LMFDB - Embedded newform 882.2.bb.b.151.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.14
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.b.625.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(0.0687040 - 1.73069i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.95950 - 2.74602i) q^{5} +(-0.689017 - 1.58911i) q^{6} +(-2.62753 - 0.309988i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99056 - 0.237810i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(0.0687040 - 1.73069i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.95950 - 2.74602i) q^{5} +(-0.689017 - 1.58911i) q^{6} +(-2.62753 - 0.309988i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99056 - 0.237810i) q^{9} +(-3.85787 - 1.19000i) q^{10} +(-1.43093 - 0.975591i) q^{11} +(-1.31027 - 1.13278i) q^{12} +(5.52779 + 3.76878i) q^{13} +(-2.50182 + 0.860752i) q^{14} +(-4.95583 + 4.93332i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(6.45457 - 0.972871i) q^{17} +(-2.79758 + 1.08330i) q^{18} +(-0.243974 - 0.422575i) q^{19} +(-3.99215 + 0.601719i) q^{20} +(-0.717014 + 4.52613i) q^{21} +(-1.71252 - 0.258120i) q^{22} +(-1.06315 - 2.70885i) q^{23} +(-1.67201 - 0.452096i) q^{24} +(0.844397 + 11.2677i) q^{25} +(6.61558 + 0.997137i) q^{26} +(-0.617039 + 5.15939i) q^{27} +(-1.88060 + 1.86101i) q^{28} +(-8.40992 + 1.26759i) q^{29} +(-2.32456 + 6.59502i) q^{30} -9.43408 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-1.78675 + 2.40946i) q^{33} +(5.39326 - 3.67706i) q^{34} +(6.92495 + 8.13266i) q^{35} +(-2.05051 + 2.18984i) q^{36} +(1.47090 - 3.74780i) q^{37} +(-0.403162 - 0.274871i) q^{38} +(6.90236 - 9.30794i) q^{39} +(-3.33572 + 2.27426i) q^{40} +(-3.49949 + 1.07945i) q^{41} +(1.31781 + 4.38901i) q^{42} +(-1.14094 - 0.351934i) q^{43} +(-1.65492 + 0.510474i) q^{44} +(8.19754 + 8.91593i) q^{45} +(-2.13319 - 1.97931i) q^{46} +(6.68783 - 3.22069i) q^{47} +(-1.70258 + 0.318133i) q^{48} +(6.80781 + 1.62901i) q^{49} +(5.64965 + 9.78547i) q^{50} +(-1.24028 - 11.2377i) q^{51} +(6.39307 - 1.97200i) q^{52} +(-4.02241 - 10.2489i) q^{53} +(1.68264 + 4.91617i) q^{54} +(1.55585 + 6.81663i) q^{55} +(-0.886896 + 2.49267i) q^{56} +(-0.748108 + 0.393210i) q^{57} +(-7.02709 + 4.79099i) q^{58} +(-1.04749 - 4.58935i) q^{59} +(0.767111 + 6.95050i) q^{60} +(-3.88819 - 4.87564i) q^{61} +(-8.49981 + 4.09329i) q^{62} +(7.78406 + 1.55189i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-6.01036 - 26.3331i) q^{65} +(-0.564382 + 2.94610i) q^{66} -8.16318 q^{67} +(3.26374 - 5.65296i) q^{68} +(-4.76122 + 1.65387i) q^{69} +(9.76779 + 4.32265i) q^{70} +(1.00838 - 1.26447i) q^{71} +(-0.897310 + 2.86266i) q^{72} +(4.03731 - 2.75259i) q^{73} +(-0.300871 - 4.01485i) q^{74} +(19.5589 - 0.687252i) q^{75} +(-0.482498 - 0.0727249i) q^{76} +(3.45739 + 3.00696i) q^{77} +(2.18025 - 11.3810i) q^{78} -6.03766 q^{79} +(-2.01862 + 3.49635i) q^{80} +(8.88689 + 1.42237i) q^{81} +(-2.68458 + 2.49092i) q^{82} +(0.582151 - 0.396904i) q^{83} +(3.09162 + 3.38258i) q^{84} +(-21.7739 - 14.8452i) q^{85} +(-1.18065 + 0.177955i) q^{86} +(1.61601 + 14.6420i) q^{87} +(-1.26954 + 1.17796i) q^{88} +(0.826034 + 11.0227i) q^{89} +(11.2542 + 4.47620i) q^{90} +(-13.3561 - 11.6161i) q^{91} +(-2.78073 - 0.857741i) q^{92} +(-0.648159 + 16.3274i) q^{93} +(4.62812 - 5.80348i) q^{94} +(-0.438358 + 1.92057i) q^{95} +(-1.39594 + 1.02535i) q^{96} +(1.64572 - 2.85048i) q^{97} +(6.84043 - 1.48612i) q^{98} +(4.04727 + 3.25785i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) $ 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	0.0687040	−	1.73069i	0.0396663	−	0.999213i
$3$	0.0687040	−	1.73069i	0.0396663	−	0.999213i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−2.95950	−	2.74602i	−1.32353	−	1.22806i	−0.954347	−	0.298701i	$-0.903447\pi$
$5$	−2.95950	−	2.74602i	−1.32353	−	1.22806i	−0.369184	−	0.929356i	$-0.620363\pi$
$6$	−0.689017	−	1.58911i	−0.281290	−	0.648750i
$7$	−2.62753	−	0.309988i	−0.993113	−	0.117164i
$7$	−2.62753	−	0.309988i	−0.993113	−	0.117164i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	−2.99056	−	0.237810i	−0.996853	−	0.0792701i
$10$	−3.85787	−	1.19000i	−1.21997	−	0.376310i
$11$	−1.43093	−	0.975591i	−0.431441	−	0.294152i	0.328061	−	0.944657i	$-0.393605\pi$
$11$	−1.43093	−	0.975591i	−0.431441	−	0.294152i	−0.759502	+	0.650505i	$0.774557\pi$
$12$	−1.31027	−	1.13278i	−0.378242	−	0.327006i
$13$	5.52779	+	3.76878i	1.53313	+	1.04527i	0.976759	+	0.214339i	$0.0687596\pi$
$13$	5.52779	+	3.76878i	1.53313	+	1.04527i	0.556372	+	0.830933i	$0.312193\pi$
$14$	−2.50182	+	0.860752i	−0.668640	+	0.230046i
$15$	−4.95583	+	4.93332i	−1.27959	+	1.27378i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	6.45457	−	0.972871i	1.56546	−	0.235956i	0.691656	−	0.722227i	$-0.256881\pi$
$17$	6.45457	−	0.972871i	1.56546	−	0.235956i	0.873808	+	0.486271i	$0.161643\pi$
$18$	−2.79758	+	1.08330i	−0.659397	+	0.255335i
$19$	−0.243974	−	0.422575i	−0.0559715	−	0.0969454i	0.836682	−	0.547689i	$-0.184492\pi$
$19$	−0.243974	−	0.422575i	−0.0559715	−	0.0969454i	−0.892654	+	0.450743i	$0.851159\pi$
$20$	−3.99215	+	0.601719i	−0.892671	+	0.134548i
$21$	−0.717014	+	4.52613i	−0.156465	+	0.987683i
$22$	−1.71252	−	0.258120i	−0.365110	−	0.0550314i
$23$	−1.06315	−	2.70885i	−0.221681	−	0.564835i	0.776158	−	0.630539i	$-0.217166\pi$
$23$	−1.06315	−	2.70885i	−0.221681	−	0.564835i	−0.997839	+	0.0657037i	$0.979071\pi$
$24$	−1.67201	−	0.452096i	−0.341297	−	0.0922836i
$25$	0.844397	+	11.2677i	0.168879	+	2.25354i
$26$	6.61558	+	0.997137i	1.29742	+	0.195555i
$27$	−0.617039	+	5.15939i	−0.118749	+	0.992924i
$28$	−1.88060	+	1.86101i	−0.355399	+	0.351698i
$29$	−8.40992	+	1.26759i	−1.56168	+	0.235386i	−0.872286	−	0.488997i	$-0.837363\pi$
$29$	−8.40992	+	1.26759i	−1.56168	+	0.235386i	−0.689398	+	0.724383i	$0.742125\pi$
$30$	−2.32456	+	6.59502i	−0.424405	+	1.20408i
$31$	−9.43408			−1.69441			−0.847206	−	0.531265i	$-0.821717\pi$
$31$	−9.43408			−1.69441			−0.847206	+	0.531265i	$0.821717\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−1.78675	+	2.40946i	−0.311034	+	0.419434i
$34$	5.39326	−	3.67706i	0.924936	−	0.630611i
$35$	6.92495	+	8.13266i	1.17053	+	1.37467i
$36$	−2.05051	+	2.18984i	−0.341752	+	0.364974i
$37$	1.47090	−	3.74780i	0.241815	−	0.616134i	−0.757512	−	0.652821i	$-0.773585\pi$
$37$	1.47090	−	3.74780i	0.241815	−	0.616134i	0.999327	+	0.0366872i	$0.0116805\pi$
$38$	−0.403162	−	0.274871i	−0.0654014	−	0.0445899i
$39$	6.90236	−	9.30794i	1.10526	−	1.49046i
$40$	−3.33572	+	2.27426i	−0.527424	+	0.359592i
$41$	−3.49949	+	1.07945i	−0.546529	+	0.168582i	−0.555710	−	0.831376i	$-0.687554\pi$
$41$	−3.49949	+	1.07945i	−0.546529	+	0.168582i	0.00918154	+	0.999958i	$0.497077\pi$
$42$	1.31781	+	4.38901i	0.203342	+	0.677238i
$43$	−1.14094	−	0.351934i	−0.173992	−	0.0536695i	0.206535	−	0.978439i	$-0.433781\pi$
$43$	−1.14094	−	0.351934i	−0.173992	−	0.0536695i	−0.380527	+	0.924770i	$0.624257\pi$
$44$	−1.65492	+	0.510474i	−0.249488	+	0.0769569i
$45$	8.19754	+	8.91593i	1.22202	+	1.32911i
$46$	−2.13319	−	1.97931i	−0.314522	−	0.291833i
$47$	6.68783	−	3.22069i	0.975520	−	0.469786i	0.122958	−	0.992412i	$-0.460762\pi$
$47$	6.68783	−	3.22069i	0.975520	−	0.469786i	0.852562	+	0.522626i	$0.175048\pi$
$48$	−1.70258	+	0.318133i	−0.245747	+	0.0459185i
$49$	6.80781	+	1.62901i	0.972545	+	0.232715i
$50$	5.64965	+	9.78547i	0.798980	+	1.38387i
$51$	−1.24028	−	11.2377i	−0.173674	−	1.57359i
$52$	6.39307	−	1.97200i	0.886559	−	0.273467i
$53$	−4.02241	−	10.2489i	−0.552520	−	1.40780i	−0.885400	−	0.464829i	$-0.846116\pi$
$53$	−4.02241	−	10.2489i	−0.552520	−	1.40780i	0.332880	−	0.942969i	$-0.391979\pi$
$54$	1.68264	+	4.91617i	0.228978	+	0.669006i
$55$	1.55585	+	6.81663i	0.209791	+	0.919154i
$56$	−0.886896	+	2.49267i	−0.118516	+	0.333097i
$57$	−0.748108	+	0.393210i	−0.0990893	+	0.0520820i
$58$	−7.02709	+	4.79099i	−0.922702	+	0.629088i
$59$	−1.04749	−	4.58935i	−0.136371	−	0.597482i	−0.996215	−	0.0869244i	$-0.972296\pi$
$59$	−1.04749	−	4.58935i	−0.136371	−	0.597482i	0.859844	−	0.510558i	$-0.170561\pi$
$60$	0.767111	+	6.95050i	0.0990337	+	0.897305i
$61$	−3.88819	−	4.87564i	−0.497832	−	0.624262i	0.467906	−	0.883778i	$-0.345008\pi$
$61$	−3.88819	−	4.87564i	−0.497832	−	0.624262i	−0.965739	+	0.259516i	$0.916437\pi$
$62$	−8.49981	+	4.09329i	−1.07948	+	0.519849i
$63$	7.78406	+	1.55189i	0.980700	+	0.195520i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−6.01036	−	26.3331i	−0.745494	−	3.26622i
$66$	−0.564382	+	2.94610i	−0.0694706	+	0.362639i
$67$	−8.16318			−0.997291			−0.498646	−	0.866806i	$-0.666169\pi$
$67$	−8.16318			−0.997291			−0.498646	+	0.866806i	$0.666169\pi$
$68$	3.26374	−	5.65296i	0.395787	−	0.685523i
$69$	−4.76122	+	1.65387i	−0.573184	+	0.199102i
$70$	9.76779	+	4.32265i	1.16747	+	0.516655i
$71$	1.00838	−	1.26447i	0.119673	−	0.150065i	−0.718386	−	0.695645i	$-0.755119\pi$
$71$	1.00838	−	1.26447i	0.119673	−	0.150065i	0.838059	+	0.545579i	$0.183690\pi$
$72$	−0.897310	+	2.86266i	−0.105749	+	0.337368i
$73$	4.03731	−	2.75259i	0.472531	−	0.322167i	−0.303532	−	0.952821i	$-0.598166\pi$
$73$	4.03731	−	2.75259i	0.472531	−	0.322167i	0.776064	+	0.630655i	$0.217214\pi$
$74$	−0.300871	−	4.01485i	−0.0349756	−	0.466717i
$75$	19.5589	−	0.687252i	2.25846	−	0.0793570i
$76$	−0.482498	−	0.0727249i	−0.0553463	−	0.00834212i
$77$	3.45739	+	3.00696i	0.394006	+	0.342675i
$78$	2.18025	−	11.3810i	0.246865	−	1.28864i
