pi$
$32$	−5.96273	−	22.2532i	−1.05407	−	3.93385i
$33$	3.41575	+	0.959574i	0.594606	+	0.167040i
$34$			15.0607i			2.58289i
$35$	3.10369	−	6.31079i	0.524620	−	1.06672i
$36$	16.5594	+	0.399759i	2.75991	+	0.0666265i
$37$	0.509969	+	0.509969i	0.0838385	+	0.0838385i	0.747782	−	0.663944i	$-0.231119\pi$
$37$	0.509969	+	0.509969i	0.0838385	+	0.0838385i	−0.663944	+	0.747782i	$0.731119\pi$
$38$	11.9353	−	0.674123i	1.93617	−	0.109357i
$39$	3.68087	+	6.55693i	0.589410	+	1.04995i
$40$	−21.5472	+	1.43559i	−3.40691	+	0.226986i
$41$		−	0.412405i		−	0.0644068i	−0.999481	−	0.0322034i	$-0.989748\pi$
$41$		−	0.412405i		−	0.0644068i	0.999481	−	0.0322034i	$-0.0102524\pi$
$42$	14.4765	−	3.69231i	2.23377	−	0.569735i
$43$	5.39773	+	1.44632i	0.823146	+	0.220561i	0.645721	−	0.763573i	$-0.276557\pi$
$43$	5.39773	+	1.44632i	0.823146	+	0.220561i	0.177425	+	0.984134i	$0.443223\pi$
$44$	−5.65510	−	9.79493i	−0.852539	−	1.47664i
$45$	1.46006	−	6.54738i	0.217653	−	0.976026i
$46$	11.8026			1.74020
$47$	−7.59819	+	7.59819i	−1.10831	+	1.10831i	−0.114937	+	0.993373i	$0.536667\pi$
$47$	−7.59819	+	7.59819i	−1.10831	+	1.10831i	−0.993373	+	0.114937i	$0.963333\pi$
$48$	−18.6844	−	19.1409i	−2.69686	−	2.76275i
$49$	2.50438	−	1.44590i	0.357768	−	0.206558i
$50$	−1.76056	+	13.5991i	−0.248981	+	1.92320i
$51$	4.65608	+	8.29413i	0.651981	+	1.16141i
$52$	6.20401	−	23.1537i	0.860341	−	3.21084i
$53$	−1.36931	+	5.11032i	−0.188089	+	0.701957i	0.805859	+	0.592107i	$0.201704\pi$
$53$	−1.36931	+	5.11032i	−0.188089	+	0.701957i	−0.993948	+	0.109850i	$0.964963\pi$
$54$	12.5912	−	6.67390i	1.71344	−	0.908202i
$55$	−4.33575	+	1.47700i	−0.584632	+	0.199158i
$56$	−26.3049	−	15.1871i	−3.51513	−	2.02946i
$57$	6.36454	−	4.06111i	0.843004	−	0.537907i
$58$	−16.4812	−	4.41612i	−2.16408	−	0.579865i
$59$	3.15625			0.410909			0.205454	−	0.978667i	$-0.434133\pi$
$59$	3.15625			0.410909			0.205454	+	0.978667i	$0.434133\pi$
$60$	−17.9099	+	11.6844i	−2.31216	+	1.50845i
$61$	−8.03628			−1.02894			−0.514470	−	0.857508i	$-0.672011\pi$
$61$	−8.03628			−1.02894			−0.514470	+	0.857508i	$0.672011\pi$
$62$	3.90253	+	14.5644i	0.495622	+	1.84969i
$63$	6.83089	−	6.50886i	0.860611	−	0.820039i
$64$			32.2964i			4.03705i
$65$	−8.71108	−	4.28417i	−1.08048	−	0.531386i
$66$	−8.36744	−	4.96654i	−1.02996	−	0.611338i
$67$	−4.55998	+	1.22184i	−0.557090	+	0.149272i	−0.526369	−	0.850256i	$-0.676447\pi$
$67$	−4.55998	+	1.22184i	−0.557090	+	0.149272i	−0.0307207	+	0.999528i	$0.509780\pi$
$68$	7.84770	−	29.2880i	0.951674	−	3.55170i
$69$	6.49986	−	3.64883i	0.782492	−	0.439267i
$70$	−12.7014	+	14.5147i	−1.51811	+	1.73484i
$71$	−0.487998	−	0.281746i	−0.0579147	−	0.0334371i	0.470763	−	0.882260i	$-0.343979\pi$
$71$	−0.487998	−	0.281746i	−0.0579147	−	0.0334371i	−0.528678	+	0.848823i	$0.677312\pi$
$72$	−27.7963	−	8.17190i	−3.27583	−	0.963067i
$73$	1.00714	+	3.75870i	0.117877	+	0.439923i	0.999486	−	0.0320576i	$-0.0102060\pi$
$73$	1.00714	+	3.75870i	0.117877	+	0.439923i	−0.881609	+	0.471980i	$0.843539\pi$
$74$	−0.988961	−	1.71293i	−0.114964	−	0.199124i
$75$	3.23465	+	8.03349i	0.373505	+	0.927628i
$76$	−23.5615	−	4.90822i	−2.70269	−	0.563012i
$77$	−6.22303	−	1.66745i	−0.709180	−	0.190024i
$78$	−5.09666	−	19.9825i	−0.577083	−	2.26258i
$79$	−0.240647	+	0.138937i	−0.0270749	+	0.0156317i	−0.513476	−	0.858104i	$-0.671643\pi$
$79$	−0.240647	+	0.138937i	−0.0270749	+	0.0156317i	0.486401	+	0.873735i	$0.338309\pi$
$80$	33.8758	+	6.70040i	3.78743	+	0.749127i
$81$	4.87086	−	7.56801i	0.541206	−	0.840890i
$82$	−0.292732	+	1.09249i	−0.0323268	+	0.120645i
$83$	3.92282	−	1.05112i	0.430585	−	0.115375i	−0.0370157	−	0.999315i	$-0.511785\pi$
$83$	3.92282	−	1.05112i	0.430585	−	0.115375i	0.467601	+	0.883940i	$0.345118\pi$
$84$	−30.0758	−	0.362975i	−3.28154	−	0.0396039i
$85$	−11.0190	−	5.41922i	−1.19518	−	0.587797i
$86$	−13.2723	−	7.66279i	−1.43119	−	0.826300i
$87$	−10.4417	+	2.66320i	−1.11946	+	0.285525i
$88$	5.12016	+	19.1087i	0.545811	+	2.03699i
$89$	−1.22481	−	2.12143i	−0.129830	−	0.224872i	0.793781	−	0.608204i	$-0.208110\pi$
$89$	−1.22481	−	2.12143i	−0.129830	−	0.224872i	−0.923610	+	0.383332i	$0.874776\pi$
$90$	−8.51524	+	16.3081i	−0.897585	+	1.71903i
$91$	−6.82706	−	11.8248i	−0.715670	−	1.23958i
$92$	−22.9522	−	6.15001i	−2.39293	−	0.641183i
$93$	6.65183	+	6.81435i	0.689763	+	0.706615i
$94$	25.5215	−	14.7348i	2.63234	−	1.51978i
$95$	−3.80142	+	8.97492i	−0.390018	+	0.920807i
$96$	19.5332	+	34.7956i	1.99360	+	3.55131i
$97$	−4.86899	+	18.1713i	−0.494371	+	1.84502i	0.0391522	+	0.999233i	$0.487534\pi$
$97$	−4.86899	+	18.1713i	−0.494371	+	1.84502i	−0.533523	+	0.845785i	$0.679132\pi$
$98$	−7.66060	+	2.05265i	−0.773837	+	0.207349i
$99$	−6.14348	−	0.148309i	−0.617443	−	0.0149056i
$100$	10.5098	−	25.5283i	1.05098	−	2.55283i
$101$			10.2559i			1.02050i	0.860027	+	0.510249i	$0.170447\pi$
$101$			10.2559i			1.02050i	−0.860027	+	0.510249i	$0.829553\pi$
$102$	−6.44697	−	25.2767i	−0.638345	−	2.50277i
$103$	−0.792012	−	0.212219i	−0.0780392	−	0.0209106i	0.219588	−	0.975593i	$-0.429529\pi$
$103$	−0.792012	−	0.212219i	−0.0780392	−	0.0209106i	−0.297627	+	0.954682i	$0.596195\pi$
$104$	−20.9635	+	36.3098i	−2.05564	+	3.56047i
$105$	−2.50756	+	11.9201i	−0.244713	+	1.16328i
$106$	7.25478	−	12.5657i	0.704647	−	1.22048i
$107$	−8.98186	+	8.98186i	−0.868310	+	0.868310i	−0.992285	−	0.123976i	$-0.960436\pi$
$107$	−8.98186	+	8.98186i	−0.868310	+	0.868310i	0.123976	+	0.992285i	$0.460436\pi$
$108$	−27.9632	+	6.41759i	−2.69076	+	0.617533i
$109$	2.24535	+	1.29635i	0.215065	+	0.124168i	0.603663	−	0.797239i	$-0.293707\pi$
$109$	2.24535	+	1.29635i	0.215065	+	0.124168i	−0.388598	+	0.921407i	$0.627040\pi$
$110$	12.5341	−	0.835087i	1.19508	−	0.0796224i
$111$	−1.07419	−	0.637592i	−0.101958	−	0.0605176i
$112$	34.3448	+	34.3448i	3.24528	+	3.24528i
$113$	4.52030	−	16.8700i	0.425234	−	1.58699i	−0.338177	−	0.941082i	$-0.609810\pi$
$113$	4.52030	−	16.8700i	0.425234	−	1.58699i	0.763411	−	0.645912i	$-0.223523\pi$
$114$	−19.7428	+	6.24050i	−1.84908	+	0.584477i
$115$	−4.24688	+	8.63526i	−0.396024	+	0.805242i
$116$	29.7492	+	17.1757i	2.76215	+	1.59473i
$117$	−8.98447	−	9.42899i	−0.830615	−	0.871710i
$118$	−8.36113	−	2.24036i	−0.769705	−	0.206242i
$119$	−8.63582	−	14.9577i	−0.791644	−	1.37117i
$120$	35.5486	−	11.6330i	3.24513	−	1.06194i
$121$	−3.40198	−	5.89240i	−0.309271	−	0.535673i
$122$	21.2887	+	5.70429i	1.92739	+	0.516442i
$123$	0.176536	+	0.692147i	0.0159177	+	0.0624088i
$124$		−	30.3565i		−	2.72609i
$125$	−9.31613	−	6.18139i	−0.833260	−	0.552881i
$126$	−22.7156	+	12.3937i	−2.02367	+	1.10412i
$127$	4.73080	−	17.6556i	0.419791	−	1.56668i	−0.355251	−	0.934771i	$-0.615605\pi$
$127$	4.73080	−	17.6556i	0.419791	−	1.56668i	0.775042	−	0.631910i	$-0.217729\pi$
$128$	10.9990	−	41.0490i	0.972186	−	3.62825i
$129$	−9.67824	−	0.116804i	−0.852121	−	0.0102840i
$130$	20.0353	+	17.5323i	1.75721	+	1.53769i
$131$		−	4.97761i		−	0.434896i	−0.976072	−	0.217448i	$-0.930227\pi$
$131$		−	4.97761i		−	0.434896i	0.976072	−	0.217448i	$-0.0697732\pi$
$132$	13.6839	+	14.0183i	1.19103	+	1.22013i
$133$	−11.4671	+	7.51324i	−0.994328	+	0.651481i
$134$	12.9470			1.11845
$135$	0.352263	+	11.6136i	0.0303180	+	0.999540i
$136$	−26.5175	+	45.9297i	−2.27386	+	3.93844i
$137$	4.42429	−	4.42429i	0.377993	−	0.377993i	−0.492385	−	0.870378i	$-0.663875\pi$
$137$	4.42429	−	4.42429i	0.377993	−	0.377993i	0.870378	+	0.492385i	$0.163875\pi$
$138$	−19.8086	+	5.05230i	−1.68622	+	0.430080i
$139$	−1.75822	−	1.01511i	−0.149131	−	0.0861006i	0.423578	−	0.905860i	$-0.360774\pi$
$139$	−1.75822	−	1.01511i	−0.149131	−	0.0861006i	−0.572709	+	0.819759i	$0.694107\pi$
$140$	32.2632	−	21.6079i	2.72673	−	1.82620i
$141$	9.49968	−	16.0047i	0.800017	−	1.34784i
$142$	1.09275	+	1.09275i	0.0917018	+	0.0917018i
$143$	−2.30166	+	8.58993i	−0.192475	+	0.718326i
$144$	39.5519	+	24.1264i	3.29599	+	2.01053i
$145$	9.16133	−	10.4692i	0.760807	−	0.869422i
$146$		−	10.6720i		−	0.883217i
$147$	−3.58421	+	3.49873i	−0.295620	+	0.288570i
$148$	1.03064	+	3.84639i	0.0847179	+	0.316172i
$149$	11.0240			0.903123			0.451562	−	0.892240i	$-0.350867\pi$
$149$	11.0240			0.903123			0.451562	+	0.892240i	$0.350867\pi$
$150$	−2.86652	−	23.5773i	−0.234050	−	1.92508i
$151$	6.98500	−	12.0984i	0.568431	−	0.984551i	−0.428291	−	0.903641i	$-0.640884\pi$
$151$	6.98500	−	12.0984i	0.568431	−	0.984551i	0.996721	−	0.0809100i	$-0.0257827\pi$
$152$	37.5854	+	18.9588i	3.04858	+	1.53777i
$153$	−11.3648	−	11.9271i	−0.918791	−	0.964250i
$154$	15.3017	+	8.83441i	1.23304	+	0.711897i
$155$	−12.0601	−	2.38541i	−0.968693	−	0.191601i
$156$	−0.501031	+	41.5150i	−0.0401146	+	3.32386i
