LMFDB - Embedded newform 12.5.d.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,5,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	12.d (of order $2$, degree $1$, 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:	$1.24043955701$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.1
Root			$1.15139 + 1.99426i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.5.d.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.302776 - 3.98852i) q^{2} -5.19615i q^{3} +(-15.8167 + 2.41526i) q^{4} +34.8444 q^{5} +(-20.7250 + 1.57327i) q^{6} +43.0318i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-0.302776 - 3.98852i) q^{2} -5.19615i q^{3} +(-15.8167 + 2.41526i) q^{4} +34.8444 q^{5} +(-20.7250 + 1.57327i) q^{6} +43.0318i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} +(-10.5500 - 138.978i) q^{10} -65.2790i q^{11} +(12.5500 + 82.1857i) q^{12} -99.0665 q^{13} +(171.633 - 13.0290i) q^{14} -181.057i q^{15} +(244.333 - 76.4025i) q^{16} -207.689 q^{17} +(8.17494 + 107.690i) q^{18} +569.960i q^{19} +(-551.122 + 84.1582i) q^{20} +223.600 q^{21} +(-260.367 + 19.7649i) q^{22} -371.198i q^{23} +(324.000 - 74.9400i) q^{24} +589.133 q^{25} +(29.9949 + 395.129i) q^{26} +140.296i q^{27} +(-103.933 - 680.619i) q^{28} +423.911 q^{29} +(-722.150 + 54.8196i) q^{30} -1174.18i q^{31} +(-378.711 - 951.396i) q^{32} -339.199 q^{33} +(62.8831 + 828.372i) q^{34} +1499.42i q^{35} +(427.050 - 65.2119i) q^{36} -1448.13 q^{37} +(2273.30 - 172.570i) q^{38} +514.764i q^{39} +(502.533 + 2172.68i) q^{40} -265.822 q^{41} +(-67.7005 - 891.833i) q^{42} -699.900i q^{43} +(157.665 + 1032.49i) q^{44} -940.799 q^{45} +(-1480.53 + 112.390i) q^{46} -1250.00i q^{47} +(-396.999 - 1269.59i) q^{48} +549.266 q^{49} +(-178.375 - 2349.77i) q^{50} +1079.18i q^{51} +(1566.90 - 239.271i) q^{52} +787.645 q^{53} +(559.574 - 42.4782i) q^{54} -2274.61i q^{55} +(-2683.20 + 620.613i) q^{56} +2961.60 q^{57} +(-128.350 - 1690.78i) q^{58} +3012.53i q^{59} +(437.299 + 2863.71i) q^{60} +4519.33 q^{61} +(-4683.23 + 355.512i) q^{62} -1161.86i q^{63} +(-3680.00 + 1798.56i) q^{64} -3451.91 q^{65} +(102.701 + 1352.91i) q^{66} +5215.70i q^{67} +(3284.94 - 501.622i) q^{68} -1928.80 q^{69} +(5980.46 - 453.987i) q^{70} -4693.16i q^{71} +(-389.400 - 1683.55i) q^{72} -5404.92 q^{73} +(438.459 + 5775.91i) q^{74} -3061.22i q^{75} +(-1376.60 - 9014.86i) q^{76} +2809.07 q^{77} +(2053.15 - 155.858i) q^{78} +7453.44i q^{79} +(8513.64 - 2662.20i) q^{80} +729.000 q^{81} +(80.4843 + 1060.24i) q^{82} -8950.92i q^{83} +(-3536.60 + 540.051i) q^{84} -7236.79 q^{85} +(-2791.57 + 211.913i) q^{86} -2202.71i q^{87} +(4070.39 - 941.466i) q^{88} -616.496 q^{89} +(284.851 + 3752.40i) q^{90} -4263.01i q^{91} +(896.538 + 5871.11i) q^{92} -6101.20 q^{93} +(-4985.66 + 378.470i) q^{94} +19859.9i q^{95} +(-4943.60 + 1967.84i) q^{96} +13723.1 q^{97} +(-166.304 - 2190.76i) q^{98} +1762.53i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 - 20 * q^4 + 24 * q^5 - 18 * q^6 - 108 * q^9	$ 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9} - 172 q^{10} + 180 q^{12} + 296 q^{13} + 600 q^{14} + 112 q^{16} - 600 q^{17} - 162 q^{18} - 1368 q^{20} - 144 q^{21} - 1128 q^{22} + 1296 q^{24} + 972 q^{25} + 1692 q^{26} + 1488 q^{28} + 888 q^{29} - 1980 q^{30} - 2784 q^{32} + 720 q^{33} - 484 q^{34} + 540 q^{36} - 4408 q^{37} + 4680 q^{38} + 1664 q^{40} + 552 q^{41} - 2088 q^{42} - 3696 q^{44} - 648 q^{45} - 384 q^{46} + 1008 q^{48} - 572 q^{49} - 1038 q^{50} + 6008 q^{52} + 5112 q^{53} + 486 q^{54} + 1728 q^{56} + 5616 q^{57} - 124 q^{58} - 2664 q^{60} + 4232 q^{61} - 7224 q^{62} - 14720 q^{64} - 18192 q^{65} + 