$79$	−6.03766			−0.679290			−0.339645	−	0.940554i	$-0.610307\pi$
$79$	−6.03766			−0.679290			−0.339645	+	0.940554i	$0.610307\pi$
$80$	−2.01862	+	3.49635i	−0.225688	+	0.390904i
$81$	8.88689	+	1.42237i	0.987432	+	0.158041i
$82$	−2.68458	+	2.49092i	−0.296462	+	0.275076i
$83$	0.582151	−	0.396904i	0.0638994	−	0.0435659i	−0.530949	−	0.847404i	$-0.678164\pi$
$83$	0.582151	−	0.396904i	0.0638994	−	0.0435659i	0.594848	+	0.803838i	$0.297212\pi$
$84$	3.09162	+	3.38258i	0.337324	+	0.369070i
$85$	−21.7739	−	14.8452i	−2.36171	−	1.61018i
$86$	−1.18065	+	0.177955i	−0.127313	+	0.0191893i
$87$	1.61601	+	14.6420i	0.173255	+	1.56979i
$88$	−1.26954	+	1.17796i	−0.135334	+	0.125571i
$89$	0.826034	+	11.0227i	0.0875594	+	1.16840i	0.851942	+	0.523636i	$0.175425\pi$
$89$	0.826034	+	11.0227i	0.0875594	+	1.16840i	−0.764382	+	0.644763i	$0.776956\pi$
$90$	11.2542	+	4.47620i	1.18630	+	0.471833i
$91$	−13.3561	−	11.6161i	−1.40010	−	1.21770i
$92$	−2.78073	−	0.857741i	−0.289911	−	0.0894257i
$93$	−0.648159	+	16.3274i	−0.0672110	+	1.69308i
$94$	4.62812	−	5.80348i	0.477354	−	0.598583i
$95$	−0.438358	+	1.92057i	−0.0449746	+	0.197046i
$96$	−1.39594	+	1.02535i	−0.142473	+	0.104649i
$97$	1.64572	−	2.85048i	0.167098	−	0.289422i	−0.770300	−	0.637681i	$-0.779894\pi$
$97$	1.64572	−	2.85048i	0.167098	−	0.289422i	0.937398	+	0.348259i	$0.113227\pi$
$98$	6.84043	−	1.48612i	0.690988	−	0.150120i
$99$	4.04727	+	3.25785i	0.406766	+	0.327427i
$100$	9.33591	+	6.36512i	0.933591	+	0.636512i
$101$	4.05234	−	1.24998i	0.403223	−	0.124378i	−0.0865084	−	0.996251i	$-0.527571\pi$
$101$	4.05234	−	1.24998i	0.403223	−	0.124378i	0.489732	+	0.871873i	$0.337095\pi$
$102$	−5.99331	−	9.58667i	−0.593426	−	0.949222i
$103$	5.11953	+	4.75023i	0.504442	+	0.468054i	0.890865	−	0.454268i	$-0.150099\pi$
$103$	5.11953	+	4.75023i	0.504442	+	0.468054i	−0.386423	+	0.922322i	$0.626289\pi$
$104$	4.90434	−	4.55056i	0.480910	−	0.446219i
$105$	14.5509	−	11.4262i	1.42002	−	1.11508i
$106$	−8.07091	−	7.48871i	−0.783916	−	0.727367i
$107$	−0.679588	−	9.06847i	−0.0656982	−	0.876682i	−0.928546	−	0.371218i	$-0.878940\pi$
$107$	−0.679588	−	9.06847i	−0.0656982	−	0.876682i	0.862848	−	0.505464i	$-0.168679\pi$
$108$	3.64905	+	3.69924i	0.351130	+	0.355960i
$109$	−0.0205953	+	0.274826i	−0.00197268	+	0.0263235i	−0.998103	−	0.0615618i	$-0.980392\pi$
$109$	−0.0205953	+	0.274826i	−0.00197268	+	0.0263235i	0.996131	+	0.0878853i	$0.0280109\pi$
$110$	4.35940	+	5.46651i	0.415652	+	0.521211i
$111$	−6.38521	−	2.80316i	−0.606057	−	0.266064i
$112$	0.282464	+	2.63063i	0.0266903	+	0.248571i
$113$	−0.107488	−	1.43433i	−0.0101117	−	0.134931i	0.989863	−	0.142024i	$-0.0453611\pi$
$113$	−0.107488	−	1.43433i	−0.0101117	−	0.134931i	−0.999975	+	0.00709348i	$0.997742\pi$
$114$	−0.503414	+	0.678862i	−0.0471491	+	0.0635813i
$115$	−4.29218	+	10.9363i	−0.400247	+	1.01981i
$116$	−4.25246	+	7.36547i	−0.394831	+	0.683867i
$117$	−15.6349	−	12.5853i	−1.44545	−	1.16351i
$118$	−2.93500	−	3.68037i	−0.270188	−	0.338806i
$119$	−17.2612	+	0.555404i	−1.58233	+	0.0509138i
$120$	3.70685	+	5.92934i	0.338388	+	0.541273i
$121$	−2.92297	−	7.44761i	−0.265725	−	0.677055i
$122$	−5.61860	−	2.70578i	−0.508685	−	0.244970i
$123$	1.62776	+	6.13069i	0.146770	+	0.552786i
$124$	−5.88205	+	7.37586i	−0.528224	+	0.662372i
$125$	15.8564	−	19.8833i	1.41824	−	1.77842i
$126$	7.68654	−	1.97917i	0.684771	−	0.176319i
$127$	7.09094	+	8.89176i	0.629219	+	0.789016i	0.989609	−	0.143786i	$-0.0459277\pi$
$127$	7.09094	+	8.89176i	0.629219	+	0.789016i	−0.360390	+	0.932802i	$0.617356\pi$
$128$	−1.00000			−0.0883883
$129$	−0.687475	+	1.95044i	−0.0605288	+	0.171726i
$130$	−16.8407	−	21.1175i	−1.47702	−	1.85213i
$131$	−6.24862	−	1.92744i	−0.545945	−	0.168402i	0.00950038	−	0.999955i	$-0.496976\pi$
$131$	−6.24862	−	1.92744i	−0.545945	−	0.168402i	−0.555445	+	0.831553i	$0.687452\pi$
$132$	0.769772	+	2.89922i	0.0670001	+	0.252344i
$133$	0.510055	+	1.18596i	0.0442274	+	0.102836i
$134$	−7.35477	+	3.54187i	−0.635356	+	0.305971i
$135$	15.9939	−	13.5748i	1.37654	−	1.16834i
$136$	0.487799	−	6.50923i	0.0418284	−	0.558162i
$137$	−8.83946	+	8.20182i	−0.755206	+	0.700729i	−0.960595	−	0.277952i	$-0.910345\pi$
$137$	−8.83946	+	8.20182i	−0.755206	+	0.700729i	0.205389	+	0.978680i	$0.434154\pi$
$138$	−3.57213	+	3.55590i	−0.304080	+	0.302698i
$139$	16.2965	−	5.02680i	1.38225	−	0.426368i	0.487574	−	0.873082i	$-0.337882\pi$
$139$	16.2965	−	5.02680i	1.38225	−	0.426368i	0.894677	+	0.446714i	$0.147406\pi$
$140$	10.6760	−	0.343517i	0.902287	−	0.0290324i
$141$	−5.11453	−	11.7958i	−0.430721	−	0.993387i
$142$	0.359888	−	1.57677i	0.0302012	−	0.132320i
$143$	−4.23308	−	10.7857i	−0.353988	−	0.901947i
$144$	0.433614	+	2.96850i	0.0361345	+	0.247375i
$145$	28.3700	+	19.3424i	2.35600	+	1.60630i
$146$	2.44319	−	4.23172i	0.202200	−	0.350220i
$147$	3.28702	−	11.6703i	0.271109	−	0.962549i
$148$	−2.01305	−	3.48671i	−0.165472	−	0.286606i
$149$	0.611644	−	8.16182i	0.0501078	−	0.668642i	−0.914438	−	0.404726i	$-0.867367\pi$
$149$	0.611644	−	8.16182i	0.0501078	−	0.668642i	0.964546	−	0.263916i	$-0.0850142\pi$
$150$	17.3237	−	9.10547i	1.41448	−	0.743459i
$151$	−16.5875	−	2.50017i	−1.34987	−	0.203461i	−0.566013	−	0.824396i	$-0.691515\pi$
$151$	−16.5875	−	2.50017i	−1.34987	−	0.203461i	−0.783862	+	0.620936i	$0.786753\pi$
$152$	−0.466270	+	0.143825i	−0.0378195	+	0.0116658i
$153$	−19.5341	+	1.37446i	−1.57924	+	0.111119i
$154$	4.41967	+	1.20908i	0.356147	+	0.0974303i
$155$	27.9202	+	25.9062i	2.24261	+	2.08083i
$156$	−2.97369	−	11.1999i	−0.238086	−	0.896709i
$157$	−1.73655	−	7.60831i	−0.138592	−	0.607210i	−0.995745	−	0.0921487i	$-0.970626\pi$
$157$	−1.73655	−	7.60831i	−0.138592	−	0.607210i	0.857154	−	0.515061i	$-0.172231\pi$
$158$	−5.43975	+	2.61964i	−0.432763	+	0.208408i
$159$	−18.0140	+	6.25739i	−1.42861	+	0.496243i
$160$	−0.301703	+	4.02595i	−0.0238517	+	0.318279i
$161$	1.95374	+	7.44715i	0.153976	+	0.586918i
$162$	8.62396	−	2.57437i	0.677562	−	0.202261i
$163$	−4.06376	+	3.77062i	−0.318299	+	0.295338i	−0.823099	−	0.567898i	$-0.807757\pi$
$163$	−4.06376	+	3.77062i	−0.318299	+	0.295338i	0.504800	+	0.863236i	$0.331566\pi$
$164$	−1.33795	+	3.40904i	−0.104476	+	0.266201i
$165$	11.9043	−	2.22436i	0.926752	−	0.173166i
$166$	0.352290	−	0.610184i	0.0273430	−	0.0473595i
$167$	−0.824500	+	2.10079i	−0.0638017	+	0.162564i	−0.959219	−	0.282664i	$-0.908782\pi$
$167$	−0.824500	+	2.10079i	−0.0638017	+	0.162564i	0.895417	+	0.445228i	$0.146877\pi$
$168$	4.25310	+	1.70620i	0.328134	+	0.131636i
$169$	11.6033	+	29.5647i	0.892559	+	2.27420i
$170$	−26.0587	−	3.92771i	−1.99861	−	0.301242i
$171$	0.629126	+	1.32176i	0.0481105	+	0.101077i
$172$	−0.986519	+	0.672597i	−0.0752214	+	0.0512851i
$173$	−2.90044	+	3.63703i	−0.220516	+	0.276519i	−0.879768	−	0.475404i	$-0.842302\pi$
$173$	−2.90044	+	3.63703i	−0.220516	+	0.276519i	0.659251	+	0.751923i	$0.270873\pi$
$174$	7.80892	+	12.4909i	0.591993	+	0.946930i
$175$	1.27417	−	29.8679i	0.0963185	−	2.25780i
$176$	−0.632719	+	1.61214i	−0.0476930	+	0.121520i
$177$	−8.01469	+	1.49757i	−0.602421	+	0.112564i
$178$	5.52678	+	9.57267i	0.414250	+	0.717502i
$179$	6.20474	−	0.935214i	0.463764	−	0.0699012i	0.0869956	−	0.996209i	$-0.472273\pi$
$179$	6.20474	−	0.935214i	0.463764	−	0.0699012i	0.376768	+	0.926308i	$0.377035\pi$
$180$	12.0818	−	0.850103i	0.900527	−	0.0633629i
$181$	2.00964	+	0.967790i	0.149375	+	0.0719353i	0.507078	−	0.861900i	$-0.330726\pi$
$181$	2.00964	+	0.967790i	0.149375	+	0.0719353i	−0.357703	+	0.933835i	$0.616440\pi$
$182$	−17.0735	−	4.67076i	−1.26557	−	0.346220i
$183$	−8.70535	+	6.39427i	−0.643518	+	0.472678i
$184$	−2.87751	+	0.433715i	−0.212133	+	0.0319739i
$185$	−14.6447	+	7.05250i	−1.07670	+	0.518510i
$186$	6.50024	+	14.9917i	0.476621	+	1.09925i
$187$	−10.1852	−	4.90492i	−0.744813	−	0.358683i
$188$	1.65176	−	7.23682i	0.120467	−	0.527799i
$189$	3.22064	−	13.3652i	0.234267	−	0.972172i
$190$	0.438358	+	1.92057i	0.0318018	+	0.139333i
$191$	4.89236	−	21.4348i	0.353999	−	1.55097i	−0.413854	−	0.910343i	$-0.635817\pi$
$191$	4.89236	−	21.4348i	0.353999	−	1.55097i	0.767852	−	0.640627i	$-0.221325\pi$
$192$	−0.812817	+	1.52949i	−0.0586600	+	0.110381i
$193$	−2.96682	+	12.9985i	−0.213556	+	0.935651i	0.748572	+	0.663053i	$0.230740\pi$
$193$	−2.96682	+	12.9985i	−0.213556	+	0.935651i	−0.962128	+	0.272597i	$0.912117\pi$
$194$	0.245970	−	3.28224i	0.0176596	−	0.235651i
$195$	−45.9874	+	8.59287i	−3.29322	+	0.615348i
$196$	5.51821	−	4.30690i	0.394158	−	0.307635i
$197$	23.7378			1.69125			0.845624	−	0.533779i	$-0.179229\pi$
$197$	23.7378			1.69125			0.845624	+	0.533779i	$0.179229\pi$
$198$	5.06000	+	1.17918i	0.359598	+	0.0838005i
$199$	−0.861623	−	0.799470i	−0.0610789	−	0.0566729i	0.649043	−	0.760752i	$-0.275170\pi$
$199$	−0.861623	−	0.799470i	−0.0610789	−	0.0566729i	−0.710122	+	0.704079i	$0.751360\pi$
$200$	11.1731	+	1.68407i	0.790057	+	0.119082i
$201$	−0.560843	+	14.1279i	−0.0395588	+	0.996506i
$202$	3.10869	−	2.88444i	0.218726	−	0.202949i
$203$	22.4903	−	0.723658i	1.57851	−	0.0507908i
$204$	−9.55928	−	6.03690i	−0.669284	−	0.422667i
$205$	13.3210	+	6.41503i	0.930376	+	0.448045i
$206$	6.67359	+	2.05853i	0.464971	+	0.143424i
$207$	2.53521	+	8.35382i	0.176209	+	0.580630i
$208$	2.44424	−	6.22782i	0.169478	−	0.431822i
$209$	−0.0631512	+	0.842694i	−0.00436826	+	0.0582904i
$210$	8.15224	−	16.6080i	0.562558	−	1.14606i