$157$	−10.9823	−	10.9823i	−0.876485	−	0.876485i	0.116684	−	0.993169i	$-0.462773\pi$
$157$	−10.9823	−	10.9823i	−0.876485	−	0.876485i	−0.993169	+	0.116684i	$0.962773\pi$
$158$	0.736110	−	0.197240i	0.0585618	−	0.0156916i
$159$	0.110584	−	9.16291i	0.00876990	−	0.726666i
$160$	−46.2270	−	22.7348i	−3.65456	−	1.79734i
$161$	−11.7219	+	6.76763i	−0.923814	+	0.533364i
$162$	−18.2751	+	16.5908i	−1.43583	+	1.30349i
$163$	−1.03076	+	1.03076i	−0.0807355	+	0.0807355i	−0.746321	−	0.665586i	$-0.768182\pi$
$163$	−1.03076	+	1.03076i	−0.0807355	+	0.0807355i	0.665586	+	0.746321i	$0.268182\pi$
$164$	1.13853	−	1.97199i	0.0889042	−	0.153987i
$165$	6.64452	−	4.33486i	0.517275	−	0.337468i
$166$	−11.1379			−0.864470
$167$	2.18053	+	8.13785i	0.168735	+	0.629726i	0.997534	+	0.0701805i	$0.0223575\pi$
$167$	2.18053	+	8.13785i	0.168735	+	0.629726i	−0.828800	+	0.559545i	$0.810976\pi$
$168$	50.6491	+	14.2287i	3.90766	+	1.09776i
$169$	−5.06399	+	2.92370i	−0.389538	+	0.224900i
$170$	25.3434	+	22.1774i	1.94375	+	1.70093i
$171$	−8.94333	+	9.54028i	−0.683913	+	0.729563i
$172$	21.8174	+	21.8174i	1.66356	+	1.66356i
$173$	−4.24179	+	15.8306i	−0.322498	+	1.20358i	0.594306	+	0.804239i	$0.297427\pi$
$173$	−4.24179	+	15.8306i	−0.322498	+	1.20358i	−0.916804	+	0.399338i	$0.869240\pi$
$174$	29.5511	+	0.356642i	2.24026	+	0.0270370i
$175$	−6.04922	−	14.5156i	−0.457278	−	1.09727i
$176$		−	31.6343i		−	2.38452i
$177$	−5.29720	+	1.35108i	−0.398162	+	0.101553i
$178$	1.73878	+	6.48922i	0.130327	+	0.486388i
$179$	7.11526			0.531820			0.265910	−	0.963998i	$-0.414328\pi$
$179$	7.11526			0.531820			0.265910	+	0.963998i	$0.414328\pi$
$180$	25.0570	−	27.2768i	1.86764	−	2.03309i
$181$	−12.7227	−	22.0363i	−0.945667	−	1.63794i	−0.754410	−	0.656404i	$-0.772077\pi$
$181$	−12.7227	−	22.0363i	−0.945667	−	1.63794i	−0.191257	−	0.981540i	$-0.561257\pi$
$182$	9.69191	+	36.1707i	0.718412	+	2.68115i
$183$	13.4875	−	3.44005i	0.997022	−	0.254296i
$184$	35.9938	+	20.7810i	2.65349	+	1.53200i
$185$	1.60910	−	0.107206i	0.118303	−	0.00788198i
$186$	−12.7842	−	22.7733i	−0.937386	−	1.66982i
$187$	−2.91147	+	10.8657i	−0.212908	+	0.794582i
$188$	−57.3086	+	15.3558i	−4.17966	+	1.11994i
$189$	−8.67821	+	13.8480i	−0.631247	+	1.00729i
$190$	16.4408	−	21.0769i	1.19274	−	1.52908i
$191$	−18.5470	−	10.7081i	−1.34201	−	0.774811i	−0.354910	−	0.934901i	$-0.615488\pi$
$191$	−18.5470	−	10.7081i	−1.34201	−	0.774811i	−0.987102	+	0.160090i	$0.948822\pi$
$192$	−13.8250	−	54.2037i	−0.997730	−	3.91181i
$193$	15.2626	−	15.2626i	1.09862	−	1.09862i	0.104051	−	0.994572i	$-0.466819\pi$
$193$	15.2626	−	15.2626i	1.09862	−	1.09862i	0.994572	−	0.104051i	$-0.0331806\pi$
$194$	25.7966	−	44.6810i	1.85209	−	3.20791i
$195$	16.4539	+	3.46130i	1.17829	+	0.247869i
$196$	15.9669			1.14049
$197$	9.31985	−	9.31985i	0.664012	−	0.664012i	−0.292311	−	0.956323i	$-0.594424\pi$
$197$	9.31985	−	9.31985i	0.664012	−	0.664012i	0.956323	+	0.292311i	$0.0944244\pi$
$198$	16.1693	+	4.75363i	1.14910	+	0.337826i
$199$	13.5770	−	7.83867i	0.962446	−	0.555669i	0.0655211	−	0.997851i	$-0.479129\pi$
$199$	13.5770	−	7.83867i	0.962446	−	0.555669i	0.896925	+	0.442183i	$0.145796\pi$
$200$	−29.3132	+	38.3725i	−2.07275	+	2.71335i
$201$	7.13007	−	4.00261i	0.502917	−	0.282322i
$202$	7.27979	−	27.1685i	0.512204	−	1.91157i
$203$	18.9006	−	5.06441i	1.32656	−	0.355452i
$204$	−0.633775	+	52.5140i	−0.0443731	+	3.67672i
$205$	−0.693975	−	0.607279i	−0.0484693	−	0.0424142i
$206$	1.94746	+	1.12437i	0.135686	+	0.0783383i
$207$	−9.34692	+	8.90627i	−0.649656	+	0.619029i
$208$	47.4077	−	47.4077i	3.28713	−	3.28713i
$209$	8.74123	+	1.82093i	0.604643	+	0.125956i
$210$	15.1038	−	29.7973i	1.04226	−	2.05621i
$211$	18.3090			1.26044			0.630220	−	0.776416i	$-0.282965\pi$
$211$	18.3090			1.26044			0.630220	+	0.776416i	$0.282965\pi$
$212$	−20.6557	+	20.6557i	−1.41864	+	1.41864i
$213$	0.939622	+	0.263965i	0.0643819	+	0.0180866i
$214$	30.1691	−	17.4181i	2.06232	−	1.19068i
$215$	10.3821	−	6.95329i	0.708054	−	0.474211i
$216$	50.1493	+	1.81641i	3.41223	+	0.123591i
$217$	−12.2271	−	12.2271i	−0.830029	−	0.830029i
$218$	−5.02791	−	5.02791i	−0.340533	−	0.340533i
$219$	−3.29928	−	5.87718i	−0.222944	−	0.397143i
$220$	−24.8097	−	4.90719i	−1.67267	−	0.330843i
$221$	−20.6468	+	11.9204i	−1.38885	+	0.801854i
$222$	2.39304	+	2.45151i	0.160610	+	0.164534i
$223$	12.0490	+	3.22853i	0.806863	+	0.216198i	0.638595	−	0.769543i	$-0.279516\pi$
$223$	12.0490	+	3.22853i	0.806863	+	0.216198i	0.168268	+	0.985741i	$0.446183\pi$
$224$	−36.2290	−	62.7506i	−2.42066	−	4.19270i
$225$	−8.86764	−	12.0981i	−0.591176	−	0.806542i
$226$	−23.9492	+	41.4812i	−1.59308	+	2.75929i
$227$	5.51322	+	20.5756i	0.365925	+	1.36565i	0.866162	+	0.499763i	$0.166580\pi$
$227$	5.51322	+	20.5756i	0.365925	+	1.36565i	−0.500237	+	0.865889i	$0.666754\pi$
$228$	41.6448	−	1.84829i	2.75799	−	0.122406i
$229$	−14.3483	+	8.28401i	−0.948165	+	0.547423i	−0.892510	−	0.451027i	$-0.851058\pi$
$229$	−14.3483	+	8.28401i	−0.948165	+	0.547423i	−0.0556543	+	0.998450i	$0.517724\pi$
$230$	17.3797	−	19.8609i	1.14599	−	1.30959i
$231$	11.1580	+	0.134662i	0.734143	+	0.00886014i
$232$	−42.4861	−	42.4861i	−2.78935	−	2.78935i
$233$	−16.1901	+	4.33813i	−1.06065	+	0.284201i	−0.746647	−	0.665221i	$-0.768337\pi$
$233$	−16.1901	+	4.33813i	−1.06065	+	0.284201i	−0.314004	+	0.949422i	$0.601671\pi$
$234$	17.1077	+	31.3554i	1.11836	+	2.04977i
$235$	1.59730	+	23.9744i	0.104196	+	1.56392i
$236$	15.0922	+	8.71349i	0.982419	+	0.567200i
$237$	0.344408	−	0.336194i	0.0223717	−	0.0218382i
$238$	12.2597	+	45.7538i	0.794678	+	2.96578i
$239$	−2.30102	−	3.98549i	−0.148841	−	0.257800i	0.781959	−	0.623330i	$-0.214221\pi$
$239$	−2.30102	−	3.98549i	−0.148841	−	0.257800i	−0.930799	+	0.365531i	$0.880888\pi$
$240$	−59.7227	+	3.25564i	−3.85508	+	0.210151i
$241$	−15.8197			−1.01904			−0.509519	−	0.860460i	$-0.670177\pi$
$241$	−15.8197			−1.01904			−0.509519	+	0.860460i	$0.670177\pi$
$242$	4.82956	+	18.0242i	0.310456	+	1.15864i
$243$	−4.93526	+	14.7866i	−0.316597	+	0.948560i
$244$	−38.4270	−	22.1858i	−2.46004	−	1.42030i
$245$	1.25468	−	6.34338i	0.0801583	−	0.405264i
$246$	0.0236408	−	1.95886i	0.00150728	−	0.124892i
$247$	10.3709	+	15.8286i	0.659883	+	1.00715i
$248$	−13.7424	+	51.2875i	−0.872646	+	3.25676i
$249$	−6.13380	+	3.44333i	−0.388714	+	0.218212i
$250$	20.2914	+	22.9877i	1.28334	+	1.45387i
$251$	−24.1812	+	13.9610i	−1.52630	+	0.881211i	−0.526789	+	0.849996i	$0.676604\pi$
$251$	−24.1812	+	13.9610i	−1.52630	+	0.881211i	−0.999513	+	0.0312142i	$0.990063\pi$
$252$	50.6322	−	12.2652i	3.18953	−	0.772636i
$253$	8.51516	+	2.28163i	0.535343	+	0.143445i
$254$	−25.0645	+	43.4129i	−1.57268	+	2.72397i
$255$	20.8132	+	4.37834i	1.30337	+	0.274182i
$256$	−25.9781	+	44.9953i	−1.62363	+	2.81221i
$257$	−5.04653	−	18.8339i	−0.314794	−	1.17483i	−0.924181	−	0.381954i	$-0.875251\pi$
$257$	−5.04653	−	18.8339i	−0.314794	−	1.17483i	0.609388	−	0.792873i	$-0.291415\pi$
$258$	25.5554	+	7.17919i	1.59101	+	0.446957i
$259$	1.96439	+	1.13414i	0.122061	+	0.0704721i
$260$	−29.8263	−	44.5343i	−1.84975	−	2.76190i
$261$	16.3844	−	8.93942i	1.01417	−	0.553336i
$262$	−3.53319	+	13.1860i	−0.218281	+	0.814637i
$263$	2.94183	−	10.9790i	0.181401	−	0.676997i	−0.813972	−	0.580904i	$-0.802699\pi$
$263$	2.94183	−	10.9790i	0.181401	−	0.676997i	0.995372	−	0.0960922i	$-0.0306344\pi$
$264$	−16.7730	−	29.8788i	−1.03231	−	1.83891i
$265$	6.58306	+	9.82931i	0.404394	+	0.603810i
$266$	35.7103	−	11.7635i	2.18954	−	0.721269i
$267$	2.96374	+	3.03615i	0.181378	+	0.185809i
$268$	−25.1775	−	6.74630i	−1.53796	−	0.412096i
$269$	−1.22733	+	2.12579i	−0.0748314	+	0.129612i	−0.901013	−	0.433792i	$-0.857175\pi$
$269$	−1.22733	+	2.12579i	−0.0748314	+	0.129612i	0.826182	+	0.563404i	$0.190509\pi$
$270$	7.31036	−	31.0153i	0.444894	−	1.88753i
$271$	0.775299	−	1.34286i	0.0470961	−	0.0815728i	−0.841516	−	0.540232i	$-0.818337\pi$
$271$	0.775299	−	1.34286i	0.0470961	−	0.0815728i	0.888612	+	0.458659i	$0.151670\pi$
$272$	59.9679	−	59.9679i	3.63609	−	3.63609i
$273$	16.5198	+	16.9234i	0.999822	+	1.02425i
$274$	−14.8607	+	8.57983i	−0.897768	+	0.518326i
$275$	−3.89910	+	9.47091i	−0.235125	+	0.571117i
$276$	41.1537	+	0.496671i	2.47716	+	0.0298961i
$277$	23.5964	−	6.32263i	1.41777	−	0.379890i	0.533077	−	0.846067i	$-0.321036\pi$
$277$	23.5964	−	6.32263i	1.41777	−	0.379890i	0.884691	+	0.466177i	$0.154369\pi$
$278$	3.93712	+	3.93712i	0.236133	+	0.236133i
$279$	−14.0809	−	8.58925i	−0.843001	−	0.514225i
$280$	−64.2908	+	21.9011i	−3.84211	+	1.30884i
$281$		−	9.06233i		−	0.540613i	−0.962774	−	0.270307i	$-0.912875\pi$
$281$		−	9.06233i		−	0.540613i	0.962774	−	0.270307i	$-0.0871251\pi$
$282$	−36.5257	+	35.6546i	−2.17508	+	2.12320i