$211$	−0.615591	−	8.21448i	−0.0423790	−	0.565508i	−0.977466	−	0.211091i	$-0.932298\pi$
$211$	−0.615591	−	8.21448i	−0.0423790	−	0.565508i	0.935087	−	0.354417i	$-0.115321\pi$
$212$	−10.5209	−	3.24526i	−0.722576	−	0.222885i
$213$	−2.11913	−	1.83207i	−0.145200	−	0.125532i
$214$	−4.54695	−	7.87554i	−0.310823	−	0.538361i
$215$	2.41021	+	4.17460i	0.164375	+	0.284705i
$216$	4.89273	+	1.74964i	0.332908	+	0.119048i
$217$	24.7883	+	2.92445i	1.68274	+	0.198525i
$218$	0.100687	+	0.256545i	0.00681936	+	0.0173754i
$219$	−4.48650	−	7.17644i	−0.303169	−	0.484939i
$220$	6.29951	+	3.03368i	0.424713	+	0.204531i
$221$	39.3460	+	18.9481i	2.64670	+	1.27458i
$222$	−6.96912	+	0.244878i	−0.467737	+	0.0164351i
$223$	−8.96161	−	22.8338i	−0.600114	−	1.52907i	−0.831108	−	0.556110i	$-0.812293\pi$
$223$	−8.96161	−	22.8338i	−0.600114	−	1.52907i	0.230994	−	0.972955i	$-0.425802\pi$
$224$	1.39588	+	2.24756i	0.0932661	+	0.150171i
$225$	0.154355	−	33.8975i	0.0102904	−	2.25983i
$226$	−0.719178	−	1.24565i	−0.0478390	−	0.0828596i
$227$	−9.33481	−	16.1684i	−0.619573	−	1.07313i	−0.989564	−	0.144096i	$-0.953972\pi$
$227$	−9.33481	−	16.1684i	−0.619573	−	1.07313i	0.369991	−	0.929035i	$-0.379361\pi$
$228$	−0.159014	+	0.830057i	−0.0105309	+	0.0549719i
$229$	−7.81486	−	2.41057i	−0.516421	−	0.159295i	0.0255800	−	0.999673i	$-0.491857\pi$
$229$	−7.81486	−	2.41057i	−0.516421	−	0.159295i	−0.542001	+	0.840378i	$0.682333\pi$
$230$	0.877960	+	11.7156i	0.0578910	+	0.772501i
$231$	5.44165	−	5.77706i	0.358034	−	0.380103i
$232$	−0.635573	+	8.48114i	−0.0417274	+	0.556814i
$233$	0.753020	−	1.91866i	0.0493320	−	0.125696i	−0.904084	−	0.427355i	$-0.859445\pi$
$233$	0.753020	−	1.91866i	0.0493320	−	0.125696i	0.953416	+	0.301660i	$0.0975406\pi$
$234$	−19.5471	−	4.55525i	−1.27784	−	0.297786i
$235$	−28.6367	−	8.83326i	−1.86805	−	0.576219i
$236$	−4.24119	−	2.04245i	−0.276078	−	0.132952i
$237$	−0.414812	+	10.4493i	−0.0269449	+	0.678756i
$238$	−15.3108	+	7.98974i	−0.992451	+	0.517898i
$239$	1.04848	−	0.972843i	0.0678202	−	0.0629280i	−0.645534	−	0.763731i	$-0.723365\pi$
$239$	1.04848	−	0.972843i	0.0678202	−	0.0629280i	0.713355	+	0.700803i	$0.247175\pi$
$240$	5.91240	+	3.73381i	0.381644	+	0.241017i
$241$	14.9481	+	2.25306i	0.962891	+	0.145132i	0.611629	−	0.791145i	$-0.290515\pi$
$241$	14.9481	+	2.25306i	0.962891	+	0.145132i	0.351262	+	0.936277i	$0.385753\pi$
$242$	−5.86490	−	5.44183i	−0.377010	−	0.349814i
$243$	3.07225	−	15.2827i	0.197085	−	0.980386i
$244$	−6.23618			−0.399231
$245$	−15.6745	−	23.5154i	−1.00141	−	1.50235i
$246$	4.12657	+	4.81730i	0.263100	+	0.307140i
$247$	0.243958	−	3.25539i	0.0155227	−	0.207136i
$248$	−2.09928	+	9.19755i	−0.133304	+	0.584045i
$249$	−0.646921	−	1.03479i	−0.0409970	−	0.0655772i
$250$	5.65909	−	24.7941i	0.357912	−	1.56812i
$251$	3.08718	+	13.5258i	0.194861	+	0.853743i	0.973938	+	0.226814i	$0.0728311\pi$
$251$	3.08718	+	13.5258i	0.194861	+	0.853743i	−0.779077	+	0.626929i	$0.784312\pi$
$252$	6.06660	−	5.11824i	0.382160	−	0.322419i
$253$	−1.12145	+	4.91337i	−0.0705047	+	0.308901i
$254$	10.2467	+	4.93455i	0.642935	+	0.309621i
$255$	−27.1883	+	36.6638i	−1.70260	+	2.29598i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	21.4910	−	3.23924i	1.34057	−	0.202058i	0.560710	−	0.828013i	$-0.310528\pi$
$257$	21.4910	−	3.23924i	1.34057	−	0.202058i	0.779860	+	0.625954i	$0.215290\pi$
$258$	0.226868	+	2.05557i	0.0141242	+	0.127974i
$259$	−5.02661	+	9.39148i	−0.312338	+	0.583558i
$260$	−24.3355	−	11.7193i	−1.50922	−	0.726803i
$261$	25.4518	−	1.79084i	1.57543	−	0.110850i
$262$	−6.46610	+	0.974608i	−0.399477	+	0.0602115i
$263$	−9.25118	−	16.0235i	−0.570452	−	0.988052i	−0.996519	−	0.0833608i	$-0.973435\pi$
$263$	−9.25118	−	16.0235i	−0.570452	−	0.988052i	0.426067	−	0.904692i	$-0.359899\pi$
$264$	1.95146	+	2.27811i	0.120104	+	0.140208i
$265$	−16.2394	+	41.3774i	−0.997579	+	2.54179i
$266$	0.974112	+	0.847206i	0.0597266	+	0.0519456i
$267$	19.1335	−	0.672306i	1.17095	−	0.0411445i
$268$	−5.08966	+	6.38223i	−0.310900	+	0.389857i
$269$	4.57732	−	3.12076i	0.279084	−	0.190276i	−0.415686	−	0.909508i	$-0.636459\pi$
$269$	4.57732	−	3.12076i	0.279084	−	0.190276i	0.694770	+	0.719232i	$0.255506\pi$
$270$	8.52011	−	19.1700i	0.518517	−	1.16665i
$271$	−10.3860	−	1.56544i	−0.630907	−	0.0950940i	−0.174199	−	0.984710i	$-0.555734\pi$
$271$	−10.3860	−	1.56544i	−0.630907	−	0.0950940i	−0.456708	+	0.889617i	$0.650972\pi$
$272$	−2.38476	−	6.07626i	−0.144597	−	0.368427i
$273$	−21.0215	+	22.3172i	−1.27228	+	1.35070i
$274$	−4.40544	+	11.2249i	−0.266142	+	0.678120i
$275$	9.78439	−	16.9471i	0.590021	−	1.02195i
$276$	−1.67553	+	4.75364i	−0.100855	+	0.286136i
$277$	−10.3844	+	26.4590i	−0.623938	+	1.58977i	0.172473	+	0.985014i	$0.444824\pi$
$277$	−10.3844	+	26.4590i	−0.623938	+	1.58977i	−0.796412	+	0.604755i	$0.793271\pi$
$278$	12.5016	−	11.5998i	0.749795	−	0.695708i
$279$	28.2132	+	2.24352i	1.68908	+	0.134316i
$280$	9.46970	−	4.94164i	0.565923	−	0.295320i
$281$	0.713532	−	9.52142i	0.0425657	−	0.568000i	−0.934625	−	0.355636i	$-0.884264\pi$
$281$	0.713532	−	9.52142i	0.0425657	−	0.568000i	0.977190	−	0.212365i	$-0.0681165\pi$
$282$	−9.72604	−	8.40856i	−0.579177	−	0.500722i
$283$	24.0078	−	11.5615i	1.42712	−	0.687262i	0.448656	−	0.893704i	$-0.351903\pi$
$283$	24.0078	−	11.5615i	1.42712	−	0.687262i	0.978459	+	0.206442i	$0.0661884\pi$
$284$	−0.359888	−	1.57677i	−0.0213554	−	0.0935643i
$285$	3.29379	+	0.890611i	0.195107	+	0.0527553i
$286$	−8.49362	−	7.88093i	−0.502238	−	0.466009i
$287$	9.52963	−	1.75149i	0.562516	−	0.103387i
$288$	1.67866	+	2.48639i	0.0989157	+	0.146512i
$289$	24.4703	−	7.54809i	1.43943	−	0.444006i
$290$	33.9529	+	5.11757i	1.99378	+	0.300514i
$291$	−4.82021	−	3.04407i	−0.282566	−	0.178447i
$292$	0.365159	−	4.87271i	0.0213693	−	0.285154i
$293$	−9.54871	−	16.5388i	−0.557841	−	0.966210i	−0.997676	−	0.0681311i	$-0.978296\pi$
$293$	−9.54871	−	16.5388i	−0.557841	−	0.966210i	0.439835	−	0.898079i	$-0.355037\pi$
$294$	−2.10204	−	11.9407i	−0.122593	−	0.696398i
$295$	−9.50239	+	16.4586i	−0.553250	+	0.958258i
$296$	−3.32653	−	2.26799i	−0.193350	−	0.131824i
$297$	5.91639	−	6.78074i	0.343304	−	0.393458i
$298$	−2.99021	−	7.61893i	−0.173218	−	0.441353i
$299$	4.33223	−	18.9807i	0.250539	−	1.09768i
$300$	11.6574	−	15.7202i	0.673043	−	0.907608i
$301$	2.88876	+	1.27840i	0.166506	+	0.0736855i
$302$	−16.0296	+	4.94449i	−0.922402	+	0.284523i
$303$	−1.88492	−	7.09922i	−0.108286	−	0.407839i
$304$	−0.357691	+	0.331889i	−0.0205150	+	0.0190351i
$305$	−1.88148	+	25.1065i	−0.107733	+	1.43760i
$306$	−17.0033	+	9.71390i	−0.972014	+	0.555307i
$307$	8.28080	−	3.98782i	0.472610	−	0.227597i	−0.182389	−	0.983226i	$-0.558383\pi$
$307$	8.28080	−	3.98782i	0.472610	−	0.227597i	0.655000	+	0.755629i	$0.272669\pi$
$308$	4.50658	−	0.828282i	0.256786	−	0.0471957i
$309$	8.57290	−	8.53395i	0.487695	−	0.485479i
$310$	36.3955	+	11.2265i	2.06713	+	0.637624i
$311$	2.58888	+	3.24635i	0.146802	+	0.184084i	0.849796	−	0.527112i	$-0.176725\pi$
$311$	2.58888	+	3.24635i	0.146802	+	0.184084i	−0.702994	+	0.711196i	$0.748154\pi$
$312$	−7.53865	−	8.80052i	−0.426792	−	0.498231i
$313$	−3.43715			−0.194279			−0.0971395	−	0.995271i	$-0.530969\pi$
$313$	−3.43715			−0.194279			−0.0971395	+	0.995271i	$0.530969\pi$
$314$	−4.86570	−	6.10139i	−0.274587	−	0.344322i
$315$	−18.7754	−	25.9680i	−1.05788	−	1.46313i
$316$	−3.76442	+	4.72044i	−0.211765	+	0.265545i
$317$	11.1355	−	13.9635i	0.625433	−	0.784268i	−0.363665	−	0.931530i	$-0.618475\pi$
$317$	11.1355	−	13.9635i	0.625433	−	0.784268i	0.989098	+	0.147262i	$0.0470460\pi$
$318$	−13.5151	+	13.4537i	−0.757890	+	0.754447i
$319$	13.2707	+	6.39081i	0.743014	+	0.357817i
$320$	1.47497	+	3.75816i	0.0824533	+	0.210087i
$321$	−15.7414	+	0.553114i	−0.878598	+	0.0308718i
$322$	4.99145	+	5.86196i	0.278163	+	0.326674i
$323$	−1.98586	−	2.49019i	−0.110496	−	0.138558i
$324$	6.65294	−	6.06122i	0.369608	−	0.336734i
$325$	−37.7978	+	65.4677i	−2.09665	+	3.63150i
$326$	−2.02531	+	5.16041i	−0.112172	+	0.285809i
$327$	0.474222	+	0.0545257i	0.0262246	+	0.00301528i
$328$	0.273676	+	3.65195i	0.0151112	+	0.201645i
$329$	−18.5708	+	6.38930i	−1.02384	+	0.352254i
$330$	9.76033	−	7.16918i	0.537288	−	0.394650i
$331$	8.88638	+	11.1432i	0.488439	+	0.612484i	0.963578	−	0.267427i	$-0.0861735\pi$
$331$	8.88638	+	11.1432i	0.488439	+	0.612484i	−0.475139	+	0.879911i	$0.657602\pi$
$332$	0.0526533	−	0.702610i	0.00288973	−	0.0385607i
$333$	−5.29008	+	10.8582i	−0.289895	+	0.595026i
$334$	0.168651	+	2.25049i	0.00922815	+	0.123141i
$335$	24.1590	+	22.4163i	1.31995	+	1.22473i
$336$	4.57221	−	0.308122i	0.249434	−	0.0168094i
$337$	−3.43227	+	3.18468i	−0.186968	+	0.173481i	−0.768103	−	0.640326i	$-0.778799\pi$
$337$	−3.43227	+	3.18468i	−0.186968	+	0.173481i	0.581135	+	0.813807i	$0.302609\pi$
$338$	23.2818	+	21.6024i	1.26636	+	1.17501i
$339$	−2.48977	+	0.0874845i	−0.135226	+	0.00475150i
$340$	−25.1822	+	7.76768i	−1.36570	+	0.421262i
$341$	13.4995	+	9.20381i	0.731039	+	0.498414i
$342$	1.14031	+	0.917894i	0.0616610	+	0.0496340i
$343$	−17.3828	−	6.39060i	−0.938581	−	0.345060i
$344$	−0.596994	+	1.03402i	−0.0321878	+	0.0557508i
$345$	18.6324	+	8.17978i	1.00314	+	0.440385i
$346$	−1.03515	+	4.53531i	−0.0556502	+	0.243820i
$347$	0.594591	−	0.745593i	0.0319193	−	0.0400255i	−0.765616	−	0.643298i	$-0.777566\pi$
$347$	0.594591	−	0.745593i	0.0319193	−	0.0400255i	0.797535	+	0.603273i	$0.206137\pi$
$348$	12.4552	+	7.86572i	0.667667	+	0.421647i
$349$	−3.81879	−	1.17794i	−0.204415	−	0.0630538i	0.190857	−	0.981618i	$-0.438873\pi$
$349$	−3.81879	−	1.17794i	−0.204415	−	0.0630538i	−0.395272	+	0.918564i	$0.629350\pi$
$350$	−11.8112	−	27.4629i	−0.631337	−	1.46796i
$351$	−22.8555	+	26.1945i	−1.21993	+	1.39816i
$352$	0.129422	+	1.72702i	0.00689822	+	0.0920503i
$353$	−3.36298	+	3.12039i	−0.178993	+	0.166081i	−0.764581	−	0.644527i	$-0.777054\pi$
$353$	−3.36298	+	3.12039i	−0.178993	+	0.166081i	0.585588	+	0.810609i	$0.300864\pi$
$354$	−6.57122	+	4.82671i	−0.349256	+	0.256537i
$355$	−6.45659	+	0.973174i	−0.342680	+	0.0516507i
$356$	9.13289	+	6.22670i	0.484042	+	0.330014i
$357$	−0.224680	+	29.9118i	−0.0118913	+	1.58310i
$358$	5.18450	−	3.53473i	0.274009	−	0.186817i
$359$	−19.5065	+	18.0994i	−1.02951	+	0.955250i	−0.999019	−	0.0442853i	$-0.985899\pi$
$359$	−19.5065	+	18.0994i	−1.02951	+	0.955250i	−0.0304953	+	0.999535i	$0.509708\pi$
$360$	10.5165	−	6.00803i	0.554269	−	0.316651i
$361$	9.38095	−	16.2483i	0.493734	−	0.855173i
$362$	2.23053			0.117234
$363$	−13.0903	+	4.54707i	−0.687063	+	0.238659i
$364$	−17.4093	+	3.19971i	−0.912494	+	0.167711i
$365$	−19.5071	−	2.94022i	−1.02105	−	0.153898i
$366$	−5.06888	+	9.53815i	−0.264954	+	0.498567i
$367$	0.705497	+	9.41420i	0.0368266	+	0.491417i	0.984872	+	0.173283i	$0.0554374\pi$
$367$	0.705497	+	9.41420i	0.0368266	+	0.491417i	−0.948046	+	0.318135i	$0.896944\pi$
$368$	−2.40436	+	1.63927i	−0.125336	+	0.0854528i
$369$	10.7221	−	2.39594i	0.558172	−	0.124728i
$370$	−10.1344	+	12.7082i	−0.526864	+	0.660666i
$371$	7.39194	+	28.1762i	0.383771	+	1.46284i
$372$	12.3612	+	10.6867i	0.640898	+	0.554082i
$373$	−9.35921	+	16.2106i	−0.484602	+	0.839354i	−0.999844	−	0.0176903i	$-0.994369\pi$
$373$	−9.35921	+	16.2106i	−0.484602	+	0.839354i	0.515242	+	0.857045i	$0.327702\pi$
$374$	−11.3047			−0.584551
$375$	−33.3224	−	28.8086i	−1.72076	−	1.48767i
$376$	−1.65176	−	7.23682i	−0.0851829	−	0.373211i
$377$	−51.2655	−	24.6882i	−2.64031	−	1.27151i
$378$	−2.89723	−	13.4390i	−0.149018	−	0.691226i
$379$	−2.79206	+	1.34459i	−0.143419	+	0.0690667i	−0.504217	−	0.863577i	$-0.668219\pi$
$379$	−2.79206	+	1.34459i	−0.143419	+	0.0690667i	0.360798	+	0.932644i	$0.382504\pi$
$380$	1.22825	+	1.54018i	0.0630080	+	0.0790095i
$381$	15.8760	−	11.6613i	0.813354	−	0.597427i
$382$	−4.89236	−	21.4348i	−0.250315	−	1.09670i
$383$	4.45731	−	3.03895i	0.227758	−	0.155283i	−0.444065	−	0.895995i	$-0.646464\pi$
$383$	4.45731	−	3.03895i	0.227758	−	0.155283i	0.671823	+	0.740712i	$0.265512\pi$
$384$	−0.0687040	+	1.73069i	−0.00350604	+	0.0883188i
$385$	−1.97497	−	18.3932i	−0.100654	−	0.937403i
$386$	2.96682	+	12.9985i	0.151007	+	0.661605i
$387$	3.32836	+	1.32381i	0.169190	+	0.0672929i
$388$	−1.20250	−	3.06392i	−0.0610477	−	0.155547i
$389$	27.2526	−	8.40632i	1.38176	−	0.426217i	0.487251	−	0.873262i	$-0.338000\pi$
$389$	27.2526	−	8.40632i	1.38176	−	0.426217i	0.894512	+	0.447045i	$0.147523\pi$
$390$	−37.7049	+	27.6951i	−1.90926	+	1.40239i
$391$	−9.49752	−	16.4502i	−0.480310	−	0.831922i
$392$	3.10304	−	6.27464i	0.156727	−	0.316917i
$393$	−3.76511	+	10.6820i	−0.189925	+	0.538835i
$394$	21.3870	−	10.2994i	1.07746	−	0.518878i
$395$	17.8685	+	16.5795i	0.899062	+	0.834207i
$396$	5.07053	−	1.13305i	0.254804	−	0.0569378i
$397$	20.5448	−	6.33724i	1.03111	−	0.318057i	0.267383	−	0.963590i	$-0.413841\pi$
$397$	20.5448	−	6.33724i	1.03111	−	0.318057i	0.763732	+	0.645534i	$0.223365\pi$
$398$	−1.12317	−	0.346453i	−0.0562996	−	0.0173661i
$399$	2.08757	−	0.801266i	0.104509	−	0.0401135i
$400$	10.7973	−	3.33052i	0.539865	−	0.166526i
$401$	11.6886	−	7.96916i	0.583702	−	0.397961i	−0.235156	−	0.971958i	$-0.575560\pi$
$401$	11.6886	−	7.96916i	0.583702	−	0.397961i	0.818858	+	0.573997i	$0.194608\pi$
$402$	5.62457	+	12.9722i	0.280528	+	0.646992i
$403$	−52.1496	−	35.5550i	−2.59776	−	1.77112i
$404$	1.54932	−	3.94760i	0.0770815	−	0.196400i
$405$	−22.3949	−	28.6131i	−1.11281	−	1.42180i
$406$	19.9490	−	10.4101i	0.990054	−	0.516647i
$407$	−5.76107	+	3.92783i	−0.285566	+	0.194695i
$408$	−11.2319	−	1.29144i	−0.556063	−	0.0639357i
$409$	−0.115195	−	0.144451i	−0.00569605	−	0.00714262i	0.778975	−	0.627055i	$-0.215740\pi$
$409$	−0.115195	−	0.144451i	−0.00569605	−	0.00714262i	−0.784671	+	0.619912i	$0.787168\pi$
$410$	14.7851			0.730186
$411$	13.5875	+	15.8618i	0.670221	+	0.782407i
$412$	6.90586	−	1.04089i	0.340227	−	0.0512810i
$413$	1.32966	+	12.3833i	0.0654284	+	0.609345i
$414$	5.90873	+	6.42654i	0.290398	+	0.315847i
$415$	−2.81279	−	0.423959i	−0.138074	−	0.0208113i
$416$	−0.499967	−	6.67159i	−0.0245129	−	0.327102i
$417$	−7.58019	−	28.5495i	−0.371204	−	1.39808i
$418$	0.308734	+	0.786642i	0.0151007	+	0.0384759i
$419$	17.4138	+	2.62471i	0.850720	+	0.128225i	0.559908	−	0.828555i	$-0.310836\pi$
$419$	17.4138	+	2.62471i	0.850720	+	0.128225i	0.290812	+	0.956780i	$0.406074\pi$
$420$	0.138964	−	18.5004i	0.00678077	−	0.902728i
$421$	28.8063	−	4.34185i	1.40393	−	0.211609i	0.596994	−	0.802246i	$-0.296362\pi$
$421$	28.8063	−	4.34185i	1.40393	−	0.211609i	0.806937	+	0.590637i	$0.201124\pi$
$422$	−4.11876	−	7.13390i	−0.200498	−	0.347273i
$423$	−20.7663	+	8.04123i	−1.00969	+	0.390978i
$424$	−10.8870	+	1.64096i	−0.528721	+	0.0796919i
$425$	16.4122	+	71.9067i	0.796110	+	3.48799i
$426$	−2.70418	−	0.731185i	−0.131018	−	0.0354260i
$427$	8.70495	+	14.0162i	0.421262	+	0.678291i
$428$	−7.51373	−	5.12277i	−0.363190	−	0.247619i
$429$	−18.9575	+	6.58512i	−0.915278	+	0.317933i
$430$	3.98281	+	2.71544i	0.192068	+	0.130950i
$431$	−34.6266	−	10.6809i	−1.66791	−	0.514481i	−0.690050	−	0.723761i	$-0.742412\pi$
$431$	−34.6266	−	10.6809i	−1.66791	−	0.514481i	−0.977856	+	0.209280i	$0.932888\pi$
$432$	5.16733	−	0.546503i	0.248613	−	0.0262936i
$433$	6.36160	−	27.8720i	0.305719	−	1.33944i	−0.555631	−	0.831429i	$-0.687523\pi$
$433$	6.36160	−	27.8720i	0.305719	−	1.33944i	0.861350	−	0.508013i	$-0.169620\pi$
$434$	23.6024	−	8.12041i	1.13295	−	0.389792i
$435$	35.4247	−	47.7708i	1.69849	−	2.29043i
$436$	0.202026	+	0.187453i	0.00967531	+	0.00897738i
$437$	−0.885315	+	1.11015i	−0.0423503	+	0.0531057i
$438$	−7.15593	−	4.51913i	−0.341924	−	0.215932i
$439$	29.1300	−	14.0283i	1.39030	−	0.669532i	0.419129	−	0.907927i	$-0.362335\pi$
$439$	29.1300	−	14.0283i	1.39030	−	0.669532i	0.971168	+	0.238395i	$0.0766212\pi$
$440$	6.99193			0.333327
$441$	−19.9718	−	6.49061i	−0.951037	−	0.309077i
$442$	43.6708			2.07721
$443$	−13.1889	+	6.35144i	−0.626624	+	0.301766i	−0.720116	−	0.693854i	$-0.755911\pi$
$443$	−13.1889	+	6.35144i	−0.626624	+	0.301766i	0.0934918	+	0.995620i	$0.470197\pi$
$444$	−6.17271	+	3.24442i	−0.292944	+	0.153973i
$445$	27.8238	−	34.8899i	1.31897	−	1.65394i
$446$	−17.9814	−	16.6843i	−0.851442	−	0.790023i
$447$	−14.0835	−	1.61931i	−0.666129	−	0.0765910i
$448$	2.23282	+	1.41933i	0.105491	+	0.0670571i
$449$	−8.51588	+	37.3105i	−0.401889	+	1.76079i	0.217848	+	0.975983i	$0.430096\pi$
$449$	−8.51588	+	37.3105i	−0.401889	+	1.76079i	−0.619737	+	0.784809i	$0.712761\pi$
$450$	−14.5685	−	30.6076i	−0.686766	−	1.44286i
$451$	6.06063	+	1.86946i	0.285384	+	0.0880292i
$452$	−1.18843	−	0.810255i	−0.0558988	−	0.0381112i
$453$	−5.46664	+	28.5361i	−0.256845	+	1.34074i
$454$	−15.4256	−	10.5170i	−0.723957	−	0.493586i
$455$	7.62945	+	71.0542i	0.357674	+	3.33107i
$456$	0.216882	+	0.816849i	0.0101564	+	0.0382525i
$457$	1.51394	+	6.63300i	0.0708191	+	0.310279i	0.997915	−	0.0645462i	$-0.0205600\pi$
$457$	1.51394	+	6.63300i	0.0708191	+	0.310279i	−0.927096	+	0.374825i	$0.877703\pi$
$458$	−8.08685	+	1.21890i	−0.377874	+	0.0569553i
$459$	1.03669	+	33.9019i	0.0483886	+	1.58241i
$460$	5.87421	+	10.1744i	0.273886	+	0.474385i
$461$	−11.4493	+	1.72570i	−0.533245	+	0.0803738i	−0.410145	−	0.912020i	$-0.634522\pi$
$461$	−11.4493	+	1.72570i	−0.533245	+	0.0803738i	−0.123101	+	0.992394i	$0.539284\pi$
$462$	2.39619	−	7.56600i	0.111481	−	0.352002i
$463$	−14.2139	−	2.14239i	−0.660574	−	0.0995655i	−0.189805	−	0.981822i	$-0.560785\pi$
$463$	−14.2139	−	2.14239i	−0.660574	−	0.0995655i	−0.470769	+	0.882256i	$0.656024\pi$
$464$	3.10720	+	7.91700i	0.144248	+	0.367538i
$465$	46.7537	−	46.5413i	2.16815	−	2.15830i
$466$	−0.154029	−	2.05538i	−0.00713527	−	0.0952136i
$467$	−0.630706	−	0.0950636i	−0.0291856	−	0.00439902i	0.134433	−	0.990923i	$-0.457079\pi$
$467$	−0.630706	−	0.0950636i	−0.0291856	−	0.00439902i	−0.163619	+	0.986524i	$0.552317\pi$
$468$	−19.5878	+	4.37705i	−0.905447	+	0.202329i
$469$	21.4490	+	2.53049i	0.990422	+	0.116847i
$470$	−29.6334	+	4.46652i	−1.36689	+	0.206025i
$471$	−13.2869	+	2.48270i	−0.612229	+	0.114397i
$472$	−4.70737			−0.216674
$473$	1.28926	+	1.61669i	0.0592804	+	0.0743353i
$474$	4.16005	+	9.59448i	0.191078	+	0.440689i
$475$	4.55544	−	3.10585i	0.209018	−	0.142506i
$476$	−10.3279	+	13.8416i	−0.473380	+	0.634429i
$477$	9.59195	+	31.6066i	0.439185	+	1.44717i
$478$	0.522543	−	1.33142i	0.0239006	−	0.0608976i
$479$	8.67319	+	5.91328i	0.396288	+	0.270185i	0.745026	−	0.667036i	$-0.232437\pi$
$479$	8.67319	+	5.91328i	0.396288	+	0.270185i	−0.348737	+	0.937220i	$0.613390\pi$
$480$	6.94693	+	0.798753i	0.317083	+	0.0364579i
$481$	22.2555	−	15.1735i	1.01476	−	0.691853i
$482$	14.4453	−	4.45579i	0.657967	−	0.202956i
$483$	13.0229	−	2.86966i	0.592564	−	0.130574i
$484$	−7.64522	−	2.35824i	−0.347510	−	0.107193i
$485$	−12.6980	+	3.91681i	−0.576586	+	0.177853i
$486$	−3.86292	−	15.1022i	−0.175226	−	0.685052i