$283$	−9.97441	+	9.97441i	−0.592917	+	0.592917i	−0.938418	−	0.345501i	$-0.887709\pi$
$283$	−9.97441	+	9.97441i	−0.592917	+	0.592917i	0.345501	+	0.938418i	$0.387709\pi$
$284$	−1.55564	−	2.69444i	−0.0923100	−	0.159886i
$285$	2.53815	−	16.6901i	0.150347	−	0.988633i
$286$	12.1945	−	21.1216i	0.721078	−	1.24894i
$287$	−0.335705	−	1.25287i	−0.0198160	−	0.0739544i
$288$	−47.6778	−	50.0367i	−2.80944	−	2.94844i
$289$	−11.3945	+	6.57861i	−0.670264	+	0.386977i
$290$	−31.7003	+	21.2309i	−1.86150	+	1.24672i
$291$	0.393216	−	32.5816i	0.0230508	−	1.90996i
$292$	−5.56085	+	20.7534i	−0.325424	+	1.21450i
$293$	−0.923766	+	3.44754i	−0.0539670	+	0.201408i	−0.987645	−	0.156705i	$-0.949913\pi$
$293$	−0.923766	+	3.44754i	−0.0539670	+	0.201408i	0.933678	+	0.358112i	$0.116580\pi$
$294$	11.9783	−	6.72424i	0.698587	−	0.392166i
$295$	4.64767	−	5.31119i	0.270598	−	0.309229i
$296$		−	6.96509i		−	0.404838i
$297$	10.3742	−	2.38090i	0.601973	−	0.138154i
$298$	−29.2034	−	7.82504i	−1.69171	−	0.453292i
$299$	9.34167	+	16.1803i	0.540243	+	0.935728i
$300$	−6.71104	+	47.3436i	−0.387462	+	2.73338i
$301$	17.5754			1.01303
$302$	−27.0914	+	27.0914i	−1.55893	+	1.55893i
$303$	−4.39018	−	17.2126i	−0.252209	−	0.988841i
$304$	−50.2077	−	44.8393i	−2.87961	−	2.57171i
$305$	−11.8337	+	13.5231i	−0.677594	+	0.774329i
$306$	21.6402	+	39.6627i	1.23709	+	2.26737i
$307$	3.59765	−	0.963988i	0.205329	−	0.0550177i	−0.154689	−	0.987963i	$-0.549437\pi$
$307$	3.59765	−	0.963988i	0.205329	−	0.0550177i	0.360017	+	0.932946i	$0.382771\pi$
$308$	−25.1532	−	25.1532i	−1.43324	−	1.43324i
$309$	1.42009	+	0.0171386i	0.0807863	+	0.000974984i
$310$	30.2550	+	14.8796i	1.71837	+	0.845105i
$311$	1.02211	−	0.590114i	0.0579584	−	0.0334623i	−0.470741	−	0.882272i	$-0.656013\pi$
$311$	1.02211	−	0.590114i	0.0579584	−	0.0334623i	0.528699	+	0.848809i	$0.322680\pi$
$312$	19.6405	−	69.9132i	1.11192	−	3.95806i
$313$	8.24682	−	8.24682i	0.466138	−	0.466138i	−0.434523	−	0.900661i	$-0.643083\pi$
$313$	8.24682	−	8.24682i	0.466138	−	0.466138i	0.900661	+	0.434523i	$0.143083\pi$
$314$	21.2975	+	36.8884i	1.20189	+	2.08173i
$315$	−0.894097	−	21.0792i	−0.0503766	−	1.18768i
$316$	−1.53426			−0.0863091
$317$	6.20352	−	6.20352i	0.348424	−	0.348424i	−0.511098	−	0.859522i	$-0.670761\pi$
$317$	6.20352	−	6.20352i	0.348424	−	0.348424i	0.859522	+	0.511098i	$0.170761\pi$
$318$	−6.79693	+	24.1947i	−0.381153	+	1.35677i
$319$	−11.0368	−	6.37213i	−0.617945	−	0.356771i
$320$	54.3468	+	47.5574i	3.03808	+	2.65854i
$321$	11.2296	−	18.9193i	0.626776	−	1.05597i
$322$	35.8559	−	9.60756i	1.99817	−	0.535408i
$323$	13.1185	+	20.0223i	0.729935	+	1.11407i
$324$	44.1840	−	22.7408i	2.45467	−	1.26338i
$325$	−20.0365	+	8.35001i	−1.11143	+	0.463175i
$326$	3.46221	−	1.99891i	0.191754	−	0.110709i
$327$	−4.32334	−	1.21454i	−0.239081	−	0.0671642i
$328$	−2.81628	+	2.81628i	−0.155503	+	0.155503i
$329$	−16.8979	+	29.2680i	−0.931612	+	1.61360i
$330$	−20.6788	+	6.76696i	−1.13833	+	0.372509i
$331$	−3.74973	+	6.49472i	−0.206104	+	0.356982i	−0.950484	−	0.310774i	$-0.899412\pi$
$331$	−3.74973	+	6.49472i	−0.206104	+	0.356982i	0.744380	+	0.667756i	$0.232745\pi$
$332$	21.6595	+	5.80365i	1.18872	+	0.318517i
$333$	2.07577	+	0.610259i	0.113752	+	0.0334420i
$334$		−	23.1055i		−	1.26428i
$335$	−4.65865	+	9.47251i	−0.254529	+	0.517538i
$336$	−72.3434	−	42.9397i	−3.94665	−	2.34256i
$337$	−17.6838	−	17.6838i	−0.963300	−	0.963300i	0.0360500	−	0.999350i	$-0.488522\pi$
$337$	−17.6838	−	17.6838i	−0.963300	−	0.963300i	−0.999350	+	0.0360500i	$0.988522\pi$
$338$	15.4902	−	4.15058i	0.842554	−	0.225762i
$339$	−0.365056	+	30.2482i	−0.0198271	+	1.64286i
$340$	−37.7285	−	56.3333i	−2.04612	−	3.05510i
$341$			11.2621i			0.609878i
$342$	30.4634	−	18.9248i	1.64727	−	1.02333i
$343$	−9.13637	+	9.13637i	−0.493318	+	0.493318i
$344$	−26.9839	−	46.7375i	−1.45487	−	2.51992i
$345$	3.43117	−	16.3107i	0.184728	−	0.878137i
$346$	22.4736	−	38.9255i	1.20819	−	2.09265i
$347$	−2.23708	+	2.23708i	−0.120093	+	0.120093i	−0.764599	−	0.644506i	$-0.777063\pi$
$347$	−2.23708	+	2.23708i	−0.120093	+	0.120093i	0.644506	+	0.764599i	$0.277063\pi$
$348$	−57.2811	−	16.0918i	−3.07059	−	0.862609i
$349$	−19.7676	−	11.4129i	−1.05814	−	0.610916i	−0.133221	−	0.991086i	$-0.542532\pi$
$349$	−19.7676	−	11.4129i	−1.05814	−	0.610916i	−0.924916	+	0.380170i	$0.875865\pi$
$350$	5.72140	+	42.7466i	0.305822	+	2.28490i
$351$	19.1150	+	11.9789i	1.02029	+	0.639388i
$352$	−12.2142	+	45.5841i	−0.651020	+	2.42964i
$353$	25.1329	−	6.73433i	1.33769	−	0.358432i	0.482112	−	0.876110i	$-0.339870\pi$
$353$	25.1329	−	6.73433i	1.33769	−	0.358432i	0.855576	+	0.517677i	$0.173203\pi$
$354$	14.9917	+	0.180930i	0.796799	+	0.00961631i
$355$	−1.19270	+	0.406300i	−0.0633019	+	0.0215642i
$356$		−	13.5254i		−	0.716844i
$357$	20.8965	+	21.4071i	1.10596	+	1.13298i
$358$	−18.8488	−	5.05053i	−0.996192	−	0.266929i
$359$	2.47848	−	4.29286i	0.130809	−	0.226569i	−0.793179	−	0.608988i	$-0.791576\pi$
$359$	2.47848	−	4.29286i	0.130809	−	0.226569i	0.923989	+	0.382419i	$0.124909\pi$
$360$	−54.6822	+	34.7410i	−2.88201	+	1.83101i
$361$	15.2801	−	11.2924i	0.804216	−	0.594337i
$362$	18.0615	+	67.4064i	0.949291	+	3.54280i
$363$	8.23194	+	8.43307i	0.432065	+	0.442621i
$364$		−	75.3901i		−	3.95151i
$365$	7.80801	+	3.84003i	0.408690	+	0.200997i
$366$	−38.1710	−	0.460674i	−1.99523	−	0.0240798i
$367$	−5.28952	−	5.28952i	−0.276111	−	0.276111i	0.555443	−	0.831554i	$-0.312549\pi$
$367$	−5.28952	−	5.28952i	−0.276111	−	0.276111i	−0.831554	+	0.555443i	$0.812549\pi$
$368$	−46.9950	−	46.9950i	−2.44979	−	2.44979i
$369$	−0.592569	−	1.08608i	−0.0308479	−	0.0565389i
$370$	−4.33871	−	0.858167i	−0.225559	−	0.0446140i
$371$			16.6396i			0.863884i
$372$	12.9945	+	50.9479i	0.673736	+	2.64152i
$373$	−13.8805	−	3.71926i	−0.718704	−	0.192576i	−0.119111	−	0.992881i	$-0.538004\pi$
$373$	−13.8805	−	3.71926i	−0.718704	−	0.192576i	−0.599593	+	0.800305i	$0.704671\pi$
$374$	15.4254	−	26.7175i	0.797627	−	1.38153i
$375$	18.2815	+	6.38645i	0.944053	+	0.329795i
$376$	103.775			5.35178
$377$	−6.99063	−	26.0894i	−0.360036	−	1.34367i
$378$	32.8187	−	30.5244i	1.68801	−	1.57001i
$379$		−	17.3198i		−	0.889657i	−0.895616	−	0.444829i	$-0.853265\pi$
$379$		−	17.3198i		−	0.889657i	0.895616	−	0.444829i	$-0.146735\pi$
$380$	−42.9544	+	32.4207i	−2.20351	+	1.66314i
$381$	−0.382056	+	31.6569i	−0.0195733	+	1.62183i
$382$	41.5315	+	41.5315i	2.12493	+	2.12493i
$383$	0.208117	+	0.208117i	0.0106343	+	0.0106343i	0.712404	−	0.701770i	$-0.247606\pi$
$383$	0.208117	+	0.208117i	0.0106343	+	0.0106343i	−0.701770	+	0.712404i	$0.747606\pi$
$384$	−0.888274	+	73.6016i	−0.0453296	+	3.75597i
$385$	−11.9695	+	8.01643i	−0.610023	+	0.408555i
$386$	−51.2652	+	29.5980i	−2.60933	+	1.50650i
$387$	16.2932	−	3.94688i	0.828229	−	0.200631i
$388$	−73.4477	+	73.4477i	−3.72874	+	3.72874i
$389$	1.34991			0.0684431			0.0342215	−	0.999414i	$-0.489105\pi$
$389$	1.34991			0.0684431			0.0342215	+	0.999414i	$0.489105\pi$
$390$	−41.1306	−	20.8485i	−2.08273	−	1.05570i
$391$	11.8167	+	20.4671i	0.597594	+	1.03506i
$392$	−26.9762	−	7.22824i	−1.36250	−	0.365081i
$393$	2.13074	+	8.35403i	0.107482	+	0.421405i
$394$	−31.3043	+	18.0736i	−1.57709	+	0.910533i
$395$	−0.120562	+	0.609538i	−0.00606615	+	0.0306692i
$396$	−28.9668	−	17.6695i	−1.45564	−	0.887928i
$397$	33.1333	−	8.87805i	1.66291	−	0.445576i	0.699727	−	0.714410i	$-0.253305\pi$
$397$	33.1333	−	8.87805i	1.66291	−	0.445576i	0.963187	+	0.268833i	$0.0866381\pi$
$398$	−41.5304	+	11.1280i	−2.08173	+	0.557798i
$399$	16.0294	−	17.5183i	0.802473	−	0.877013i
$400$	61.1583	−	47.1380i	3.05791	−	2.35690i
$401$		−	34.1720i		−	1.70647i	−0.521527	−	0.853235i	$-0.674637\pi$
$401$		−	34.1720i		−	1.70647i	0.521527	−	0.853235i	$-0.325363\pi$
$402$	−21.7292	+	5.54215i	−1.08375	+	0.276418i
$403$	−16.8776	+	16.8776i	−0.840734	+	0.840734i
$404$	−28.3135	+	49.0404i	−1.40865	+	2.43985i
$405$	−5.56259	−	19.3406i	−0.276407	−	0.961041i
$406$	−53.6639			−2.66329
$407$	−0.382363	−	1.42700i	−0.0189530	−	0.0707336i
$408$	24.8440	−	88.4360i	1.22996	−	4.37824i
$409$	28.7055	+	16.5731i	1.41940	+	0.819488i	0.996246	−	0.0865717i	$-0.0275912\pi$
$409$	28.7055	+	16.5731i	1.41940	+	0.819488i	0.423150	+	0.906060i	$0.360924\pi$
$410$	1.40733	+	2.10132i	0.0695032	+	0.103777i
$411$	−5.53149	+	9.31927i	−0.272849	+	0.459686i
$412$	−3.20128	−	3.20128i	−0.157716	−	0.157716i
$413$	9.58855	−	2.56924i	0.471822	−	0.126424i
$414$	31.0825	−	16.9587i	1.52762	−	0.833477i
$415$	4.00770	−	8.14893i	0.196730	−	0.400015i
$416$	−86.6175	+	50.0086i	−4.24677	+	2.45187i
$417$	3.38540	+	0.951047i	0.165784	+	0.0465730i
$418$	−21.8636	−	11.0284i	−1.06938	−	0.539419i
$419$	−6.37702	−	11.0453i	−0.311538	−	0.539599i	0.667158	−	0.744917i	$-0.267511\pi$
$419$	−6.37702	−	11.0453i	−0.311538	−	0.539599i	−0.978695	+	0.205317i	$0.934177\pi$
$420$	−44.8984	+	50.0756i	−2.19082	+	2.44344i
$421$	5.12027	+	8.86856i	0.249547	+	0.432227i	0.963400	−	0.268068i	$-0.0863851\pi$
$421$	5.12027	+	8.86856i	0.249547	+	0.432227i	−0.713854	+	0.700295i	$0.753052\pi$
$422$	−48.5017	−	12.9960i	−2.36103	−	0.632635i
$423$	−9.09244	+	30.9275i	−0.442090	+	1.50375i
$424$	44.2489	−	25.5471i	2.14892	−	1.24068i
$425$	−25.3450	+	10.5623i	−1.22941	+	0.512345i
$426$	−2.30176	−	1.36622i	−0.111521	−	0.0661936i
$427$	−24.4139	+	6.54168i	−1.18147	+	0.316574i
$428$	−67.7448	+	18.1522i	−3.27457	+	0.877418i
$429$	0.185881	−	15.4019i	0.00897441	−	0.743611i
$430$	−32.4385	+	11.0504i	−1.56432	+	0.532896i
$431$	19.2807	−	11.1317i	0.928716	−	0.536195i	0.0423110	−	0.999104i	$-0.486528\pi$
$431$	19.2807	−	11.1317i	0.928716	−	0.536195i	0.886405	+	0.462910i	$0.153195\pi$
$432$	−76.7085	−	23.5610i	−3.69064	−	1.13358i
$433$	0.935652	+	0.250707i	0.0449645	+	0.0120482i	0.281231	−	0.959640i	$-0.409257\pi$
$433$	0.935652	+	0.250707i	0.0449645	+	0.0120482i	−0.236267	+	0.971688i	$0.575924\pi$
$434$	23.7114	+	41.0694i	1.13819	+	1.97140i
$435$	−10.8941	+	21.4924i	−0.522334	+	1.03048i
$436$	7.15770	+	12.3975i	0.342792	+	0.593733i
$437$	15.6909	−	10.2806i	0.750595	−	0.491788i
$438$	4.56829	+	17.9110i	0.218281	+	0.855819i
$439$	1.43887	−	0.830730i	0.0686733	−	0.0396486i	−0.465270	−	0.885169i	$-0.654043\pi$
$439$	1.43887	−	0.830730i	0.0686733	−	0.0396486i	0.533944	+	0.845520i	$0.320709\pi$
$440$	39.6948	+	19.5222i	1.89238	+	0.930684i
$441$	4.51777	−	7.40626i	0.215132	−	0.352679i
$442$	63.1561	−	16.9226i	3.00403	−	0.804927i
$443$	−9.56416	−	9.56416i	−0.454407	−	0.454407i	0.442407	−	0.896814i	$-0.354125\pi$
$443$	−9.56416	−	9.56416i	−0.454407	−	0.454407i	−0.896814	+	0.442407i	$0.854125\pi$
$444$	−3.37625	−	6.01430i	−0.160230	−	0.285426i
$445$	−5.37342	−	1.06282i	−0.254724	−	0.0503827i
$446$	−29.6271	−	17.1052i	−1.40288	−	0.809955i
$447$	−18.5018	+	4.71900i	−0.875107	+	0.223201i
$448$	26.2898	+	98.1150i	1.24208	+	4.63550i
$449$	31.6541			1.49385			0.746924	−	0.664909i	$-0.231530\pi$
$449$	31.6541			1.49385			0.746924	+	0.664909i	$0.231530\pi$
$450$	14.9036	+	38.3432i	0.702561	+	1.80752i
$451$	−0.422390	+	0.731601i	−0.0198896	+	0.0344497i
$452$	68.1878	−	68.1878i	3.20728	−	3.20728i
$453$	−6.54417	+	23.2950i	−0.307472	+	1.09449i
$454$		−	58.4197i		−	2.74177i
$455$	−29.9513	−	5.92415i	−1.40414	−	0.277728i
$456$	−71.1960	−	15.7300i	−3.33406	−	0.736625i
$457$	−28.5059	+	7.63813i	−1.33345	+	0.357297i	−0.854000	−	0.520272i	$-0.825830\pi$
$457$	−28.5059	+	7.63813i	−1.33345	+	0.357297i	−0.479450	+	0.877569i	$0.659164\pi$
$458$	43.8899	−	11.7603i	2.05084	−	0.549521i
$459$	24.1794	+	15.1526i	1.12860	+	0.707264i
$460$	−44.1467	+	29.5667i	−2.05835	+	1.37855i
$461$	23.4485	−	13.5380i	1.09211	−	0.630528i	0.157970	−	0.987444i	$-0.449505\pi$
$461$	23.4485	−	13.5380i	1.09211	−	0.630528i	0.934136	+	0.356916i	$0.116172\pi$
$462$	−29.4628	−	8.27687i	−1.37073	−	0.385075i
$463$	12.3945	+	3.32110i	0.576021	+	0.154344i	0.535057	−	0.844816i	$-0.320290\pi$
$463$	12.3945	+	3.32110i	0.576021	+	0.154344i	0.0409647	+	0.999161i	$0.486957\pi$
$464$	48.0399	+	83.2076i	2.23020	+	3.86282i
$465$	21.2619	−	1.15904i	0.985996	−	0.0537493i
$466$	45.9681			2.12943
$467$	8.41520	−	8.41520i	0.389409	−	0.389409i	−0.485068	−	0.874477i	$-0.661205\pi$
$467$	8.41520	−	8.41520i	0.389409	−	0.389409i	0.874477	+	0.485068i	$0.161205\pi$
$468$	−16.9302	−	69.8900i	−0.782601	−	3.23067i
$469$	−12.8584	+	7.42380i	−0.593746	+	0.342799i
$470$	12.7861	−	64.6438i	0.589778	−	2.98179i
$471$	23.1330	+	13.7307i	1.06591	+	0.632678i
$472$	−21.5538	−	21.5538i	−0.992094	−	0.992094i
$473$	−8.09417	−	8.09417i	−0.372170	−	0.372170i
$474$	−1.15100	+	0.646136i	−0.0528671	+	0.0296780i
$475$	9.50486	+	19.6127i	0.436113	+	0.899892i
$476$		−	95.3639i		−	4.37100i
$477$	3.73673	+	15.4256i	0.171093	+	0.706292i
$478$	3.26661	+	12.1911i	0.149411	+	0.557610i
$479$	10.5561			0.482320			0.241160	−	0.970485i	$-0.422472\pi$
$479$	10.5561			0.482320			0.241160	+	0.970485i	$0.422472\pi$
$480$	87.3156	+	18.3680i	3.98539	+	0.838383i
$481$	1.56551	−	2.71154i	0.0713809	−	0.123635i
$482$	41.9076	+	11.2291i	1.90884	+	0.511471i
$483$	16.7761	−	16.3760i	0.763339	−	0.745133i
$484$		−	37.5675i		−	1.70761i
$485$	23.4081	+	34.9511i	1.06291	+	1.58705i
$486$	23.5696	−	35.6676i	1.06914	−	1.61792i
$487$	−7.22449	−	7.22449i	−0.327373	−	0.327373i	0.524214	−	0.851587i	$-0.324359\pi$
$487$	−7.22449	−	7.22449i	−0.327373	−	0.327373i	−0.851587	+	0.524214i	$0.824359\pi$
$488$	54.8792	+	54.8792i	2.48426	+	2.48426i
$489$	1.28872	−	2.17118i	0.0582777	−	0.0981842i
$490$	−7.82636	+	15.9135i	−0.353559	+	0.718898i
$491$			0.697845i			0.0314933i	0.999876	+	0.0157466i	$0.00501252\pi$
$491$			0.697845i			0.0314933i	−0.999876	+	0.0157466i	$0.994987\pi$
$492$	−1.06668	+	3.79700i	−0.0480895	+	0.171182i
$493$	−8.84273	−	33.0015i	−0.398257	−	1.48631i
$494$	−16.2378	−	49.2926i	−0.730571	−	2.21778i
$495$	−9.29604	+	10.1196i	−0.417826	+	0.454841i
$496$	42.4530	−	73.5307i	1.90620	−	3.30163i
$497$	−1.71186	−	0.458692i	−0.0767875	−	0.0205752i
$498$	18.6930	−	4.76776i	0.837653	−	0.213648i
$499$		−	2.14900i		−	0.0962025i	−0.998842	−	0.0481012i	$-0.984683\pi$
$499$		−	2.14900i		−	0.0962025i	0.998842	−	0.0481012i	$-0.0153170\pi$
$500$	−27.4818	−	55.2766i	−1.22902	−	2.47205i
$501$	−7.14316	−	12.7245i	−0.319133	−	0.568489i
$502$	73.9674	−	19.8195i	3.30133	−	0.884587i
$503$	7.25739	−	27.0850i	0.323591	−	1.20766i	−0.592129	−	0.805843i	$-0.701713\pi$
$503$	7.25739	−	27.0850i	0.323591	−	1.20766i	0.915720	−	0.401816i	$-0.131621\pi$
$504$	−91.0961	−	2.19914i	−4.05774	−	0.0979575i
$505$	17.2581	+	15.1021i	0.767975	+	0.672034i
$506$	−20.9377	−	12.0884i	−0.930795	−	0.537395i
$507$	7.24747	−	7.07462i	0.321871	−	0.314195i
$508$	71.3632	−	71.3632i	3.16623	−	3.16623i
$509$	−1.24436	+	2.15530i	−0.0551554	+	0.0955319i	−0.892285	−	0.451473i	$-0.850899\pi$
$509$	−1.24436	+	2.15530i	−0.0551554	+	0.0955319i	0.837129	+	0.547005i	$0.184232\pi$
$510$	−52.0278	−	26.3721i	−2.30383	−	1.16778i
$511$	6.11930	+	10.5989i	0.270702	+	0.468870i
$512$	40.6564	−	40.6564i	1.79678	−	1.79678i
$513$	10.9259	−	19.8400i	0.482391	−	0.875956i
$514$			53.4745i			2.35866i
$515$	−1.52337	+	1.02026i	−0.0671278	+	0.0449580i
$516$	−45.9559	−	27.2773i	−2.02309	−	1.20082i
$517$	21.2613	−	5.69694i	0.935069	−	0.250551i
$518$	−4.39878	−	4.39878i	−0.193271	−	0.193271i
$519$	0.342564	−	28.3846i	0.0150369	−	1.24594i
$520$	30.2310	+	88.7436i	1.32572	+	3.89166i
$521$		−	23.5385i		−	1.03124i	−0.856818	−	0.515620i	$-0.827562\pi$
$521$		−	23.5385i		−	1.03124i	0.856818	−	0.515620i	$-0.172438\pi$
$522$	−49.7488	+	12.0512i	−2.17745	+	0.527468i
$523$	2.16011	+	0.578799i	0.0944550	+	0.0253091i	0.305737	−	0.952116i	$-0.401097\pi$
$523$	2.16011	+	0.578799i	0.0944550	+	0.0253091i	−0.211282	+	0.977425i	$0.567764\pi$
$524$	13.7417	−	23.8014i	0.600311	−	1.03977i
$525$	16.3661	+	21.7723i	0.714277	+	0.950223i
$526$	−15.5862	+	26.9961i	−0.679591	+	1.17709i
$527$	−21.3492	+	21.3492i	−0.929985	+	0.929985i
$528$	13.5415	+	53.0925i	0.589320	+	2.31055i
$529$	−3.87917	+	2.23964i	−0.168659	+	0.0973755i
$530$	−10.4620	−	30.7113i	−0.454440	−	1.33401i
$531$	8.31205	−	4.53509i	0.360712	−	0.196806i
$532$	−75.5742	+	4.26852i	−3.27656	+	0.185064i
$533$	−1.72939	+	0.463389i	−0.0749082	+	0.0200716i
$534$	−5.69604	−	10.1467i	−0.246492	−	0.439090i
$535$	1.88818	+	28.3403i	0.0816331	+	1.22526i
$536$	39.4836	+	22.7959i	1.70543	+	0.984632i
$537$	−11.9417	+	3.04580i	−0.515322	+	0.131436i
$538$	4.76020	−	4.76020i	0.205227	−	0.205227i
$539$	−5.92365			−0.255150
$540$	−30.3774	+	56.5052i	−1.30723	+	2.43159i
$541$	−0.691618	−	1.19792i	−0.0297350	−	0.0515025i	0.850775	−	0.525530i	$-0.176133\pi$
$541$	−0.691618	−	1.19792i	−0.0297350	−	0.0515025i	−0.880510	+	0.474028i	$0.842800\pi$
$542$	−3.00701	+	3.00701i	−0.129162	+	0.129162i
$543$	30.7857	+	31.5378i	1.32114	+	1.35342i
$544$	−109.566	+	63.2579i	−4.69760	+	2.71216i
$545$	5.48778	−	1.86944i	0.235071	−	0.0800782i
$546$	−31.7496	−	56.5573i	−1.35876	−	2.42043i
$547$	−7.64456	−	7.64456i	−0.326858	−	0.326858i	0.524533	−	0.851390i	$-0.324240\pi$
$547$	−7.64456	−	7.64456i	−0.326858	−	0.326858i	−0.851390	+	0.524533i	$0.824240\pi$
$548$	33.3698	−	8.94140i	1.42549	−	0.381958i
$549$	−21.1637	+	11.5470i	−0.903245	+	0.492815i
$550$	17.0516	−	22.3215i	0.727083	−	0.951791i
$551$	−25.7573	+	8.48486i	−1.09730	+	0.361467i