$487$	24.1867	+	22.4420i	1.09600	+	1.01694i	0.999767	+	0.0215835i	$0.00687078\pi$
$487$	24.1867	+	22.4420i	1.09600	+	1.01694i	0.0962359	+	0.995359i	$0.469320\pi$
$488$	−5.61860	+	2.70578i	−0.254342	+	0.122485i
$489$	6.24657	+	7.29216i	0.282480	+	0.329763i
$490$	−24.3252	−	14.3858i	−1.09890	−	0.649883i
$491$	−21.0949	−	36.5375i	−0.952001	−	1.64891i	−0.741086	−	0.671411i	$-0.765689\pi$
$491$	−21.0949	−	36.5375i	−0.952001	−	1.64891i	−0.210916	−	0.977504i	$-0.567645\pi$
$492$	5.80806	+	2.54979i	0.261847	+	0.114953i
$493$	−53.0493	+	16.3635i	−2.38922	+	0.736977i
$494$	−1.19266	−	3.03885i	−0.0536604	−	0.136725i
$495$	−3.03180	−	20.7555i	−0.136269	−	0.932891i
$496$	2.09928	+	9.19755i	0.0942605	+	0.412982i
$497$	−3.04153	+	3.00986i	−0.136431	+	0.135010i
$498$	−1.03183	−	0.651626i	−0.0462376	−	0.0292001i
$499$	2.65648	−	1.81116i	0.118920	−	0.0810785i	−0.502399	−	0.864636i	$-0.667549\pi$
$499$	2.65648	−	1.81116i	0.118920	−	0.0810785i	0.621320	+	0.783557i	$0.286597\pi$
$500$	−5.65909	−	24.7941i	−0.253082	−	1.10883i
$501$	3.57917	+	1.57128i	0.159905	+	0.0701998i
$502$	8.65009	+	10.8469i	0.386073	+	0.484120i
$503$	−38.9680	+	18.7660i	−1.73750	+	0.836734i	−0.753751	+	0.657160i	$0.771758\pi$
$503$	−38.9680	+	18.7660i	−1.73750	+	0.836734i	−0.983744	+	0.179574i	$0.942528\pi$
$504$	3.24510	−	7.24357i	0.144548	−	0.322654i
$505$	−15.4254	−	7.42848i	−0.686421	−	0.330563i
$506$	1.12145	+	4.91337i	0.0498543	+	0.218426i
$507$	51.9644	−	18.0504i	2.30782	−	0.801648i
$508$	11.3730			0.504595
$509$	−1.22501	+	2.12178i	−0.0542976	+	0.0940461i	−0.891897	−	0.452239i	$-0.850625\pi$
$509$	−1.22501	+	2.12178i	−0.0542976	+	0.0940461i	0.837599	+	0.546285i	$0.183959\pi$
$510$	−8.58797	+	44.8295i	−0.380282	+	1.98509i
$511$	−11.4614	+	5.98100i	−0.507023	+	0.264584i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	2.33077	−	0.998011i	0.102906	−	0.0440632i
$514$	17.9572	−	12.2430i	0.792060	−	0.540017i
$515$	−2.10705	−	28.1167i	−0.0928478	−	1.23897i
$516$	1.09628	+	1.75357i	0.0482610	+	0.0771965i
$517$	−12.7119	−	1.91601i	−0.559068	−	0.0842660i
$518$	−0.454007	+	10.6424i	−0.0199479	+	0.467600i
$519$	6.09530	+	5.26963i	0.267554	+	0.231311i
$520$	−27.0103			−1.18448
$521$	11.4373	−	19.8099i	0.501075	−	0.867888i	−0.498924	−	0.866646i	$-0.666271\pi$
$521$	11.4373	−	19.8099i	0.501075	−	0.867888i	0.999999	−	0.00124191i	$-0.000395313\pi$
$522$	22.1543	−	12.6566i	0.969667	−	0.553965i
$523$	23.6492	−	21.9432i	1.03411	−	0.959510i	0.0349011	−	0.999391i	$-0.488888\pi$
$523$	23.6492	−	21.9432i	1.03411	−	0.959510i	0.999204	+	0.0398811i	$0.0126979\pi$
$524$	−5.40289	+	3.68363i	−0.236026	+	0.160920i
$525$	−51.6045	−	4.25725i	−2.25221	−	0.185801i
$526$	−15.2874	−	10.4228i	−0.666561	−	0.454454i
$527$	−60.8930	+	9.17814i	−2.65254	+	0.399806i
$528$	2.74664	+	1.20580i	0.119532	+	0.0524757i
$529$	10.6526	−	9.88416i	0.463156	−	0.429746i
$530$	3.32175	+	44.3257i	0.144288	+	1.92539i
$531$	2.04118	+	13.9738i	0.0885798	+	0.606412i
$532$	1.24523	+	0.340655i	0.0539877	+	0.0147693i
$533$	−23.4126	−	7.22184i	−1.01411	−	0.312813i
$534$	16.9470	−	8.90746i	0.733369	−	0.385463i
$535$	−22.8909	+	28.7043i	−0.989662	+	1.24100i
$536$	−1.81648	+	7.95851i	−0.0784599	+	0.343755i
$537$	−1.19227	−	10.8027i	−0.0514504	−	0.466172i
$538$	2.76997	−	4.79773i	0.119422	−	0.206845i
$539$	−8.15226	−	8.97263i	−0.351143	−	0.386479i
$540$	−0.641192	−	20.9683i	−0.0275925	−	0.902332i
$541$	−23.2353	−	15.8415i	−0.998962	−	0.681081i	−0.0507475	−	0.998712i	$-0.516160\pi$
$541$	−23.2353	−	15.8415i	−0.998962	−	0.681081i	−0.948214	+	0.317631i	$0.897113\pi$
$542$	−10.0367	+	3.09592i	−0.431114	+	0.132981i
$543$	1.81301	−	3.41156i	0.0778038	−	0.146404i
$544$	−4.78498	−	4.43981i	−0.205154	−	0.190355i
$545$	0.815629	−	0.756793i	0.0349377	−	0.0324174i
$546$	−9.25664	+	29.2280i	−0.396148	+	1.25084i
$547$	6.71291	+	6.22867i	0.287023	+	0.266319i	0.810522	−	0.585708i	$-0.199183\pi$
$547$	6.71291	+	6.22867i	0.287023	+	0.266319i	−0.523499	+	0.852026i	$0.675374\pi$
$548$	0.901128	+	12.0247i	0.0384943	+	0.513671i
$549$	10.4684	+	15.5056i	0.446780	+	0.661761i
$550$	1.46238	−	19.5141i	0.0623560	−	0.832082i
$551$	2.58746	+	3.24457i	0.110229	+	0.138223i
$552$	0.552928	+	5.00987i	0.0235342	+	0.213234i
$553$	15.8641	+	1.87160i	0.674612	+	0.0795887i
$554$	2.12412	+	28.3444i	0.0902451	+	1.20424i
$555$	11.1995	+	25.8299i	0.475393	+	1.09642i
$556$	6.23059	−	15.8753i	0.264236	−	0.673262i
$557$	−8.12472	+	14.0724i	−0.344255	+	0.596268i	−0.985218	−	0.171304i	$-0.945202\pi$
$557$	−8.12472	+	14.0724i	−0.344255	+	0.596268i	0.640963	+	0.767572i	$0.278535\pi$
$558$	26.3926	−	10.2199i	1.11729	−	0.432643i
$559$	−4.98052	−	6.24538i	−0.210654	−	0.264151i
$560$	6.38781	−	8.56101i	0.269934	−	0.361769i
$561$	−9.18864	+	17.2903i	−0.387945	+	0.729999i
$562$	−3.48832	−	8.88809i	−0.147146	−	0.374922i
$563$	−15.0259	−	7.23609i	−0.633266	−	0.304965i	0.0895742	−	0.995980i	$-0.471449\pi$
$563$	−15.0259	−	7.23609i	−0.633266	−	0.304965i	−0.722840	+	0.691015i	$0.757164\pi$
$564$	−12.4112	−	3.35587i	−0.522606	−	0.141308i
$565$	−3.62060	+	4.54008i	−0.152320	+	0.191003i
$566$	16.6139	−	20.8332i	0.698335	−	0.875684i
$567$	−22.9096	−	6.49216i	−0.962115	−	0.272645i
$568$	−1.00838	−	1.26447i	−0.0423109	−	0.0530562i
$569$	−18.4710			−0.774346			−0.387173	−	0.922007i	$-0.626548\pi$
$569$	−18.4710			−0.774346			−0.387173	+	0.922007i	$0.626548\pi$
$570$	3.35403	−	0.626710i	0.140485	−	0.0262500i
$571$	14.2645	+	17.8871i	0.596949	+	0.748550i	0.984899	−	0.173130i	$-0.0553882\pi$
$571$	14.2645	+	17.8871i	0.596949	+	0.748550i	−0.387950	+	0.921680i	$0.626817\pi$
$572$	−11.0719	−	3.41523i	−0.462939	−	0.142798i
$573$	−36.7609	−	9.93981i	−1.53571	−	0.415241i
$574$	7.82596	−	5.71278i	0.326649	−	0.238447i
$575$	29.6248	−	14.2666i	1.23544	−	0.594957i
$576$	2.59122	+	1.51181i	0.107967	+	0.0629923i
$577$	0.0987080	−	1.31717i	0.00410927	−	0.0548344i	−0.994772	−	0.102119i	$-0.967438\pi$
$577$	0.0987080	−	1.31717i	0.00410927	−	0.0548344i	0.998881	+	0.0472846i	$0.0150568\pi$
$578$	18.7720	−	17.4179i	0.780812	−	0.724488i
$579$	22.2925	+	6.02768i	0.926443	+	0.250502i
$580$	32.8109	−	10.1208i	1.36240	−	0.420244i
$581$	−1.65266	+	0.862417i	−0.0685637	+	0.0357791i
$582$	−5.66364	−	0.651200i	−0.234765	−	0.0269931i
$583$	−4.24298	+	18.5897i	−0.175726	+	0.769907i
$584$	−1.78519	−	4.54860i	−0.0738718	−	0.188222i
$585$	11.7121	+	80.1801i	0.484234	+	3.31504i
$586$	−15.7790	−	10.7580i	−0.651825	−	0.444407i
$587$	−4.59398	+	7.95701i	−0.189614	+	0.328421i	−0.945122	−	0.326719i	$-0.894057\pi$
$587$	−4.59398	+	7.95701i	−0.189614	+	0.328421i	0.755508	+	0.655140i	$0.227390\pi$
$588$	−7.07477	−	9.84620i	−0.291759	−	0.406050i
$589$	2.30167	+	3.98661i	0.0948387	+	0.164265i
$590$	−1.42023	+	18.9516i	−0.0584699	+	0.780226i
$591$	1.63088	−	41.0827i	0.0670855	−	1.68992i
$592$	−3.98114	−	0.600060i	−0.163624	−	0.0246623i
$593$	−36.1542	+	11.1521i	−1.48467	+	0.457961i	−0.927940	−	0.372730i	$-0.878422\pi$
$593$	−36.1542	+	11.1521i	−1.48467	+	0.457961i	−0.556734	+	0.830691i	$0.687946\pi$
$594$	2.38843	−	8.67626i	0.0979985	−	0.355991i
$595$	52.6096	+	45.7558i	2.15678	+	1.87580i
$596$	−5.99982	−	5.56702i	−0.245762	−	0.228034i
$597$	−1.44283	+	1.43627i	−0.0590511	+	0.0587828i
$598$	−4.33223	−	18.9807i	−0.177158	−	0.776180i
$599$	−4.93075	+	2.37452i	−0.201465	+	0.0970205i	−0.531896	−	0.846810i	$-0.678520\pi$
$599$	−4.93075	+	2.37452i	−0.201465	+	0.0970205i	0.330431	+	0.943830i	$0.392806\pi$
$600$	3.68224	−	19.2214i	0.150327	−	0.784711i
$601$	−2.85000	+	38.0306i	−0.116254	+	1.55130i	0.568596	+	0.822617i	$0.307487\pi$
$601$	−2.85000	+	38.0306i	−0.116254	+	1.55130i	−0.684850	+	0.728684i	$0.740132\pi$
$602$	3.15736	−	0.101593i	0.128684	−	0.00414062i
$603$	24.4125	+	1.94129i	0.994153	+	0.0790554i
$604$	−12.2969	+	11.4098i	−0.500353	+	0.464259i
$605$	−11.8007	+	30.0678i	−0.479768	+	1.22243i
$606$	−4.77849	−	5.57834i	−0.194113	−	0.226605i
$607$	4.39318	−	7.60922i	0.178314	−	0.308849i	−0.762989	−	0.646411i	$-0.776269\pi$
$607$	4.39318	−	7.60922i	0.178314	−	0.308849i	0.941303	+	0.337563i	$0.109602\pi$
$608$	−0.178267	+	0.454218i	−0.00722970	+	0.0184210i
$609$	0.292745	−	38.9733i	0.0118626	−	1.57928i
$610$	9.19817	+	23.4366i	0.372423	+	0.948918i
$611$	49.1070	+	7.40168i	1.98665	+	0.299440i
$612$	−11.1047	+	16.1294i	−0.448883	+	0.651991i
$613$	−8.27129	+	5.63927i	−0.334074	+	0.227768i	−0.718725	−	0.695294i	$-0.755274\pi$
$613$	−8.27129	+	5.63927i	−0.334074	+	0.227768i	0.384651	+	0.923062i	$0.374322\pi$
$614$	5.73049	−	7.18581i	0.231264	−	0.289996i
$615$	12.0176	−	22.6137i	0.484597	−	0.911871i
$616$	3.70091	−	2.70159i	0.149114	−	0.108850i
$617$	−7.83793	+	19.9707i	−0.315543	+	0.803990i	0.681827	+	0.731513i	$0.261186\pi$
$617$	−7.83793	+	19.9707i	−0.315543	+	0.803990i	−0.997370	+	0.0724770i	$0.976910\pi$
$618$	4.02117	−	11.4085i	0.161755	−	0.458916i
$619$	−3.53772	−	6.12752i	−0.142193	−	0.246286i	0.786129	−	0.618062i	$-0.212082\pi$
$619$	−3.53772	−	6.12752i	−0.142193	−	0.246286i	−0.928322	+	0.371777i	$0.878749\pi$
$620$	37.6622	−	5.67667i	1.51255	−	0.227980i
$621$	14.6320	−	3.81372i	0.587163	−	0.153039i
$622$	3.74104	+	1.80159i	0.150002	+	0.0722371i
$623$	1.24647	−	29.2184i	0.0499386	−	1.17061i
$624$	−10.6105	−	4.65809i	−0.424760	−	0.186473i
$625$	−45.6617	+	6.88240i	−1.82647	+	0.275296i
$626$	−3.09676	+	1.49132i	−0.123772	+	0.0596052i