$552$	−69.3047	−	19.4695i	−2.94980	−	0.828677i
$553$	−0.617977	+	0.617977i	−0.0262790	+	0.0262790i
$554$	−66.9964			−2.84640
$555$	−2.65469	+	0.868726i	−0.112685	+	0.0368753i
$556$	−5.60485	−	9.70789i	−0.237699	−	0.411706i
$557$	20.0092	+	5.36144i	0.847816	+	0.227172i	0.656471	−	0.754351i	$-0.272048\pi$
$557$	20.0092	+	5.36144i	0.847816	+	0.227172i	0.191345	+	0.981523i	$0.438715\pi$
$558$	31.2045	+	32.7484i	1.32099	+	1.38635i
$559$		−	24.2601i		−	1.02609i
$560$	108.367	−	7.22000i	4.57936	−	0.305101i
$561$	0.235128	−	19.4825i	0.00992711	−	0.822552i
$562$	−6.43259	+	24.0068i	−0.271343	+	1.01266i
$563$	6.96061	−	25.9773i	0.293355	−	1.09481i	−0.649161	−	0.760651i	$-0.724880\pi$
$563$	6.96061	−	25.9773i	0.293355	−	1.09481i	0.942515	−	0.334163i	$-0.108454\pi$
$564$	89.6089	−	50.3037i	3.77321	−	2.11817i
$565$	−21.7317	−	32.4481i	−0.914260	−	1.36510i
$566$	33.5029	−	19.3429i	1.40823	−	0.813044i
$567$	8.63696	−	26.9562i	0.362718	−	1.13206i
$568$	1.40848	+	5.25652i	0.0590986	+	0.220559i
$569$	−3.10266	+	5.37396i	−0.130070	+	0.225288i	−0.923703	−	0.383108i	$-0.874854\pi$
$569$	−3.10266	+	5.37396i	−0.130070	+	0.225288i	0.793633	+	0.608396i	$0.208187\pi$
$570$	−18.5706	+	42.4115i	−0.777838	+	1.77642i
$571$	−0.466542	−	0.808075i	−0.0195242	−	0.0338169i	0.856098	−	0.516813i	$-0.172882\pi$
$571$	−0.466542	−	0.808075i	−0.0195242	−	0.0338169i	−0.875622	+	0.482996i	$0.839548\pi$
$572$	−34.7201	+	34.7201i	−1.45172	+	1.45172i
$573$	35.7115	+	10.0323i	1.49187	+	0.419106i
$574$			3.55722i			0.148476i
$575$	8.27733	+	19.8621i	0.345189	+	0.828308i
$576$	46.4054	+	85.0532i	1.93356	+	3.54388i
$577$	5.22963	+	5.22963i	0.217713	+	0.217713i	0.807534	−	0.589821i	$-0.200802\pi$
$577$	5.22963	+	5.22963i	0.217713	+	0.217713i	−0.589821	+	0.807534i	$0.700802\pi$
$578$	34.8544	−	9.33922i	1.44975	−	0.388460i
$579$	−19.0821	+	32.1488i	−0.793025	+	1.33606i
$580$	72.7091	−	24.7688i	3.01908	−	1.02847i
$581$	11.0617	−	6.38649i	0.458917	−	0.264956i
$582$	−24.1686	+	86.0318i	−1.00182	+	3.56613i
$583$	7.66319	−	7.66319i	0.317377	−	0.317377i
$584$	18.7902	−	32.5456i	0.777544	−	1.34675i
$585$	−29.0966	+	1.23416i	−1.20299	+	0.0510263i
$586$	4.89424	−	8.47708i	0.202179	−	0.350185i
$587$	1.11217	+	0.298004i	0.0459040	+	0.0122999i	0.281698	−	0.959503i	$-0.409102\pi$
$587$	1.11217	+	0.298004i	0.0459040	+	0.0122999i	−0.235794	+	0.971803i	$0.575769\pi$
$588$	−26.7975	+	6.83486i	−1.10511	+	0.281865i
$589$	17.8744	+	15.9632i	0.736503	+	0.657754i
$590$	−16.0820	+	10.7707i	−0.662085	+	0.443423i
$591$	−11.6522	+	19.6312i	−0.479307	+	0.807520i
$592$	−2.88266	+	10.7582i	−0.118477	+	0.442161i
$593$	1.59472	−	5.95157i	0.0654872	−	0.244401i	−0.925421	−	0.378940i	$-0.876289\pi$
$593$	1.59472	−	5.95157i	0.0654872	−	0.244401i	0.990908	+	0.134539i	$0.0429553\pi$
$594$	−29.1721	−	1.05662i	−1.19694	−	0.0433534i
$595$	−37.8866	−	7.49370i	−1.55320	−	0.307212i
$596$	52.7135	+	30.4341i	2.15923	+	1.24663i
$597$	−19.4311	+	18.9676i	−0.795260	+	0.776293i
$598$	−13.2617	−	49.4935i	−0.542313	−	2.02394i
$599$	10.8122	−	18.7272i	0.441773	−	0.765173i	−0.556048	−	0.831150i	$-0.687683\pi$
$599$	10.8122	−	18.7272i	0.441773	−	0.765173i	0.997821	+	0.0659768i	$0.0210163\pi$
$600$	32.7709	−	76.9493i	1.33787	−	3.14144i
$601$	−19.5219	+	33.8128i	−0.796313	+	1.37925i	0.125689	+	0.992070i	$0.459886\pi$
$601$	−19.5219	+	33.8128i	−0.796313	+	1.37925i	−0.922002	+	0.387185i	$0.873447\pi$
$602$	−46.5585	−	12.4753i	−1.89758	−	0.508455i
$603$	−10.2532	+	9.76980i	−0.417541	+	0.397857i
$604$	66.8001	−	38.5671i	2.71806	−	1.56927i
$605$	−14.9250	−	2.95205i	−0.606786	−	0.120018i
$606$	−0.587911	+	48.7138i	−0.0238822	+	1.97886i
$607$	11.2762	−	42.0832i	0.457685	−	1.70810i	−0.222386	−	0.974959i	$-0.571385\pi$
$607$	11.2762	−	42.0832i	0.457685	−	1.70810i	0.680071	−	0.733146i	$-0.261949\pi$
$608$	55.0350	+	83.9976i	2.23196	+	3.40655i
$609$	−29.5534	+	16.5904i	−1.19756	+	0.672277i
$610$	40.9471	−	27.4238i	1.65790	−	1.11036i
$611$	40.4000	+	23.3249i	1.63441	+	0.943626i
$612$	−21.4158	−	88.4067i	−0.865681	−	3.57363i
$613$	5.54619	+	20.6987i	0.224008	+	0.836011i	0.982799	+	0.184677i	$0.0591237\pi$
$613$	5.54619	+	20.6987i	0.224008	+	0.836011i	−0.758791	+	0.651334i	$0.774210\pi$
$614$	−10.2147			−0.412231
$615$	1.42467	+	0.722142i	0.0574481	+	0.0291196i
$616$	31.1097	+	53.8835i	1.25344	+	2.17103i
$617$	−0.616159	−	2.29954i	−0.0248056	−	0.0925758i	0.952413	−	0.304810i	$-0.0985928\pi$
$617$	−0.616159	−	2.29954i	−0.0248056	−	0.0925758i	−0.977219	+	0.212234i	$0.931926\pi$
$618$	−3.74976	−	1.05341i	−0.150838	−	0.0423742i
$619$	33.8408	+	19.5380i	1.36018	+	0.785298i	0.989647	−	0.143522i	$-0.0458428\pi$
$619$	33.8408	+	19.5380i	1.36018	+	0.785298i	0.370530	+	0.928821i	$0.379176\pi$
$620$	−51.0824	−	44.7008i	−2.05152	−	1.79523i
$621$	11.8747	−	18.9487i	0.476514	−	0.760384i
$622$	−3.12651	+	0.837745i	−0.125361	+	0.0335905i
$623$	−5.44781	−	5.44781i	−0.218262	−	0.218262i
$624$	−59.2717	+	99.8588i	−2.37277	+	3.99755i
$625$	−24.1200	+	6.57445i	−0.964802	+	0.262978i
$626$	−27.7002	+	15.9927i	−1.10712	+	0.639196i
$627$	−15.4501	+	0.685709i	−0.617016	+	0.0273846i
$628$	−22.1950	−	82.8330i	−0.885679	−	3.30540i
$629$	1.98027	−	3.42993i	0.0789586	−	0.136760i
$630$	−12.5938	+	56.4749i	−0.501750	+	2.25001i
$631$	4.57113	+	7.91743i	0.181974	+	0.315188i	0.942553	−	0.334058i	$-0.108418\pi$
$631$	4.57113	+	7.91743i	0.181974	+	0.315188i	−0.760579	+	0.649246i	$0.775085\pi$
$632$	2.59215	+	0.694565i	0.103110	+	0.0276283i
$633$	−30.7283	+	7.83743i	−1.22134	+	0.311510i
$634$	−20.8369	+	12.0302i	−0.827540	+	0.477780i
$635$	−22.7437	−	33.9592i	−0.902558	−	1.34763i
$636$	25.8249	−	43.5089i	1.02402	−	1.72524i
$637$	−8.87728	−	8.87728i	−0.351730	−	0.351730i
$638$	24.7144	+	24.7144i	0.978451	+	0.978451i
$639$	−1.68998	−	0.0407976i	−0.0668546	−	0.00161393i
$640$	−52.8788	−	78.9545i	−2.09022	−	3.12095i
$641$	−37.6530	+	21.7390i	−1.48720	+	0.858638i	−0.999894	−	0.0145903i	$-0.995356\pi$
$641$	−37.6530	+	21.7390i	−1.48720	+	0.858638i	−0.487311	+	0.873228i	$0.662022\pi$
$642$	−43.1773	+	42.1475i	−1.70407	+	1.66343i
$643$	−30.1315	+	30.1315i	−1.18827	+	1.18827i	−0.210724	+	0.977546i	$0.567582\pi$
$643$	−30.1315	+	30.1315i	−1.18827	+	1.18827i	−0.977546	+	0.210724i	$0.932418\pi$
$644$	−74.7339			−2.94493
$645$	−14.4481	+	16.1141i	−0.568891	+	0.634491i
$646$	−20.5398	−	62.3522i	−0.808127	−	2.45321i
$647$	18.2243	−	18.2243i	0.716473	−	0.716473i	−0.251408	−	0.967881i	$-0.580894\pi$
$647$	18.2243	−	18.2243i	0.716473	−	0.716473i	0.967881	+	0.251408i	$0.0808937\pi$
$648$	−84.9441	+	18.4186i	−3.33692	+	0.723553i
$649$	−5.59915	−	3.23267i	−0.219786	−	0.126893i
$650$	59.0051	−	7.89752i	2.31437	−	0.309766i
$651$	25.7550	+	15.2870i	1.00942	+	0.599144i
$652$	−7.77442	+	2.08315i	−0.304470	+	0.0815824i
$653$	10.3585	−	38.6585i	0.405360	−	1.51282i	−0.398031	−	0.917372i	$-0.630306\pi$
$653$	10.3585	−	38.6585i	0.405360	−	1.51282i	0.803391	−	0.595452i	$-0.203027\pi$
$654$	10.5907	+	6.28618i	0.414130	+	0.245809i
$655$	−8.37609	−	7.32969i	−0.327281	−	0.286395i
$656$	5.51559	−	3.18443i	0.215348	−	0.124331i
$657$	8.05306	+	8.45150i	0.314180	+	0.329724i
$658$	65.5387	−	65.5387i	2.55496	−	2.55496i
$659$	8.36383			0.325809			0.162904	−	0.986642i	$-0.447914\pi$
$659$	8.36383			0.325809			0.162904	+	0.986642i	$0.447914\pi$
$660$	43.7393	−	2.38435i	1.70255	−	0.0928106i
$661$	−11.3609	+	19.6777i	−0.441889	+	0.765374i	−0.997830	−	0.0658479i	$-0.979025\pi$
$661$	−11.3609	+	19.6777i	−0.441889	+	0.765374i	0.555941	+	0.831222i	$0.312358\pi$
$662$	14.5434	−	14.5434i	0.565244	−	0.565244i
$663$	29.5492	−	28.8444i	1.14759	−	1.12023i
$664$	−33.9666	−	19.6106i	−1.31816	−	0.761040i
$665$	−4.24280	+	30.3598i	−0.164529	+	1.17730i
$666$	−5.06569	−	3.09004i	−0.196292	−	0.119736i
$667$	−25.8623	+	6.92978i	−1.00139	+	0.268322i
$668$	−12.0396	+	44.9325i	−0.465827	+	1.73849i
$669$	−21.6042	−	0.260734i	−0.835266	−	0.0100806i
$670$	19.0648	−	21.7866i	0.736539	−	0.841688i
$671$	14.2563	+	8.23086i	0.550357	+	0.317749i
$672$	87.6653	+	89.8072i	3.38176	+	3.46439i
$673$	−2.71749	−	10.1418i	−0.104752	−	0.390938i	0.893565	−	0.448933i	$-0.148196\pi$
$673$	−2.71749	−	10.1418i	−0.104752	−	0.390938i	−0.998317	+	0.0579951i	$0.981529\pi$
$674$	34.2935	+	59.3980i	1.32094	+	2.28793i
$675$	20.0615	+	16.5086i	0.772169	+	0.635417i
$676$	−32.2859			−1.24177
$677$	−9.54404	−	35.6189i	−0.366807	−	1.36894i	−0.864954	−	0.501851i	$-0.832653\pi$
$677$	−9.54404	−	35.6189i	−0.366807	−	1.36894i	0.498147	−	0.867093i	$-0.334014\pi$
$678$	22.4378	−	79.8706i	0.861717	−	3.06741i
$679$			59.1671i			2.27063i
$680$	38.2404	+	112.255i	1.46645	+	4.30480i
$681$	−18.0607	−	32.1725i	−0.692086	−	1.23285i
$682$	7.99404	−	29.8342i	0.306108	−	1.14241i
$683$	2.92551	+	2.92551i	0.111941	+	0.111941i	0.760859	−	0.648917i	$-0.224778\pi$
$683$	2.92551	+	2.92551i	0.111941	+	0.111941i	−0.648917	+	0.760859i	$0.724778\pi$
$684$	−69.1021	+	20.9287i	−2.64219	+	0.800229i
$685$	−0.930080	−	13.9599i	−0.0355365	−	0.533380i
$686$	30.6880	−	17.7178i	1.17168	−	0.676467i
$687$	20.5350	−	20.0453i	0.783459	−	0.764774i
$688$	22.3358	+	83.3583i	0.851544	+	3.17801i
$689$	22.9684			0.875025
$690$	−20.6670	+	40.7726i	−0.786780	+	1.55219i
$691$	−12.2054	+	21.1404i	−0.464315	+	0.804218i	−0.999170	−	0.0407262i	$-0.987033\pi$
$691$	−12.2054	+	21.1404i	−0.464315	+	0.804218i	0.534855	+	0.844944i	$0.320366\pi$
$692$	−63.9866	+	63.9866i	−2.43241	+	2.43241i
$693$	−18.7844	+	4.55035i	−0.713559	+	0.172854i
$694$	7.51411	−	4.33827i	0.285232	−	0.164679i
$695$	−4.29722	+	1.46387i	−0.163003	+	0.0555279i
$696$	89.4921	+	53.1185i	3.39219	+	2.01345i
$697$	−2.18758	+	0.586159i	−0.0828603	+	0.0222024i
$698$	44.2649	+	44.2649i	1.67545	+	1.67545i
$699$	25.3152	−	14.2112i	0.957510	−	0.537517i
$700$	11.1478	−	86.1091i	0.421349	−	3.25462i
$701$	16.1617	+	9.33098i	0.610420	+	0.352426i	0.773130	−	0.634248i	$-0.218690\pi$
$701$	16.1617	+	9.33098i	0.610420	+	0.352426i	−0.162710	+	0.986674i	$0.552023\pi$
$702$	−42.1343	−	45.3012i	−1.59026	−	1.70978i
$703$	−2.80680	−	1.41581i	−0.105860	−	0.0533981i
$704$	33.0783	−	57.2934i	1.24669	−	2.15933i
$705$	−12.9434	−	39.5530i	−0.487477	−	1.48965i
$706$	−71.3589			−2.68563
$707$	8.34847	+	31.1569i	0.313976	+	1.17178i
$708$	−29.0595	−	8.16358i	−1.09212	−	0.306806i
$709$			17.6587i			0.663185i	0.943423	+	0.331593i	$0.107586\pi$
$709$			17.6587i			0.663185i	−0.943423	+	0.331593i	$0.892414\pi$
$710$	3.44795	−	0.229720i	0.129399	−	0.00862124i
$711$	−0.434114	+	0.711671i	−0.0162806	+	0.0266897i
$712$	−6.12298	+	22.8513i	−0.229468	+	0.856387i
$713$	16.7307	+	16.7307i	0.626570	+	0.626570i
$714$	−40.1613	−	71.5416i	−1.50300	−	2.67738i
$715$	11.0654	+	16.5221i	0.413824	+	0.617890i
$716$	34.0230	+	19.6432i	1.27150	+	0.734100i
$717$	5.56790	+	5.70394i	0.207937	+	0.213017i
$718$	−9.61283	+	9.61283i	−0.358747	+	0.358747i
$719$	11.4221	−	19.7837i	0.425973	−	0.737806i	−0.570538	−	0.821271i	$-0.693265\pi$
$719$	11.4221	−	19.7837i	0.425973	−	0.737806i	0.996511	+	0.0834647i	$0.0265986\pi$
$720$	98.8402	−	31.0292i	3.68356	−	1.15639i
$721$	−2.57885			−0.0960413
$722$	−48.4936	+	19.0683i	−1.80475	+	0.709650i
$723$	26.5506	−	6.77187i	0.987426	−	0.251849i
$724$		−	140.494i		−	5.22142i
$725$	−4.12676	−	30.8325i	−0.153264	−	1.14509i
$726$	−15.8211	−	28.1830i	−0.587175	−	1.04597i
$727$	−2.57574	+	9.61281i	−0.0955290	+	0.356519i	−0.997099	−	0.0761138i	$-0.975749\pi$
$727$	−2.57574	+	9.61281i	−0.0955290	+	0.356519i	0.901570	+	0.432633i	$0.142415\pi$
$728$	−34.1293	+	127.372i	−1.26492	+	4.72073i
$729$	1.95332	−	26.9293i	0.0723453	−	0.997380i
$730$	−17.9583	−	15.7148i	−0.664665	−	0.581630i
$731$		−	30.6876i		−	1.13502i
$732$	73.9898	+	20.7857i	2.73474	+	0.768261i
$733$	−18.0281	−	4.83062i	−0.665884	−	0.178423i	−0.0899841	−	0.995943i	$-0.528682\pi$
$733$	−18.0281	−	4.83062i	−0.665884	−	0.178423i	−0.575900	+	0.817520i	$0.695348\pi$
$734$	10.2577	+	17.7669i	0.378620	+	0.655789i
$735$	0.609632	+	11.1833i	0.0224866	+	0.412503i
$736$	49.5733	+	85.8635i	1.82730	+	3.16497i
$737$	9.34077	+	2.50285i	0.344072	+	0.0921937i
$738$	0.798841	+	3.29771i	0.0294058	+	0.121390i
$739$	−1.70786	−	0.986033i	−0.0628246	−	0.0362718i	0.468259	−	0.883591i	$-0.344882\pi$
$739$	−1.70786	−	0.986033i	−0.0628246	−	0.0362718i	−0.531083	+	0.847320i	$0.678215\pi$
$740$	7.99017	+	3.92962i	0.293724	+	0.144456i
$741$	−24.1813	−	22.1261i	−0.888323	−	0.812823i
$742$	11.8110	−	44.0794i	0.433597	−	1.61821i
$743$	23.3393	+	23.3393i	0.856236	+	0.856236i	0.990892	−	0.134657i	$-0.0429931\pi$
$743$	23.3393	+	23.3393i	0.856236	+	0.856236i	−0.134657	+	0.990892i	$0.542993\pi$
$744$	1.10983	−	91.9596i	0.0406884	−	3.37140i
$745$	16.2332	−	18.5507i	0.594739	−	0.679645i
$746$	34.1304	+	19.7052i	1.24960	+	0.721458i
$747$	8.82051	−	8.40468i	0.322726	−	0.307511i
$748$	−43.9189	+	43.9189i	−1.60583	+	1.60583i
$749$	−19.9751	+	34.5979i	−0.729875	+	1.26418i
$750$	−43.8958	−	29.8947i	−1.60285	−	1.09160i
$751$	−24.5486	+	42.5195i	−0.895792	+	1.55156i	−0.0629712	+	0.998015i	$0.520058\pi$
$751$	−24.5486	+	42.5195i	−0.895792	+	1.55156i	−0.832821	+	0.553542i	$0.813276\pi$
$752$	−160.290	−	42.9496i	−5.84518	−	1.56621i
$753$	34.6075	−	33.7822i	1.26117	−	1.23109i
$754$			74.0747i			2.69764i
$755$	−10.0729	−	29.5692i	−0.366591	−	1.07613i
$756$	−79.7268	+	42.2589i	−2.89964	+	1.53694i
$757$	22.8461	−	6.12160i	0.830357	−	0.222493i	0.181487	−	0.983393i	$-0.441909\pi$
$757$	22.8461	−	6.12160i	0.830357	−	0.222493i	0.648869	+	0.760900i	$0.275242\pi$
$758$	−12.2939	+	45.8813i	−0.446533	+	1.66648i
$759$	−15.2679	−	0.184263i	−0.554188	−	0.00668832i
$760$	87.2487	−	35.3295i	3.16484	−	1.28153i
$761$	−10.0535	+	5.80440i	−0.364440	+	0.210409i	−0.671027	−	0.741433i	$-0.734146\pi$
$761$	−10.0535	+	5.80440i	−0.364440	+	0.210409i	0.306587	+	0.951843i	$0.400813\pi$
$762$	23.4826	−	83.5901i	0.850687	−	3.02815i
$763$	7.87652	+	2.11051i	0.285149	+	0.0764055i
$764$	−59.1239	−	102.406i	−2.13903	−	3.70490i
$765$	−36.8054	+	1.56114i	−1.33070	+	0.0564432i
$766$	−0.403591	−	0.699040i	−0.0145823	−	0.0252573i
$767$	−3.54645	−	13.2355i	−0.128055	−	0.477907i
$768$	24.3386	−	86.6369i	0.878243	−	3.12624i
$769$	32.8577	+	18.9704i	1.18488	+	0.684090i	0.957138	−	0.289632i	$-0.0935330\pi$
$769$	32.8577	+	18.9704i	1.18488	+	0.684090i	0.227740	+	0.973722i	$0.426866\pi$
$770$	37.3983	−	12.7399i	1.34774	−	0.459116i
$771$	16.5318	+	29.4491i	0.595379	+	1.06058i
$772$	115.116	−	30.8453i	4.14313	−	1.11015i
$773$	−9.61201	+	35.8725i	−0.345720	+	1.29024i	0.546049	+	0.837753i	$0.316131\pi$
$773$	−9.61201	+	35.8725i	−0.345720	+	1.29024i	−0.891769	+	0.452491i	$0.850535\pi$
$774$	−45.9634	−	1.10960i	−1.65212	−	0.0398836i
$775$	−21.7730	+	16.7816i	−0.782108	+	0.602814i
$776$	157.341	−	90.8407i	5.64820	−	3.26099i
$777$	−3.78236	−	1.06256i	−0.135691	−	0.0381193i
$778$	−3.57600	−	0.958187i	−0.128206	−	0.0343527i
$779$	0.562437	+	1.70738i	0.0201514	+	0.0611732i
$780$	69.1217	+	61.9753i	2.47495	+	2.21907i
$781$	0.577135	+	0.999627i	0.0206515	+	0.0357695i
$782$	−16.7753	−	62.6063i	−0.599884	−	2.23880i
$783$	−23.6717	+	22.0168i	−0.845956	+	0.786817i
$784$	38.6757	+	22.3294i	1.38127	+	0.797479i
$785$	−34.6523	+	2.30872i	−1.23679	+	0.0824017i
$786$	0.285338	−	23.6429i	0.0101777	−	0.843313i
$787$	6.64861	−	24.8130i	0.236997	−	0.884486i	−0.740241	−	0.672342i	$-0.765289\pi$
$787$	6.64861	−	24.8130i	0.236997	−	0.884486i	0.977238	−	0.212145i	$-0.0680448\pi$
$788$	70.2940	−	18.8352i	2.50412	−	0.670977i
$789$	−0.237580	+	19.6856i	−0.00845806	+	0.700827i
$790$	0.752039	−	1.52913i	0.0267563	−	0.0544041i
$791$		−	54.9299i		−	1.95308i
$792$	40.9406	+	42.9662i	1.45476	+	1.52674i
$793$	9.02978	+	33.6996i	0.320657	+	1.19671i
$794$	−94.0743			−3.33857
$795$	−15.2561	−	13.6788i	−0.541077	−	0.485135i
$796$	86.5611			3.06808
$797$	17.0885	+	4.57884i	0.605304	+	0.162191i	0.548438	−	0.836191i	$-0.315223\pi$
$797$	17.0885	+	4.57884i	0.605304	+	0.162191i	0.0568661	+	0.998382i	$0.481889\pi$
$798$	−54.8978	+	35.0293i	−1.94336	+	1.24003i
$799$	51.1036	+	29.5047i	1.80792	+	1.04380i
$800$	−106.328	+	44.3109i	−3.75925	+	1.56663i
$801$	−6.27377	−	3.82696i	−0.221673	−	0.135219i
$802$	−24.2559	+	90.5241i	−0.856504	+	3.19652i
$803$	2.06305	−	7.69942i	0.0728036	−	0.271707i
$804$	45.1438	+	0.544826i	1.59210	+	0.0192145i
$805$	−5.87259	+	29.6906i	−0.206981	+	1.04646i
$806$	56.6900	−	32.7300i	1.99682	−	1.15286i
$807$	1.14987	−	4.09314i	0.0404773	−	0.144085i
$808$	70.0366	−	70.0366i	2.46388	−	2.46388i
$809$	27.2834			0.959234			0.479617	−	0.877478i	$-0.340776\pi$
$809$	27.2834			0.959234			0.479617	+	0.877478i	$0.340776\pi$
$810$	1.00745	+	55.1830i	0.0353982	+	1.93893i
$811$	−3.76047	−	6.51332i	−0.132048	−	0.228714i	0.792418	−	0.609978i	$-0.208822\pi$
$811$	−3.76047	−	6.51332i	−0.132048	−	0.228714i	−0.924466	+	0.381265i	$0.875489\pi$
$812$	104.358	+	27.9627i	3.66226	+	0.981298i
$813$	−0.726370	+	2.58562i	−0.0254749	+	0.0906818i
$814$			4.05162i			0.142009i
$815$	0.216688	+	3.25234i	0.00759025	+	0.113925i
$816$	−74.9752	+	126.315i	−2.62466	+	4.42193i
$817$	−24.3194	+	1.37359i	−0.850827	+	0.0480557i
$818$	−64.2790	−	64.2790i	−2.24746	−	2.24746i
$819$	−34.9698	−	21.3313i	−1.22194	−	0.745377i
$820$	−1.64185	−	4.81968i	−0.0573360	−	0.168311i