$627$	1.45410	+	0.167192i	0.0580712	+	0.00667699i
$628$	−7.03114	−	3.38602i	−0.280573	−	0.135117i
$629$	5.84792	−	25.6214i	0.233172	−	1.02159i
$630$	−28.1832	−	15.2500i	−1.12285	−	0.607575i
$631$	−7.18455	−	31.4776i	−0.286012	−	1.25310i	−0.889945	−	0.456067i	$-0.849258\pi$
$631$	−7.18455	−	31.4776i	−0.286012	−	1.25310i	0.603933	−	0.797035i	$-0.293599\pi$
$632$	−1.34351	+	5.88629i	−0.0534418	+	0.234144i
$633$	−14.2590	+	0.501027i	−0.566744	+	0.0199140i
$634$	3.97422	−	17.4122i	0.157836	−	0.691527i
$635$	3.43127	−	45.7870i	0.136166	−	1.81700i
$636$	−6.33935	+	17.9854i	−0.251372	+	0.713166i
$637$	31.4928	+	34.6620i	1.24779	+	1.37336i
$638$	14.7293			0.583139
$639$	−3.31634	+	3.54168i	−0.131192	+	0.140107i
$640$	2.95950	+	2.74602i	0.116985	+	0.108546i
$641$	25.6246	+	3.86228i	1.01211	+	0.152551i	0.634100	−	0.773251i	$-0.281371\pi$
$641$	25.6246	+	3.86228i	1.01211	+	0.152551i	0.378009	+	0.925802i	$0.376609\pi$
$642$	−13.9425	+	7.32826i	−0.550267	+	0.289224i
$643$	35.3463	−	32.7966i	1.39392	−	1.29337i	0.486168	−	0.873866i	$-0.338394\pi$
$643$	35.3463	−	32.7966i	1.39392	−	1.29337i	0.907753	−	0.419504i	$-0.137796\pi$
$644$	7.04055	+	3.11573i	0.277437	+	0.122777i
$645$	7.39052	−	3.88450i	0.291002	−	0.152952i
$646$	−2.86965	−	1.38195i	−0.112905	−	0.0543721i
$647$	10.4192	+	3.21389i	0.409620	+	0.126351i	0.492715	−	0.870191i	$-0.336004\pi$
$647$	10.4192	+	3.21389i	0.409620	+	0.126351i	−0.0830952	+	0.996542i	$0.526481\pi$
$648$	3.36423	−	8.34757i	0.132159	−	0.327924i
$649$	−2.97844	+	7.58895i	−0.116914	+	0.297892i
$650$	−5.64927	+	75.3843i	−0.221583	+	2.95681i
$651$	6.76437	−	42.6999i	0.265117	−	1.67354i
$652$	0.414276	+	5.52812i	0.0162243	+	0.216498i
$653$	7.58039	+	2.33824i	0.296644	+	0.0915024i	0.439505	−	0.898240i	$-0.355154\pi$
$653$	7.58039	+	2.33824i	0.296644	+	0.0915024i	−0.142861	+	0.989743i	$0.545630\pi$
$654$	0.450917	−	0.156631i	0.0176323	−	0.00612477i
$655$	13.2000	+	22.8631i	0.515768	+	0.893336i
$656$	1.83110	+	3.17155i	0.0714923	+	0.123828i
$657$	−12.7284	+	7.27168i	−0.496583	+	0.283695i
$658$	−13.9595	+	13.8141i	−0.544199	+	0.538532i
$659$	15.8629	+	40.4181i	0.617932	+	1.57447i	0.805746	+	0.592261i	$0.201765\pi$
$659$	15.8629	+	40.4181i	0.617932	+	1.57447i	−0.187813	+	0.982205i	$0.560140\pi$
$660$	5.68316	−	10.6941i	0.221217	−	0.416266i
$661$	5.41667	+	2.60853i	0.210684	+	0.101460i	0.536250	−	0.844059i	$-0.319840\pi$
$661$	5.41667	+	2.60853i	0.210684	+	0.101460i	−0.325566	+	0.945519i	$0.605555\pi$
$662$	12.8412	+	6.18399i	0.499087	+	0.240348i
$663$	35.4964	−	66.7939i	1.37857	−	2.59406i
$664$	−0.257412	−	0.655875i	−0.00998952	−	0.0254529i
$665$	1.74715	−	4.91047i	0.0677517	−	0.190420i
$666$	−0.0549992	+	12.0782i	−0.00213117	+	0.468021i
$667$	12.3747	+	21.4336i	0.479150	+	0.829913i
$668$	1.12840	+	1.95444i	0.0436590	+	0.0756196i
$669$	−40.1339	+	13.9410i	−1.55167	+	0.538989i
$670$	31.4925	+	9.71416i	1.21666	+	0.375291i
$671$	0.807099	+	10.7700i	0.0311577	+	0.415771i
$672$	3.98573	−	2.26141i	0.153753	−	0.0872359i
$673$	0.333855	−	4.45498i	0.0128692	−	0.171727i	−0.987066	−	0.160316i	$-0.948749\pi$
$673$	0.333855	−	4.45498i	0.0128692	−	0.171727i	0.999935	−	0.0114109i	$-0.00363228\pi$
$674$	−1.71059	+	4.35850i	−0.0658893	+	0.167883i
$675$	−58.6554	−	2.59604i	−2.25765	−	0.0999215i
$676$	30.3491	+	9.36146i	1.16727	+	0.360056i
$677$	1.93589	+	0.932274i	0.0744022	+	0.0358302i	0.470715	−	0.882285i	$-0.343996\pi$
$677$	1.93589	+	0.932274i	0.0744022	+	0.0358302i	−0.396313	+	0.918116i	$0.629710\pi$
$678$	−2.20525	+	1.15909i	−0.0846920	+	0.0445146i
$679$	−5.20780	+	6.97955i	−0.199857	+	0.267851i
$680$	−19.3181	+	17.9246i	−0.740816	+	0.687377i
$681$	−28.6237	+	15.0448i	−1.09686	+	0.576518i
$682$	16.1560	+	2.43513i	0.618646	+	0.0932458i
$683$	−22.0669	−	20.4751i	−0.844367	−	0.783458i	0.133859	−	0.991000i	$-0.457263\pi$
$683$	−22.0669	−	20.4751i	−0.844367	−	0.783458i	−0.978226	+	0.207542i	$0.933454\pi$
$684$	1.42564	+	0.332231i	0.0545109	+	0.0127032i
$685$	48.6828			1.86007
$686$	−18.4341	+	1.78436i	−0.703817	+	0.0681273i
$687$	−4.70885	+	13.3595i	−0.179654	+	0.509696i
$688$	−0.0892268	+	1.19065i	−0.00340174	+	0.0453931i
$689$	16.3909	−	71.8134i	0.624445	−	2.73587i
$690$	20.3363	−	0.714568i	0.774189	−	0.0272031i
$691$	0.922430	−	4.04143i	0.0350909	−	0.153743i	−0.954347	−	0.298700i	$-0.903447\pi$
$691$	0.922430	−	4.04143i	0.0350909	−	0.153743i	0.989438	+	0.144957i	$0.0463042\pi$
$692$	1.03515	+	4.53531i	0.0393507	+	0.172406i
$693$	−9.62443	−	9.81471i	−0.365602	−	0.372830i
$694$	0.212207	−	0.929740i	0.00805527	−	0.0352924i
$695$	−62.0333	−	29.8736i	−2.35306	−	1.13317i
$696$	14.6345	+	1.68267i	0.554720	+	0.0637813i
$697$	−21.5376	+	10.3719i	−0.815793	+	0.392865i
$698$	−3.95171	+	0.595624i	−0.149574	+	0.0225447i
$699$	−3.26887	−	1.43506i	−0.123640	−	0.0542790i
$700$	−22.5573	−	19.6185i	−0.852585	−	0.741511i
$701$	22.0566	+	10.6219i	0.833068	+	0.401184i	0.801265	−	0.598310i	$-0.204161\pi$
$701$	22.0566	+	10.6219i	0.833068	+	0.401184i	0.0318028	+	0.999494i	$0.489875\pi$
$702$	−9.22668	+	33.5170i	−0.348239	+	1.26502i
$703$	−1.94259	+	0.292798i	−0.0732661	+	0.0110431i
$704$	0.865930	+	1.49983i	0.0326360	+	0.0565271i
$705$	−17.2551	+	48.9544i	−0.649864	+	1.84373i
$706$	−1.67605	+	4.27051i	−0.0630791	+	0.160723i
$707$	−11.0351	+	2.02819i	−0.415019	+	0.0762778i
$708$	−3.82623	+	7.19986i	−0.143799	+	0.270587i
$709$	25.8916	−	32.4671i	0.972381	−	1.21933i	−0.00326880	−	0.999995i	$-0.501040\pi$
$709$	25.8916	−	32.4671i	0.972381	−	1.21933i	0.975650	−	0.219333i	$-0.0703881\pi$
$710$	−5.39494	+	3.67821i	−0.202469	+	0.138041i
$711$	18.0560	+	1.43582i	0.677153	+	0.0538474i
$712$	10.9301	+	1.64745i	0.409623	+	0.0617408i
$713$	10.0298	+	25.5555i	0.375619	+	0.957063i
$714$	12.7758	+	27.0471i	0.478123	+	1.01221i
$715$	−17.0900	+	43.5445i	−0.639128	+	1.62847i
$716$	3.13741	−	5.43416i	0.117251	−	0.203084i
$717$	−1.61165	−	1.88142i	−0.0601883	−	0.0702630i
$718$	−9.72172	+	24.7705i	−0.362812	+	0.924429i
$719$	−14.2827	+	13.2524i	−0.532655	+	0.494232i	−0.900022	−	0.435844i	$-0.856450\pi$
$719$	−14.2827	+	13.2524i	−0.532655	+	0.494232i	0.367367	+	0.930076i	$0.380259\pi$
$720$	6.86827	−	9.97600i	0.255965	−	0.371783i
$721$	−11.9792	−	14.0684i	−0.446129	−	0.523933i
$722$	1.40208	−	18.7094i	0.0521800	−	0.696293i
$723$	4.92634	−	25.7157i	0.183213	−	0.956377i
$724$	2.00964	−	0.967790i	0.0746876	−	0.0359676i
$725$	−21.3842	−	93.6901i	−0.794188	−	3.47956i
$726$	−9.82106	+	9.77644i	−0.364494	+	0.362838i
$727$	11.2441	+	10.4330i	0.417022	+	0.386940i	0.860588	−	0.509302i	$-0.170096\pi$
$727$	11.2441	+	10.4330i	0.417022	+	0.386940i	−0.443566	+	0.896242i	$0.646287\pi$
$728$	−14.2969	+	10.4364i	−0.529879	+	0.386800i
$729$	−26.2385	−	6.36708i	−0.971797	−	0.235818i
$730$	−18.8510	+	5.81477i	−0.697707	+	0.215214i
$731$	−7.70669	−	1.16160i	−0.285042	−	0.0429632i
$732$	−0.428451	+	10.7929i	−0.0158360	+	0.398916i
$733$	−0.558571	+	7.45361i	−0.0206313	+	0.275305i	0.977342	+	0.211667i	$0.0678893\pi$
$733$	−0.558571	+	7.45361i	−0.0206313	+	0.275305i	−0.997973	+	0.0636379i	$0.979730\pi$
$734$	4.72030	+	8.17580i	0.174229	+	0.301774i
$735$	−41.7748	+	25.5120i	−1.54089	+	0.941025i
$736$	−1.45501	+	2.52014i	−0.0536322	+	0.0928937i
$737$	11.6809	+	7.96393i	0.430273	+	0.293355i
$738$	8.62075	−	6.81083i	0.317334	−	0.250710i
$739$	−18.3708	−	46.8080i	−0.675781	−	1.72186i	−0.691903	−	0.721991i	$-0.743227\pi$
$739$	−18.3708	−	46.8080i	−0.675781	−	1.72186i	0.0161222	−	0.999870i	$-0.494868\pi$
$740$	−3.61693	+	15.8468i	−0.132961	+	0.582541i
$741$	−5.61730	−	0.645873i	−0.206357	−	0.0237267i
$742$	18.8851	+	22.1787i	0.693295	+	0.814205i
$743$	−44.5189	+	13.7323i	−1.63324	+	0.503788i	−0.969689	−	0.244343i	$-0.921428\pi$
$743$	−44.5189	+	13.7323i	−1.63324	+	0.503788i	−0.663551	+	0.748131i	$0.730951\pi$
$744$	15.7739	+	4.26511i	0.578298	+	0.156366i
$745$	−24.2227	+	22.4754i	−0.887450	+	0.823434i
$746$	−1.39883	+	18.6661i	−0.0512148	+	0.683414i
$747$	−1.83535	+	1.04852i	−0.0671518	+	0.0383635i
$748$	−10.1852	+	4.90492i	−0.372406	+	0.179342i
$749$	−1.02548	+	24.0383i	−0.0374703	+	0.878341i
$750$	−42.5221	−	11.4976i	−1.55269	−	0.419832i
$751$	44.3956	+	13.6942i	1.62002	+	0.499710i	0.966385	−	0.257101i	$-0.0827673\pi$
$751$	44.3956	+	13.6942i	1.62002	+	0.499710i	0.653634	+	0.756811i	$0.273243\pi$
$752$	−4.62812	−	5.80348i	−0.168770	−	0.211631i
$753$	23.6211	−	4.41367i	0.860800	−	0.160843i
$754$	−56.9004			−2.07219
$755$	42.2254	+	52.9490i	1.53674	+	1.92701i
$756$	−8.44127	−	10.8510i	−0.307006	−	0.394648i
$757$	27.1890	−	34.0939i	0.988201	−	1.23916i	0.0172582	−	0.999851i	$-0.494506\pi$
$757$	27.1890	−	34.0939i	0.988201	−	1.23916i	0.970942	−	0.239313i	$-0.0769223\pi$
$758$	−1.93217	+	2.42286i	−0.0701795	+	0.0880022i
$759$	8.42647	+	2.27844i	0.305861	+	0.0827022i
$760$	1.77487	+	0.854735i	0.0643815	+	0.0310045i
$761$	14.0039	+	35.6814i	0.507642	+	1.29345i	0.923353	+	0.383953i	$0.125438\pi$
$761$	14.0039	+	35.6814i	0.507642	+	1.29345i	−0.415711	+	0.909497i	$0.636467\pi$
$762$	9.24416	−	17.3948i	0.334881	−	0.630148i
$763$	0.139308	−	0.715728i	0.00504327	−	0.0259111i
$764$	−13.7081	−	17.1894i	−0.495941	−	0.621891i
$765$	61.5857	+	49.5734i	2.22664	+	1.79233i
$766$	2.69735	−	4.67195i	0.0974593	−	0.168804i
$767$	11.5059	−	29.3167i	0.415456	−	1.05856i
$768$	0.689017	+	1.58911i	0.0248628	+	0.0573419i
$769$	−1.05238	−	14.0431i	−0.0379499	−	0.506406i	−0.983497	−	0.180922i	$-0.942092\pi$
$769$	−1.05238	−	14.0431i	−0.0379499	−	0.506406i	0.945548	−	0.325484i	$-0.105527\pi$
$770$	−9.75988	−	15.7148i	−0.351722	−	0.566321i
$771$	−4.12960	−	37.4167i	−0.148724	−	1.34753i
$772$	8.31284	+	10.4240i	0.299186	+	0.375167i
$773$	0.199499	−	2.66213i	0.00717550	−	0.0957503i	−0.992466	−	0.122519i	$-0.960903\pi$
$773$	0.199499	−	2.66213i	0.00717550	−	0.0957503i	0.999642	+	0.0267688i	$0.00852178\pi$
$774$	3.57313	−	0.251413i	0.128434	−	0.00903684i
$775$	−7.96611	−	106.300i	−0.286151	−	3.81842i
$776$	−2.41280	−	2.23875i	−0.0866145	−	0.0803665i
$777$	15.9084	+	9.34472i	0.570710	+	0.335240i
$778$	20.9064	−	19.3983i	0.749531	−	0.695463i
$779$	1.30993	+	1.21544i	0.0469332	+	0.0435477i
$780$	−21.9545	+	41.3119i	−0.786096	+	1.47920i
$781$	−2.67654	+	0.825602i	−0.0957740	+	0.0295424i
$782$	−15.6944	−	10.7003i	−0.561232	−	0.382642i
$783$	−1.35075	−	44.1722i	−0.0482717	−	1.57859i
$784$	0.0732816	−	6.99962i	0.00261720	−	0.249986i
$785$	−15.7533	+	27.2854i	−0.562258	+	0.973859i
$786$	1.24249	+	11.2578i	0.0443183	+	0.401551i
$787$	2.63820	−	11.5587i	0.0940418	−	0.412024i	−0.905892	−	0.423508i	$-0.860798\pi$
$787$	2.63820	−	11.5587i	0.0940418	−	0.412024i	0.999934	+	0.0114842i	$0.00365563\pi$
$788$	14.8003	−	18.5590i	0.527238	−	0.661135i
$789$	−28.3673	+	14.9100i	−1.00990	+	0.530811i
$790$	23.2926	+	7.18480i	0.828712	+	0.255624i
$791$	−0.162197	+	3.80207i	−0.00576708	+	0.135186i
$792$	4.07677	−	3.22086i	0.144862	−	0.114448i
$793$	−3.11788	−	41.6053i	−0.110719	−	1.47745i
$794$	15.7606	−	14.6237i	0.559323	−	0.518976i
$795$	70.4956	+	30.9481i	2.50022	+	1.09762i
$796$	−1.16226	+	0.175183i	−0.0411954	+	0.00620920i
$797$	24.0460	+	16.3943i	0.851753	+	0.580715i	0.908600	−	0.417668i	$-0.137152\pi$
$797$	24.0460	+	16.3943i	0.851753	+	0.580715i	−0.0568469	+	0.998383i	$0.518105\pi$
$798$	1.53318	−	1.62768i	0.0542738	−	0.0576191i
$799$	40.0338	−	27.2946i	1.41629	−	0.965612i
$800$	8.28297	−	7.68547i	0.292847	−	0.271722i
$801$	0.150999	−	33.1604i	0.00533528	−	1.17166i
$802$	7.07339	−	12.2515i	0.249770	−	0.432614i
$803$	−8.46251			−0.298636
$804$	10.6960	+	9.24710i	0.377218	+	0.326120i
$805$	14.6679	−	27.4049i	0.516977	−	0.965895i
$806$	−62.4119	−	9.40708i	−2.19836	−	0.331350i
$807$	−5.08658	−	8.13632i	−0.179056	−	0.286412i
$808$	−0.316911	−	4.22889i	−0.0111489	−	0.148772i
$809$	−5.01166	+	3.41689i	−0.176201	+	0.120132i	−0.648209	−	0.761463i	$-0.724482\pi$
$809$	−5.01166	+	3.41689i	−0.176201	+	0.120132i	0.472008	+	0.881594i	$0.343529\pi$
$810$	−32.5919	−	16.0627i	−1.14516	−	0.564386i
$811$	−1.50583	+	1.88825i	−0.0528769	+	0.0663055i	−0.807567	−	0.589776i	$-0.799216\pi$
$811$	−1.50583	+	1.88825i	−0.0528769	+	0.0663055i	0.754690	+	0.656082i	$0.227787\pi$
$812$	13.4567	−	18.0348i	0.472236	−	0.632897i
$813$	−3.42286	+	17.8674i	−0.120045	+	0.626639i
$814$	−3.48633	+	6.03849i	−0.122196	+	0.211649i
$815$	22.3809			0.783970
$816$	−10.6800	+	3.70981i	−0.373873	+	0.129869i
$817$	0.129642	+	0.567997i	0.00453559	+	0.0198717i
$818$	−0.166462	−	0.0801640i	−0.00582022	−	0.00280287i
$819$	37.1799	+	37.9149i	1.29917	+	1.32486i
$820$	13.3210	−	6.41503i	0.465188	−	0.224023i
$821$	−30.0392	−	37.6680i	−1.04838	−	1.31462i	−0.947511	−	0.319722i	$-0.896410\pi$
$821$	−30.0392	−	37.6680i	−1.04838	−	1.31462i	−0.100865	−	0.994900i	$-0.532161\pi$
$822$	19.1241	+	8.39564i	0.667029	+	0.292832i
$823$	8.15600	+	35.7338i	0.284300	+	1.24560i	0.892219	+	0.451602i	$0.149147\pi$
$823$	8.15600	+	35.7338i	0.284300	+	1.24560i	−0.607919	+	0.793999i	$0.707995\pi$
$824$	5.77034	−	3.93415i	0.201019	−	0.137053i
$825$	−28.6578	−	18.0981i	−0.997738	−	0.630093i
$826$	6.57092	+	10.5801i	0.228632	+	0.368129i
$827$	1.23555	+	5.41332i	0.0429644	+	0.188240i	0.991856	−	0.127362i	$-0.0406509\pi$
$827$	1.23555	+	5.41332i	0.0429644	+	0.188240i	−0.948892	+	0.315601i	$0.897794\pi$
$828$	8.11195	+	3.22641i	0.281910	+	0.112126i
$829$	5.10188	+	12.9994i	0.177196	+	0.451487i	0.991685	−	0.128692i	$-0.0410779\pi$
$829$	5.10188	+	12.9994i	0.177196	+	0.451487i	−0.814489	+	0.580179i	$0.802983\pi$
$830$	−2.71818	+	0.838448i	−0.0943495	+	0.0291030i
$831$	45.0789	+	19.7900i	1.56377	+	0.686508i
$832$	−3.34515	−	5.79397i	−0.115972	−	0.200870i
$833$	45.5264	+	3.89141i	1.57739	+	0.134830i
$834$	−19.2167	−	22.4333i	−0.665419	−	0.776801i
$835$	8.20893	−	3.95321i	0.284082	−	0.136806i
$836$	0.619471	+	0.574785i	0.0214248	+	0.0198794i
$837$	5.82120	−	48.6741i	0.201210	−	1.68242i
$838$	16.8281	−	5.19079i	0.581318	−	0.179313i
$839$	−20.7478	−	6.39984i	−0.716292	−	0.220947i	−0.0848766	−	0.996391i	$-0.527050\pi$
$839$	−20.7478	−	6.39984i	−0.716292	−	0.220947i	−0.631416	+	0.775445i	$0.717526\pi$
$840$	−7.90183	−	16.7286i	−0.272639	−	0.577192i
$841$	41.4084	−	12.7728i	1.42788	−	0.440442i
$842$	24.0697	−	16.4104i	0.829496	−	0.565541i
$843$	−16.4296	−	1.88906i	−0.565865	−	0.0650627i
$844$	−6.80616	−	4.64036i	−0.234278	−	0.159728i
$845$	46.8452	−	119.360i	1.61152	−	4.10609i
$846$	−15.2208	+	16.2550i	−0.523302	+	0.558860i
$847$	5.37152	+	20.4749i	0.184568	+	0.703526i
$848$	−9.09689	+	6.20216i	−0.312389	+	0.212983i
$849$	−18.3600	−	42.3443i	−0.630113	−	1.45325i
$850$	45.9861	+	57.6647i	1.57731	+	1.97788i
$851$	−11.7160			−0.401620
$852$	−2.75363	+	0.514523i	−0.0943377	+	0.0176273i
$853$	13.7811	−	2.07716i	0.471855	−	0.0711206i	0.0911894	−	0.995834i	$-0.470933\pi$
$853$	13.7811	−	2.07716i	0.471855	−	0.0711206i	0.380665	+	0.924713i	$0.375695\pi$
$854$	13.9243	+	8.85121i	0.476479	+	0.302882i
$855$	1.76767	−	5.63934i	0.0604529	−	0.192861i
$856$	−8.99232	−	1.35537i	−0.307351	−	0.0463258i
$857$	3.37218	+	44.9986i	0.115191	+	1.53712i	0.692993	+	0.720944i	$0.256292\pi$
$857$	3.37218	+	44.9986i	0.115191	+	1.53712i	−0.577801	+	0.816177i	$0.696089\pi$
$858$	−14.2230	+	14.1584i	−0.485564	+	0.483358i
$859$	4.41024	+	11.2371i	0.150475	+	0.383405i	0.986158	−	0.165808i	$-0.0530231\pi$
$859$	4.41024	+	11.2371i	0.150475	+	0.383405i	−0.835683	+	0.549212i	$0.814928\pi$
$860$	4.76657	+	0.718445i	0.162539	+	0.0244988i
$861$	−2.37655	−	16.6131i	−0.0809926	−	0.566174i
$862$	−35.8318	+	5.40077i	−1.22044	+	0.183951i
$863$	−20.3135	−	35.1841i	−0.691481	−	1.19768i	−0.971353	−	0.237642i	$-0.923625\pi$
$863$	−20.3135	−	35.1841i	−0.691481	−	1.19768i	0.279872	−	0.960037i	$-0.409708\pi$
$864$	4.41849	−	2.73440i	0.150320	−	0.0930263i
$865$	18.5712	−	2.79916i	0.631440	−	0.0951743i
$866$	−6.36160	−	27.8720i	−0.216176	−	0.947129i
$867$	−11.3822	−	42.8691i	−0.386559	−	1.45591i
$868$	17.7417	−	17.5569i	0.602192	−	0.595921i
$869$	8.63947	+	5.89029i	0.293074	+	0.199814i
$870$	11.1896	−	58.4102i	0.379363	−	1.98029i
$871$	−45.1243	−	30.7652i	−1.52898	−	1.04244i
$872$	0.263352	+	0.0812334i	0.00891824	+	0.00275091i
$873$	−5.59950	+	8.13315i	−0.189514	+	0.275265i
$874$	−0.315965	+	1.38433i	−0.0106877	+	0.0468258i
$875$	−47.8268	+	47.3287i	−1.61684	+	1.60000i
$876$	−8.40805	−	0.966751i	−0.284082	−	0.0326635i
$877$	−31.8492	−	29.5518i	−1.07547	−	0.997892i	−1.00000		0.000744203i	$-0.999763\pi$
$877$	−31.8492	−	29.5518i	−1.07547	−	0.997892i	−0.0754722	−	0.997148i	$-0.524046\pi$
$878$	20.1586	−	25.2780i	0.680319	−	0.853092i
$879$	−29.2796	+	15.3895i	−0.987577	+	0.519076i
$880$	6.29951	−	3.03368i	0.212356	−	0.102265i
$881$	−13.5460			−0.456375			−0.228187	−	0.973617i	$-0.573280\pi$
$881$	−13.5460			−0.456375			−0.228187	+	0.973617i	$0.573280\pi$
$882$	−20.8101	+	2.81760i	−0.700713	+	0.0948734i
$883$	9.13131			0.307293			0.153647	−	0.988126i	$-0.450898\pi$
$883$	9.13131			0.307293			0.153647	+	0.988126i	$0.450898\pi$
$884$	39.3460	−	18.9481i	1.32335	−	0.637292i
$885$	27.8319	+	17.5764i	0.935558	+	0.590825i
$886$	−9.12701	+	11.4449i	−0.306628	+	0.384499i
$887$	19.4501	+	18.0470i	0.653070	+	0.605960i	0.935500	−	0.353328i	$-0.114950\pi$
$887$	19.4501	+	18.0470i	0.653070	+	0.605960i	−0.282430	+	0.959288i	$0.591140\pi$
$888$	−4.15372	+	5.60136i	−0.139390	+	0.187969i
$889$	−15.8753	−	25.5615i	−0.532441	−	0.857304i
$890$	9.93019	−	43.5070i	0.332861	−	1.45836i
$891$	−11.3289	−	10.7053i	−0.379531	−	0.358641i
$892$	−23.4397	−	7.23018i	−0.784818	−	0.242084i
$893$	−2.99264	−	2.04035i	−0.100145	−	0.0682776i
$894$	−13.3914	+	4.65167i	−0.447876	+	0.155575i
$895$	−20.9311	−	14.2706i	−0.699649	−	0.477012i
$896$	2.62753	+	0.309988i	0.0877796	+	0.0103560i
$897$	−32.5521	−	8.80178i	−1.08688	−	0.293883i
$898$	8.51588	+	37.3105i	0.284179	+	1.24507i
$899$	79.3399	−	11.9586i	2.64613	−	0.398841i
$900$	−26.4059	−	21.2554i	−0.880197	−	0.708515i
$901$	−35.9338	−	62.2392i	−1.19713	−	2.07349i
$902$	6.27156	−	0.945286i	0.208820	−	0.0314746i
$903$	2.41097	−	4.91172i	0.0802322	−	0.163452i
$904$	−1.42229	−	0.214376i	−0.0473047	−	0.00713003i
$905$	−3.28996	−	8.38268i	−0.109362	−	0.278650i
$906$	7.45606	+	28.0820i	0.247711	+	0.932962i
$907$	0.553595	+	7.38721i	0.0183818	+	0.245288i	0.998824	+	0.0484815i	$0.0154382\pi$
$907$	0.553595	+	7.38721i	0.0183818	+	0.245288i	−0.980442	+	0.196807i	$0.936943\pi$
$908$	−18.4611	−	2.78256i	−0.612653	−	0.0923426i
$909$	−12.4160	+	2.77446i	−0.411814	+	0.0920229i
$910$	37.7032	+	60.7073i	1.24985	+	2.01243i
$911$	−10.7812	+	1.62501i	−0.357198	+	0.0538389i	−0.325190	−	0.945649i	$-0.605428\pi$
$911$	−10.7812	+	1.62501i	−0.357198	+	0.0538389i	−0.0320079	+	0.999488i	$0.510190\pi$
$912$	0.549821	+	0.641854i	0.0182064	+	0.0212539i
$913$	−1.22023			−0.0403838