$821$		−	22.5922i		−	0.788473i	−0.919009	−	0.394236i	$-0.871009\pi$
$821$		−	22.5922i		−	0.788473i	0.919009	−	0.394236i	$-0.128991\pi$
$822$	21.2683	−	20.7611i	0.741817	−	0.724125i
$823$	−9.17490	−	34.2412i	−0.319817	−	1.19357i	−0.919420	−	0.393276i	$-0.871342\pi$
$823$	−9.17490	−	34.2412i	−0.319817	−	1.19357i	0.599603	−	0.800297i	$-0.295325\pi$
$824$	3.95936	+	6.85782i	0.137931	+	0.238903i
$825$	2.48977	−	17.5643i	0.0866827	−	0.611510i
$826$	−27.2244			−0.947260
$827$	12.1626	+	3.25896i	0.422935	+	0.113325i	0.464008	−	0.885831i	$-0.346411\pi$
$827$	12.1626	+	3.25896i	0.422935	+	0.113325i	−0.0410729	+	0.999156i	$0.513078\pi$
$828$	−69.2817	+	16.7829i	−2.40770	+	0.583246i
$829$			0.431819i			0.0149977i	0.999972	+	0.00749885i	$0.00238698\pi$
$829$			0.431819i			0.0149977i	−0.999972	+	0.00749885i	$0.997613\pi$
$830$	−16.4009	+	18.7424i	−0.569285	+	0.650557i
$831$	−36.8958	+	20.7122i	−1.27990	+	0.718497i
$832$	135.433	−	36.2891i	4.69528	−	1.25810i
$833$	−11.2292	−	11.2292i	−0.389070	−	0.389070i
$834$	−8.29309	−	4.92240i	−0.287166	−	0.170449i
$835$	16.9049	+	8.31394i	0.585018	+	0.287716i
$836$	36.7708	+	32.8391i	1.27174	+	1.13576i
$837$	27.3090	+	8.38797i	0.943937	+	0.289931i
$838$	9.05303	+	33.7864i	0.312732	+	1.16713i
$839$	8.48335	+	14.6936i	0.292878	+	0.507279i	0.974489	−	0.224435i	$-0.0720538\pi$
$839$	8.48335	+	14.6936i	0.292878	+	0.507279i	−0.681611	+	0.731715i	$0.738720\pi$
$840$	98.5256	−	64.2777i	3.39946	−	2.21779i
$841$	9.70694			0.334722
$842$	−7.26890	−	27.1279i	−0.250503	−	0.934889i
$843$	3.87927	+	15.2095i	0.133609	+	0.523843i
$844$	87.5477	+	50.5457i	3.01352	+	1.73985i
$845$	−2.53703	+	12.8267i	−0.0872763	+	0.441251i
$846$	46.0394	−	75.4753i	1.58287	−	2.59489i
$847$	−15.1316	−	15.1316i	−0.519927	−	0.519927i
$848$	−78.9199	+	21.1465i	−2.71012	+	0.726174i
$849$	12.4706	−	21.0100i	0.427989	−	0.721060i
$850$	74.6380	−	9.98989i	2.56006	−	0.342650i
$851$	−2.68794	−	1.55188i	−0.0921412	−	0.0531978i
$852$	3.76425	+	3.85622i	0.128961	+	0.132112i
$853$	42.2152	+	11.3115i	1.44542	+	0.387299i	0.894428	−	0.447212i	$-0.147583\pi$
$853$	42.2152	+	11.3115i	1.44542	+	0.387299i	0.550992	+	0.834511i	$0.314250\pi$
$854$	69.3175			2.37200
$855$	2.88460	+	29.0978i	0.0986512	+	0.995122i
$856$	122.673			4.19288
$857$	−21.9519	−	5.88200i	−0.749864	−	0.200925i	−0.136406	−	0.990653i	$-0.543555\pi$
$857$	−21.9519	−	5.88200i	−0.749864	−	0.200925i	−0.613458	+	0.789728i	$0.710222\pi$
$858$	−11.4249	+	40.6688i	−0.390041	+	1.38841i
$859$	6.62770	+	3.82650i	0.226134	+	0.130559i	0.608787	−	0.793333i	$-0.291656\pi$
$859$	6.62770	+	3.82650i	0.226134	+	0.130559i	−0.382653	+	0.923892i	$0.624990\pi$
$860$	68.8400	−	4.58648i	2.34743	−	0.156398i
$861$	1.09973	+	1.95901i	0.0374787	+	0.0667629i
$862$	−58.9773	+	15.8029i	−2.00877	+	0.538249i
$863$	2.26838	+	2.26838i	0.0772165	+	0.0772165i	0.744660	−	0.667444i	$-0.232612\pi$
$863$	2.26838	+	2.26838i	0.0772165	+	0.0772165i	−0.667444	+	0.744660i	$0.732612\pi$
$864$	101.438	+	63.5684i	3.45098	+	2.16264i
$865$	20.3928	+	30.4489i	0.693375	+	1.03529i
$866$	−2.30065	−	1.32828i	−0.0781793	−	0.0451369i
$867$	16.3075	−	15.9186i	0.553833	−	0.540624i
$868$	−24.7107	−	92.2216i	−0.838736	−	3.13020i
$869$	0.569206			0.0193090
$870$	44.1150	−	49.2020i	1.49564	−	1.66810i
$871$	10.2474	+	17.7490i	0.347220	+	0.601403i
$872$	−6.48062	−	24.1860i	−0.219462	−	0.819042i
$873$	13.2871	+	54.8506i	0.449700	+	1.85641i
$874$	−48.8635	+	16.0964i	−1.65283	+	0.544470i
$875$	−33.3338	−	11.1953i	−1.12689	−	0.378471i
$876$	0.449090	−	37.2112i	0.0151733	−	1.25725i
$877$	−12.5292	−	12.5292i	−0.423080	−	0.423080i	0.463183	−	0.886263i	$-0.346707\pi$
$877$	−12.5292	−	12.5292i	−0.423080	−	0.423080i	−0.886263	+	0.463183i	$0.846707\pi$
$878$	−4.40132	+	1.17933i	−0.148537	+	0.0398005i
$879$	0.0746027	−	6.18151i	0.00251629	−	0.208497i
$880$	−53.2326	−	46.5824i	−1.79447	−	1.57029i
$881$			26.6755i			0.898722i	0.893350	+	0.449361i	$0.148348\pi$
$881$			26.6755i			0.898722i	−0.893350	+	0.449361i	$0.851652\pi$
$882$	−17.2250	+	16.4129i	−0.579995	+	0.552652i
$883$	−0.845857	−	0.226647i	−0.0284653	−	0.00762727i	0.244558	−	0.969635i	$-0.421357\pi$
$883$	−0.845857	−	0.226647i	−0.0284653	−	0.00762727i	−0.273024	+	0.962007i	$0.588024\pi$
$884$	−131.635			−4.42737
$885$	−5.52675	+	10.9034i	−0.185780	+	0.366513i
$886$	18.5473	+	32.1249i	0.623110	+	1.07926i
$887$	10.0611	+	37.5486i	0.337819	+	1.26076i	0.900780	+	0.434276i	$0.142996\pi$
$887$	10.0611	+	37.5486i	0.337819	+	1.26076i	−0.562961	+	0.826484i	$0.690338\pi$
$888$	2.98151	+	11.6897i	0.100053	+	0.392279i
$889$		−	57.4879i		−	1.92808i
$890$	13.4802	+	6.62964i	0.451856	+	0.222226i
$891$	−16.3921	+	8.43676i	−0.549156	+	0.282642i
$892$	48.7017	+	48.7017i	1.63065	+	1.63065i
$893$	21.0945	−	41.8193i	0.705901	−	1.39943i
$894$	52.3623	+	0.631944i	1.75126	+	0.0211354i
$895$	10.4774	−	11.9732i	0.350222	−	0.400221i
$896$		−	133.658i		−	4.46521i
$897$	−22.6045	−	23.1568i	−0.754743	−	0.773183i
$898$	−83.8539	−	22.4686i	−2.79824	−	0.749786i
$899$	−17.1027	−	29.6228i	−0.570407	−	0.987974i
$900$	−9.00287	−	82.3305i	−0.300096	−	2.74435i
$901$	29.0536			0.967916
$902$	1.63824	−	1.63824i	0.0545476	−	0.0545476i
$903$	−29.4971	+	7.52342i	−0.981604	+	0.250364i
$904$	−146.073	+	84.3351i	−4.85831	+	2.80494i
$905$	−55.8161	−	11.0400i	−1.85539	−	0.366983i
$906$	33.8711	−	57.0649i	1.12529	−	1.89585i
$907$	−12.3860	+	46.2251i	−0.411270	+	1.53488i	0.380922	+	0.924607i	$0.375607\pi$
$907$	−12.3860	+	46.2251i	−0.411270	+	1.53488i	−0.792191	+	0.610273i	$0.791060\pi$
$908$	−30.4408	+	113.607i	−1.01021	+	3.77017i
$909$	14.7363	+	27.0091i	0.488771	+	0.895834i
$910$	75.1380	+	36.9534i	2.49080	+	1.22499i
$911$	−23.5165	−	13.5772i	−0.779135	−	0.449834i	0.0569886	−	0.998375i	$-0.481850\pi$
$911$	−23.5165	−	13.5772i	−0.779135	−	0.449834i	−0.836124	+	0.548541i	$0.815183\pi$
$912$	103.459	+	53.7625i	3.42586	+	1.78026i
$913$	−8.03559	−	2.15313i	−0.265939	−	0.0712582i
$914$	80.9359			2.67712
$915$	14.0719	−	27.7616i	0.465204	−	0.917771i
$916$	−91.4790			−3.02255
$917$	−4.05187	−	15.1218i	−0.133804	−	0.499365i
$918$	−53.2974	−	57.3033i	−1.75907	−	1.89129i
$919$		−	21.5381i		−	0.710477i	−0.934776	−	0.355238i	$-0.884400\pi$
$919$		−	21.5381i		−	0.710477i	0.934776	−	0.355238i	$-0.115600\pi$
$920$	87.9712	−	29.9679i	2.90032	−	0.988012i
$921$	−5.62536	+	3.15791i	−0.185362	+	0.104057i
$922$	−71.7263	+	19.2190i	−2.36218	+	0.632944i
$923$	−0.633154	+	2.36296i	−0.0208405	+	0.0777778i
$924$	52.9824	+	31.4479i	1.74299	+	1.03456i
$925$	2.18904	−	2.86558i	0.0719753	−	0.0942196i
$926$	−30.4766	−	17.5956i	−1.00152	−	0.578229i
$927$	−2.39071	+	0.579128i	−0.0785212	+	0.0190211i
$928$	−37.0971	−	138.448i	−1.21777	−	4.54479i
$929$	21.2903	+	36.8758i	0.698511	+	1.20986i	0.968983	+	0.247129i	$0.0794872\pi$
$929$	21.2903	+	36.8758i	0.698511	+	1.20986i	−0.270471	+	0.962728i	$0.587179\pi$
$930$	−57.1470	−	12.0216i	−1.87392	−	0.394205i
$931$	−8.39634	+	9.40158i	−0.275179	+	0.308124i
$932$	−89.3925	−	23.9526i	−2.92815	−	0.784595i
$933$	−1.46282	+	1.42793i	−0.0478904	+	0.0467483i
$934$	−28.2657	+	16.3192i	−0.924882	+	0.533981i
$935$	13.9971	+	20.8994i	0.457755	+	0.683484i
$936$	−3.03557	+	125.744i	−0.0992208	+	4.11008i
$937$	−3.43386	+	12.8153i	−0.112179	+	0.418658i	−0.999060	−	0.0433391i	$-0.986200\pi$
$937$	−3.43386	+	12.8153i	−0.112179	+	0.418658i	0.886881	+	0.461997i	$0.152867\pi$
$938$	39.3324	−	10.5391i	1.28425	−	0.344113i
$939$	−10.3106	+	17.3710i	−0.336475	+	0.566881i
$940$	−58.5486	+	119.048i	−1.90965	+	3.88292i
$941$	−14.6734	−	8.47168i	−0.478339	−	0.276169i	0.241385	−	0.970429i	$-0.422398\pi$
$941$	−14.6734	−	8.47168i	−0.478339	−	0.276169i	−0.719724	+	0.694260i	$0.755732\pi$
$942$	−51.5347	−	52.7938i	−1.67909	−	1.72012i
$943$	0.459355	+	1.71434i	0.0149587	+	0.0558265i
$944$	24.3713	+	42.2124i	0.793219	+	1.37390i
$945$	10.5238	+	34.9949i	0.342341	+	1.13838i
$946$	15.6967	+	27.1874i	0.510342	+	0.883939i
$947$	10.3979	+	2.78610i	0.337886	+	0.0905362i	0.423772	−	0.905769i	$-0.360706\pi$
$947$	10.3979	+	2.78610i	0.337886	+	0.0905362i	−0.0858867	+	0.996305i	$0.527372\pi$
$948$	2.57499	−	0.656765i	0.0836317	−	0.0213307i
$949$	14.6302	−	8.44675i	0.474916	−	0.274193i
$950$	−11.2576	−	58.7021i	−0.365246	−	1.90455i
$951$	−7.75598	+	13.0670i	−0.251505	+	0.423727i
$952$	−43.1715	+	161.118i	−1.39920	+	5.22187i
$953$	−36.4559	+	9.76833i	−1.18092	+	0.316427i	−0.795292	−	0.606226i	$-0.792683\pi$
$953$	−36.4559	+	9.76833i	−1.18092	+	0.316427i	−0.385630	+	0.922653i	$0.626016\pi$
$954$	1.05051	−	43.5160i	0.0340117	−	1.40888i
$955$	−45.3301	+	15.4420i	−1.46685	+	0.499690i