$914$	4.24196	+	5.31925i	0.140312	+	0.175945i
$915$	43.3223	+	4.98117i	1.43219	+	0.164672i
$916$	−6.75714	+	4.60694i	−0.223262	+	0.152218i
$917$	15.8210	+	7.00142i	0.522454	+	0.231207i
$918$	15.6435	+	30.0948i	0.516313	+	0.993276i
$919$	−7.54759	+	19.2309i	−0.248972	+	0.634370i	−0.999654	−	0.0262932i	$-0.991630\pi$
$919$	−7.54759	+	19.2309i	−0.248972	+	0.634370i	0.750682	+	0.660663i	$0.229725\pi$
$920$	9.70699	+	6.61812i	0.320030	+	0.218193i
$921$	−6.33275	−	14.6055i	−0.208671	−	0.481266i
$922$	−9.56668	+	6.52245i	−0.315062	+	0.214805i
$923$	10.3397	−	3.18936i	0.340334	−	0.104979i
$924$	−1.12388	−	7.85640i	−0.0369728	−	0.258456i
$925$	43.4711	+	13.4090i	1.42932	+	0.440887i
$926$	−13.7358	+	4.23693i	−0.451386	+	0.139234i
$927$	−14.1806	−	15.4233i	−0.465752	−	0.506569i
$928$	6.23455	+	5.78481i	0.204659	+	0.189896i
$929$	8.90770	−	4.28972i	0.292252	−	0.140741i	−0.282013	−	0.959411i	$-0.591002\pi$
$929$	8.90770	−	4.28972i	0.292252	−	0.140741i	0.574265	+	0.818669i	$0.305288\pi$
$930$	21.9301	−	62.2179i	0.719117	−	2.04021i
$931$	−0.972552	−	3.27425i	−0.0318741	−	0.107309i
$932$	−1.03057	−	1.78500i	−0.0337575	−	0.0584697i
$933$	5.79628	−	4.25750i	0.189762	−	0.139384i
$934$	−0.609493	+	0.188004i	−0.0199432	+	0.00615167i
$935$	16.6740	+	42.4848i	0.545300	+	1.38940i
$936$	−15.7489	+	12.4424i	−0.514768	+	0.406693i
$937$	11.5813	+	50.7411i	0.378345	+	1.65764i	0.702537	+	0.711648i	$0.252051\pi$
$937$	11.5813	+	50.7411i	0.378345	+	1.65764i	−0.324191	+	0.945992i	$0.605092\pi$
$938$	20.4228	−	7.02648i	0.666828	−	0.229423i
$939$	−0.236146	+	5.94863i	−0.00770633	+	0.194126i
$940$	−24.7608	+	16.8817i	−0.807609	+	0.550619i
$941$	−8.03972	−	35.2243i	−0.262087	−	1.14828i	−0.918983	−	0.394298i	$-0.870988\pi$
$941$	−8.03972	−	35.2243i	−0.262087	−	1.14828i	0.656895	−	0.753982i	$-0.271869\pi$
$942$	−10.8939	+	8.00181i	−0.354942	+	0.260713i
$943$	6.64454	+	8.33199i	0.216376	+	0.271327i
$944$	−4.24119	+	2.04245i	−0.138039	+	0.0664761i
$945$	−46.2325	+	30.7103i	−1.50394	+	0.999007i
$946$	1.86304	+	0.897193i	0.0605727	+	0.0291703i
$947$	6.47996	+	28.3906i	0.210570	+	0.922569i	0.964180	+	0.265247i	$0.0854536\pi$
$947$	6.47996	+	28.3906i	0.210570	+	0.922569i	−0.753610	+	0.657322i	$0.771689\pi$
$948$	7.91097	+	6.83935i	0.256936	+	0.222132i
$949$	32.6913			1.06120
$950$	2.75673	−	4.77480i	0.0894402	−	0.154915i
$951$	−23.4014	−	20.2314i	−0.758842	−	0.656050i
$952$	−3.29949	+	16.9520i	−0.106937	+	0.549417i
$953$	26.7413	−	33.5325i	0.866235	−	1.08622i	−0.129279	−	0.991608i	$-0.541266\pi$
$953$	26.7413	−	33.5325i	0.866235	−	1.08622i	0.995514	−	0.0946155i	$-0.0301622\pi$
$954$	22.3556	+	24.3148i	0.723790	+	0.787220i
$955$	−73.3394	+	50.0020i	−2.37321	+	1.61803i
$956$	−0.106886	−	1.42629i	−0.00345693	−	0.0461295i
$957$	11.9722	−	22.5283i	0.387008	−	0.728236i
$958$	10.3800	+	1.56453i	0.335361	+	0.0505476i
$959$	25.7684	−	18.8104i	0.832105	−	0.607419i
$960$	6.60554	−	2.29451i	0.213193	−	0.0740550i
$961$	58.0019			1.87103
$962$	13.4679	−	23.3271i	0.434224	−	0.752097i
$963$	−0.124228	+	27.2814i	−0.00400320	+	0.879131i
$964$	11.0815	−	10.2821i	0.356911	−	0.331165i
$965$	44.4744	−	30.3221i	1.43168	−	0.976103i
$966$	10.4882	−	8.23591i	0.337451	−	0.264986i
$967$	3.90524	+	2.66255i	0.125584	+	0.0856217i	0.624483	−	0.781038i	$-0.285310\pi$
$967$	3.90524	+	2.66255i	0.125584	+	0.0856217i	−0.498899	+	0.866660i	$0.666262\pi$
$968$	−7.91130	+	1.19244i	−0.254279	+	0.0383264i
$969$	−4.44618	+	3.26582i	−0.142832	+	0.104913i
$970$	−9.74105	+	9.03837i	−0.312766	+	0.290205i
$971$	3.57017	+	47.6406i	0.114572	+	1.52886i	0.697648	+	0.716441i	$0.254230\pi$
$971$	3.57017	+	47.6406i	0.114572	+	1.52886i	−0.583075	+	0.812418i	$0.698151\pi$
$972$	−10.0330	−	11.9306i	−0.321808	−	0.382674i
$973$	−44.3778	+	8.15635i	−1.42269	+	0.261481i
$974$	31.5286	+	9.72530i	1.01024	+	0.311619i
$975$	110.707	+	69.9141i	3.54547	+	2.23904i
$976$	−3.88819	+	4.87564i	−0.124458	+	0.156065i
$977$	3.43375	−	15.0442i	0.109855	−	0.481307i	−0.889832	−	0.456289i	$-0.849178\pi$
$977$	3.43375	−	15.0442i	0.109855	−	0.481307i	0.999687	−	0.0250185i	$-0.00796447\pi$
$978$	8.79192	+	3.85973i	0.281135	+	0.123420i
$979$	9.57161	−	16.5785i	0.305910	−	0.529852i
$980$	−28.1580	−	2.40683i	−0.899474	−	0.0768835i
$981$	0.126948	−	0.816985i	0.00405314	−	0.0260843i
$982$	−34.8589	−	23.7664i	−1.11239	−	0.758417i
$983$	29.0854	−	8.97166i	0.927680	−	0.286151i	0.206139	−	0.978523i	$-0.433910\pi$
$983$	29.0854	−	8.97166i	0.927680	−	0.286151i	0.721541	+	0.692371i	$0.243434\pi$
$984$	6.33919	−	0.222744i	0.202086	−	0.00710081i
$985$	−70.2521	−	65.1844i	−2.23842	−	2.07695i
$986$	−40.6959	+	37.7603i	−1.29602	+	1.20253i
$987$	9.78200	+	32.5793i	0.311364	+	1.03701i
$988$	−2.39306	−	2.22044i	−0.0761334	−	0.0706415i
$989$	0.259651	+	3.46480i	0.00825643	+	0.110174i
$990$	−11.7370	−	17.3846i	−0.373028	−	0.552520i
$991$	2.21796	−	29.5967i	0.0704559	−	0.940169i	−0.844224	−	0.535990i	$-0.819938\pi$
$991$	2.21796	−	29.5967i	0.0704559	−	0.940169i	0.914680	−	0.404179i	$-0.132443\pi$
$992$	5.88205	+	7.37586i	0.186755	+	0.234184i
$993$	19.8959	−	14.6140i	0.631376	−	0.463760i
$994$	−1.43440	+	4.03146i	−0.0454963	+	0.127870i
$995$	0.354620	+	4.73207i	0.0112422	+	0.150017i
$996$	−1.21238	−	0.139399i	−0.0384158	−	0.00441701i
$997$	−0.594366	+	1.51442i	−0.0188237	+	0.0479621i	−0.939977	−	0.341239i	$-0.889154\pi$
$997$	−0.594366	+	1.51442i	−0.0188237	+	0.0479621i	0.921153	+	0.389201i	$0.127249\pi$
$998$	1.60757	−	2.78440i	0.0508868	−	0.0881386i
$999$	18.4287	+	9.90149i	0.583059	+	0.313269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.b.151.14	yes	336
9.4	even	3		882.2.y.a.445.2	yes	336
49.37	even	21		882.2.y.a.331.2	✓	336
441.184	even	21	inner	882.2.bb.b.625.14	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.331.2	✓	336	49.37	even	21
882.2.y.a.445.2	yes	336	9.4	even	3
882.2.bb.b.151.14	yes	336	1.1	even	1	trivial
882.2.bb.b.625.14	yes	336	441.184	even	21	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(0.0687040 - 1.73069i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.95950 - 2.74602i) q^{5} +(-0.689017 - 1.58911i) q^{6} +(-2.62753 - 0.309988i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99056 - 0.237810i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(0.0687040 - 1.73069i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.95950 - 2.74602i) q^{5} +(-0.689017 - 1.58911i) q^{6} +(-2.62753 - 0.309988i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99056 - 0.237810i) q^{9} +(-3.85787 - 1.19000i) q^{10} +(-1.43093 - 0.975591i) q^{11} +(-1.31027 - 1.13278i) q^{12} +(5.52779 + 3.76878i) q^{13} +(-2.50182 + 0.860752i) q^{14} +(-4.95583 + 4.93332i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(6.45457 - 0.972871i) q^{17} +(-2.79758 + 1.08330i) q^{18} +(-0.243974 - 0.422575i) q^{19} +(-3.99215 + 0.601719i) q^{20} +(-0.717014 + 4.52613i) q^{21} +(-1.71252 - 0.258120i) q^{22} +(-1.06315 - 2.70885i) q^{23} +(-1.67201 - 0.452096i) q^{24} +(0.844397 + 11.2677i) q^{25} +(6.61558 + 0.997137i) q^{26} +(-0.617039 + 5.15939i) q^{27} +(-1.88060 + 1.86101i) q^{28} +(-8.40992 + 1.26759i) q^{29} +(-2.32456 + 6.59502i) q^{30} -9.43408 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-1.78675 + 2.40946i) q^{33} +(5.39326 - 3.67706i) q^{34} +(6.92495 + 8.13266i) q^{35} +(-2.05051 + 2.18984i) q^{36} +(1.47090 - 3.74780i) q^{37} +(-0.403162 - 0.274871i) q^{38} +(6.90236 - 9.30794i) q^{39} +(-3.33572 + 2.27426i) q^{40} +(-3.49949 + 1.07945i) q^{41} +(1.31781 + 4.38901i) q^{42} +(-1.14094 - 0.351934i) q^{43} +(-1.65492 + 0.510474i) q^{44} +(8.19754 + 8.91593i) q^{45} +(-2.13319 - 1.97931i) q^{46} +(6.68783 - 3.22069i) q^{47} +(-1.70258 + 0.318133i) q^{48} +(6.80781 + 1.62901i) q^{49} +(5.64965 + 9.78547i) q^{50} +(-1.24028 - 11.2377i) q^{51} +(6.39307 - 1.97200i) q^{52} +(-4.02241 - 10.2489i) q^{53} +(1.68264 + 4.91617i) q^{54} +(1.55585 + 6.81663i) q^{55} +(-0.886896 + 2.49267i) q^{56} +(-0.748108 + 0.393210i) q^{57} +(-7.02709 + 4.79099i) q^{58} +(-1.04749 - 4.58935i) q^{59} +(0.767111 + 6.95050i) q^{60} +(-3.88819 - 4.87564i) q^{61} +(-8.49981 + 4.09329i) q^{62} +(7.78406 + 1.55189i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-6.01036 - 26.3331i) q^{65} +(-0.564382 + 2.94610i) q^{66} -8.16318 q^{67} +(3.26374 - 5.65296i) q^{68} +(-4.76122 + 1.65387i) q^{69} +(9.76779 + 4.32265i) q^{70} +(1.00838 - 1.26447i) q^{71} +(-0.897310 + 2.86266i) q^{72} +(4.03731 - 2.75259i) q^{73} +(-0.300871 - 4.01485i) q^{74} +(19.5589 - 0.687252i) q^{75} +(-0.482498 - 0.0727249i) q^{76} +(3.45739 + 3.00696i) q^{77} +(2.18025 - 11.3810i) q^{78} -6.03766 q^{79} +(-2.01862 + 3.49635i) q^{80} +(8.88689 + 1.42237i) q^{81} +(-2.68458 + 2.49092i) q^{82} +(0.582151 - 0.396904i) q^{83} +(3.09162 + 3.38258i) q^{84} +(-21.7739 - 14.8452i) q^{85} +(-1.18065 + 0.177955i) q^{86} +(1.61601 + 14.6420i) q^{87} +(-1.26954 + 1.17796i) q^{88} +(0.826034 + 11.0227i) q^{89} +(11.2542 + 4.47620i) q^{90} +(-13.3561 - 11.6161i) q^{91} +(-2.78073 - 0.857741i) q^{92} +(-0.648159 + 16.3274i) q^{93} +(4.62812 - 5.80348i) q^{94} +(-0.438358 + 1.92057i) q^{95} +(-1.39594 + 1.02535i) q^{96} +(1.64572 - 2.85048i) q^{97} +(6.84043 - 1.48612i) q^{98} +(4.04727 + 3.25785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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