$956$		−	25.4098i		−	0.821812i
$957$	21.2511	+	5.96998i	0.686949	+	0.192982i
$958$	−27.9638	−	7.49289i	−0.903470	−	0.242084i
$959$	9.83935	−	17.0423i	0.317729	−	0.550323i
$960$	−111.569	−	56.5526i	−3.60087	−	1.82523i
$961$	0.386299	−	0.669090i	0.0124613	−	0.0215835i
$962$	−6.07183	+	6.07183i	−0.195764	+	0.195764i
$963$	−10.7482	+	36.5596i	−0.346357	+	1.17812i
$964$	−75.6450	−	43.6736i	−2.43636	−	1.40663i
$965$	−3.20852	−	48.1577i	−0.103286	−	1.55025i
$966$	−56.0650	+	31.4732i	−1.80386	+	1.01263i
$967$	−31.2467	−	31.2467i	−1.00483	−	1.00483i	−0.999988	−	0.00483936i	$-0.998460\pi$
$967$	−31.2467	−	31.2467i	−1.00483	−	1.00483i	−0.00483936	−	0.999988i	$-0.501540\pi$
$968$	−17.0069	+	63.4706i	−0.546623	+	2.04002i
$969$	−30.5879	−	27.9882i	−0.982626	−	0.899111i
$970$	−37.2008	−	109.204i	−1.19445	−	3.50631i
$971$	−18.3342	−	10.5853i	−0.588373	−	0.339697i	0.176081	−	0.984376i	$-0.443658\pi$
$971$	−18.3342	−	10.5853i	−0.588373	−	0.339697i	−0.764454	+	0.644679i	$0.776991\pi$
$972$	−64.4203	+	57.0800i	−2.06628	+	1.83084i
$973$	−6.16773	−	1.65264i	−0.197728	−	0.0529811i
$974$	14.0101	+	24.2663i	0.448914	+	0.777541i
$975$	30.0534	−	22.5909i	0.962478	−	0.723489i
$976$	−62.0531	−	107.479i	−1.98627	−	3.44032i
$977$	21.4959	+	5.75981i	0.687715	+	0.184273i	0.585722	−	0.810512i	$-0.300811\pi$
$977$	21.4959	+	5.75981i	0.687715	+	0.184273i	0.101994	+	0.994785i	$0.467478\pi$
$978$	−4.95504	+	4.83686i	−0.158445	+	0.154666i
$979$			5.01786i			0.160372i
$980$	23.5117	−	26.8683i	0.751054	−	0.858276i
$981$	7.77585	+	0.187716i	0.248264	+	0.00599330i
$982$	0.495342	−	1.84864i	0.0158070	−	0.0589925i
$983$	4.38757	−	16.3746i	0.139942	−	0.522270i	−0.859987	−	0.510316i	$-0.829528\pi$
$983$	4.38757	−	16.3746i	0.139942	−	0.522270i	0.999929	−	0.0119535i	$-0.00380501\pi$
$984$	3.52107	−	5.93218i	0.112248	−	0.189111i
$985$	−1.95923	−	29.4068i	−0.0624263	−	0.936977i
$986$			93.7001i			2.98402i
$987$	15.8315	−	56.3545i	0.503921	−	1.79378i
$988$	5.89204	+	104.319i	0.187451	+	3.31881i
$989$	−24.0490			−0.764712
$990$	31.8089	−	20.2090i	1.01095	−	0.642284i
$991$	7.63743	−	13.2284i	0.242611	−	0.420215i	−0.718846	−	0.695169i	$-0.755329\pi$
$991$	7.63743	−	13.2284i	0.242611	−	0.420215i	0.961457	+	0.274955i	$0.0886628\pi$
$992$	−89.5642	+	89.5642i	−2.84367	+	2.84367i
$993$	3.51308	−	12.5054i	0.111484	−	0.396845i
$994$	4.20926	+	2.43022i	0.133510	+	0.0770818i
$995$	6.80197	−	34.3894i	0.215637	−	1.09022i
$996$	−38.8359	−	0.468699i	−1.23056	−	0.0148513i
$997$	22.2013	+	22.2013i	0.703123	+	0.703123i	0.965080	−	0.261956i	$-0.0843676\pi$
$997$	22.2013	+	22.2013i	0.703123	+	0.703123i	−0.261956	+	0.965080i	$0.584368\pi$
$998$	−1.52540	+	5.69285i	−0.0482856	+	0.180204i
$999$	−3.74504	−	0.135646i	−0.118488	−	0.00429164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.ci.a.182.2	yes	464
5.3	odd	4	inner	855.2.ci.a.353.2	yes	464
9.5	odd	6		855.2.bx.a.752.2	yes	464
19.7	even	3		855.2.bx.a.767.115	yes	464
45.23	even	12		855.2.bx.a.68.115	✓	464
95.83	odd	12		855.2.bx.a.83.2	yes	464
171.140	odd	6	inner	855.2.ci.a.482.2	yes	464
855.653	even	12	inner	855.2.ci.a.653.2	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.bx.a.68.115	✓	464	45.23	even	12
855.2.bx.a.83.2	yes	464	95.83	odd	12
855.2.bx.a.752.2	yes	464	9.5	odd	6
855.2.bx.a.767.115	yes	464	19.7	even	3
855.2.ci.a.182.2	yes	464	1.1	even	1	trivial
855.2.ci.a.353.2	yes	464	5.3	odd	4	inner
855.2.ci.a.482.2	yes	464	171.140	odd	6	inner
855.2.ci.a.653.2	yes	464	855.653	even	12	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.ci (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.64907 - 0.709817i) q^{2} +(-1.67832 + 0.428065i) q^{3} +(4.78169 + 2.76071i) q^{4} +(1.47253 - 1.68275i) q^{5} +(4.74984 + 0.0573243i) q^{6} +(3.03796 - 0.814018i) q^{7} +(-6.82893 - 6.82893i) q^{8} +(2.63352 - 1.43686i) q^{9} +O(q^{10})\)	\(q+(-2.64907 - 0.709817i) q^{2} +(-1.67832 + 0.428065i) q^{3} +(4.78169 + 2.76071i) q^{4} +(1.47253 - 1.68275i) q^{5} +(4.74984 + 0.0573243i) q^{6} +(3.03796 - 0.814018i) q^{7} +(-6.82893 - 6.82893i) q^{8} +(2.63352 - 1.43686i) q^{9} +(-5.09528 + 3.41250i) q^{10} +(-1.77399 - 1.02421i) q^{11} +(-9.20697 - 2.58648i) q^{12} +(-1.12363 - 4.19343i) q^{13} -8.62557 q^{14} +(-1.75105 + 3.45454i) q^{15} +(7.72161 + 13.3742i) q^{16} +(-1.42132 - 5.30444i) q^{17} +(-7.99629 + 1.93703i) q^{18} +(-4.14005 + 1.36380i) q^{19} +(11.6868 - 3.98117i) q^{20} +(-4.75021 + 2.66663i) q^{21} +(3.97242 + 3.97242i) q^{22} +(-4.15693 + 1.11385i) q^{23} +(14.3844 + 8.53790i) q^{24} +(-0.663308 - 4.95581i) q^{25} +11.9063i q^{26} +(-3.80482 + 3.53883i) q^{27} +(16.7738 + 4.49453i) q^{28} +6.22149 q^{29} +(7.09075 - 7.90839i) q^{30} +(-2.74897 - 4.76136i) q^{31} +(-5.96273 - 22.2532i) q^{32} +(3.41575 + 0.959574i) q^{33} +15.0607i q^{34} +(3.10369 - 6.31079i) q^{35} +(16.5594 + 0.399759i) q^{36} +(0.509969 + 0.509969i) q^{37} +(11.9353 - 0.674123i) q^{38} +(3.68087 + 6.55693i) q^{39} +(-21.5472 + 1.43559i) q^{40} -0.412405i q^{41} +(14.4765 - 3.69231i) q^{42} +(5.39773 + 1.44632i) q^{43} +(-5.65510 - 9.79493i) q^{44} +(1.46006 - 6.54738i) q^{45} +11.8026 q^{46} +(-7.59819 + 7.59819i) q^{47} +(-18.6844 - 19.1409i) q^{48} +(2.50438 - 1.44590i) q^{49} +(-1.76056 + 13.5991i) q^{50} +(4.65608 + 8.29413i) q^{51} +(6.20401 - 23.1537i) q^{52} +(-1.36931 + 5.11032i) q^{53} +(12.5912 - 6.67390i) q^{54} +(-4.33575 + 1.47700i) q^{55} +(-26.3049 - 15.1871i) q^{56} +(6.36454 - 4.06111i) q^{57} +(-16.4812 - 4.41612i) q^{58} +3.15625 q^{59} +(-17.9099 + 11.6844i) q^{60} -8.03628 q^{61} +(3.90253 + 14.5644i) q^{62} +(6.83089 - 6.50886i) q^{63} +32.2964i q^{64} +(-8.71108 - 4.28417i) q^{65} +(-8.36744 - 4.96654i) q^{66} +(-4.55998 + 1.22184i) q^{67} +(7.84770 - 29.2880i) q^{68} +(6.49986 - 3.64883i) q^{69} +(-12.7014 + 14.5147i) q^{70} +(-0.487998 - 0.281746i) q^{71} +(-27.7963 - 8.17190i) q^{72} +(1.00714 + 3.75870i) q^{73} +(-0.988961 - 1.71293i) q^{74} +(3.23465 + 8.03349i) q^{75} +(-23.5615 - 4.90822i) q^{76} +(-6.22303 - 1.66745i) q^{77} +(-5.09666 - 19.9825i) q^{78} +(-0.240647 + 0.138937i) q^{79} +(33.8758 + 6.70040i) q^{80} +(4.87086 - 7.56801i) q^{81} +(-0.292732 + 1.09249i) q^{82} +(3.92282 - 1.05112i) q^{83} +(-30.0758 - 0.362975i) q^{84} +(-11.0190 - 5.41922i) q^{85} +(-13.2723 - 7.66279i) q^{86} +(-10.4417 + 2.66320i) q^{87} +(5.12016 + 19.1087i) q^{88} +(-1.22481 - 2.12143i) q^{89} +(-8.51524 + 16.3081i) q^{90} +(-6.82706 - 11.8248i) q^{91} +(-22.9522 - 6.15001i) q^{92} +(6.65183 + 6.81435i) q^{93} +(25.5215 - 14.7348i) q^{94} +(-3.80142 + 8.97492i) q^{95} +(19.5332 + 34.7956i) q^{96} +(-4.86899 + 18.1713i) q^{97} +(-7.66060 + 2.05265i) q^{98} +(-6.14348 - 0.148309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7}+O(q^{10}) \) 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7	\( 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7} - 4 q^{10} - 24 q^{11} + 2 q^{12} + 2 q^{13} + 10 q^{15} + 212 q^{16} + 18 q^{17} - 24 q^{18} - 12 q^{20} - 4 q^{21} - 20 q^{22} + 18 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{28} + 2 q^{30} - 8 q^{31} - 30 q^{32} + 10 q^{33} - 68 q^{36} - 16 q^{37} + 30 q^{38} - 36 q^{40} - 14 q^{42} + 2 q^{43} + 6 q^{45} - 56 q^{46} + 42 q^{48} - 108 q^{50} + 12 q^{51} - 34 q^{52} - 14 q^{55} - 24 q^{56} - 78 q^{57} - 12 q^{58} - 42 q^{60} - 8 q^{61} - 12 q^{62} + 92 q^{63} - 84 q^{65} - 52 q^{66} + 2 q^{67} - 60 q^{68} - 84 q^{70} - 118 q^{72} - 4 q^{73} + 98 q^{75} - 60 q^{76} - 12 q^{77} + 92 q^{78} + 120 q^{80} - 12 q^{81} + 4 q^{82} - 12 q^{83} + 2 q^{85} - 264 q^{86} + 102 q^{87} + 48 q^{88} - 34 q^{90} - 8 q^{91} + 54 q^{92} - 52 q^{93} - 36 q^{95} + 96 q^{96} + 2 q^{97} + 42 q^{98}+O(q^{100}) \) 464 * q - 6 * q^2 - 2 * q^3 - 4 * q^6 - 4 * q^7 - 4 * q^10 - 24 * q^11 + 2 * q^12 + 2 * q^13 + 10 * q^15 + 212 * q^16 + 18 * q^17 - 24 * q^18 - 12 * q^20 - 4 * q^21 - 20 * q^22 + 18 * q^23 - 4 * q^25 - 2 * q^27 - 20 * q^28 + 2 * q^30 - 8 * q^31 - 30 * q^32 + 10 * q^33 - 68 * q^36 - 16 * q^37 + 30 * q^38 - 36 * q^40 - 14 * q^42 + 2 * q^43 + 6 * q^45 - 56 * q^46 + 42 * q^48 - 108 * q^50 + 12 * q^51 - 34 * q^52 - 14 * q^55 - 24 * q^56 - 78 * q^57 - 12 * q^58 - 42 * q^60 - 8 * q^61 - 12 * q^62 + 92 * q^63 - 84 * q^65 - 52 * q^66 + 2 * q^67 - 60 * q^68 - 84 * q^70 - 118 * q^72 - 4 * q^73 + 98 * q^75 - 60 * q^76 - 12 * q^77 + 92 * q^78 + 120 * q^80 - 12 * q^81 + 4 * q^82 - 12 * q^83 + 2 * q^85 - 264 * q^86 + 102 * q^87 + 48 * q^88 - 34 * q^90 - 8 * q^91 + 54 * q^92 - 52 * q^93 - 36 * q^95 + 96 * q^96 + 2 * q^97 + 42 * q^98

Introduction

L-functions

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