4824 q^{66} + 5496 q^{68} - 9792 q^{69} + 6096 q^{70} + 8840 q^{73} - 4116 q^{74} - 1872 q^{76} + 20928 q^{77} + 9900 q^{78} + 25632 q^{80} + 2916 q^{81} + 3740 q^{82} - 10512 q^{84} - 10256 q^{85} - 19560 q^{86} - 8640 q^{88} - 25080 q^{89} + 4644 q^{90} + 18816 q^{92} - 17136 q^{93} - 5232 q^{94} - 8352 q^{96} + 23048 q^{97} - 5850 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 - 20 * q^4 + 24 * q^5 - 18 * q^6 - 108 * q^9 - 172 * q^10 + 180 * q^12 + 296 * q^13 + 600 * q^14 + 112 * q^16 - 600 * q^17 - 162 * q^18 - 1368 * q^20 - 144 * q^21 - 1128 * q^22 + 1296 * q^24 + 972 * q^25 + 1692 * q^26 + 1488 * q^28 + 888 * q^29 - 1980 * q^30 - 2784 * q^32 + 720 * q^33 - 484 * q^34 + 540 * q^36 - 4408 * q^37 + 4680 * q^38 + 1664 * q^40 + 552 * q^41 - 2088 * q^42 - 3696 * q^44 - 648 * q^45 - 384 * q^46 + 1008 * q^48 - 572 * q^49 - 1038 * q^50 + 6008 * q^52 + 5112 * q^53 + 486 * q^54 + 1728 * q^56 + 5616 * q^57 - 124 * q^58 - 2664 * q^60 + 4232 * q^61 - 7224 * q^62 - 14720 * q^64 - 18192 * q^65 + 4824 * q^66 + 5496 * q^68 - 9792 * q^69 + 6096 * q^70 + 8840 * q^73 - 4116 * q^74 - 1872 * q^76 + 20928 * q^77 + 9900 * q^78 + 25632 * q^80 + 2916 * q^81 + 3740 * q^82 - 10512 * q^84 - 10256 * q^85 - 19560 * q^86 - 8640 * q^88 - 25080 * q^89 + 4644 * q^90 + 18816 * q^92 - 17136 * q^93 - 5232 * q^94 - 8352 * q^96 + 23048 * q^97 - 5850 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.302776	−	3.98852i	−0.0756939	−	0.997131i
$2$	−0.302776	−	3.98852i	−0.0756939	−	0.997131i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−15.8167	+	2.41526i	−0.988541	+	0.150954i
$5$	34.8444			1.39378			0.696888	−	0.717180i	$-0.254567\pi$
$5$	34.8444			1.39378			0.696888	+	0.717180i	$0.254567\pi$
$6$	−20.7250	+	1.57327i	−0.575694	+	0.0437019i
$7$			43.0318i			0.878200i	0.898438	+	0.439100i	$0.144703\pi$
$7$			43.0318i			0.878200i	−0.898438	+	0.439100i	$0.855297\pi$
$8$	14.4222	+	62.3538i	0.225347	+	0.974279i
$9$	−27.0000			−0.333333
$10$	−10.5500	−	138.978i	−0.105500	−	1.38978i
$11$		−	65.2790i		−	0.539495i	−0.962931	−	0.269748i	$-0.913060\pi$
$11$		−	65.2790i		−	0.539495i	0.962931	−	0.269748i	$-0.0869403\pi$
$12$	12.5500	+	82.1857i	0.0871530	+	0.570734i
$13$	−99.0665			−0.586192			−0.293096	−	0.956083i	$-0.594686\pi$
$13$	−99.0665			−0.586192			−0.293096	+	0.956083i	$0.594686\pi$
$14$	171.633	−	13.0290i	0.875680	−	0.0664744i
$15$		−	181.057i		−	0.804697i
$16$	244.333	−	76.4025i	0.954426	−	0.298447i
$17$	−207.689			−0.718646			−0.359323	−	0.933213i	$-0.616992\pi$
$17$	−207.689			−0.718646			−0.359323	+	0.933213i	$0.616992\pi$
$18$	8.17494	+	107.690i	0.0252313	+	0.332377i
$19$			569.960i			1.57884i	0.613856	+	0.789418i	$0.289618\pi$
$19$			569.960i			1.57884i	−0.613856	+	0.789418i	$0.710382\pi$
$20$	−551.122	+	84.1582i	−1.37780	+	0.210395i
$21$	223.600			0.507029
$22$	−260.367	+	19.7649i	−0.537948	+	0.0408365i
$23$		−	371.198i		−	0.701697i	−0.936432	−	0.350849i	$-0.885893\pi$
$23$		−	371.198i		−	0.701697i	0.936432	−	0.350849i	$-0.114107\pi$
$24$	324.000	−	74.9400i	0.562500	−	0.130104i
$25$	589.133			0.942613
$26$	29.9949	+	395.129i	0.0443712	+	0.584510i
$27$			140.296i			0.192450i
$28$	−103.933	−	680.619i	−0.132567	−	0.868136i
$29$	423.911			0.504056			0.252028	−	0.967720i	$-0.418903\pi$
$29$	423.911			0.504056			0.252028	+	0.967720i	$0.418903\pi$
$30$	−722.150	+	54.8196i	−0.802389	+	0.0609107i
$31$		−	1174.18i		−	1.22183i	−0.791697	−	0.610914i	$-0.790802\pi$
$31$		−	1174.18i		−	1.22183i	0.791697	−	0.610914i	$-0.209198\pi$
$32$	−378.711	−	951.396i	−0.369835	−	0.929097i
$33$	−339.199			−0.311478
$34$	62.8831	+	828.372i	0.0543972	+	0.716585i
$35$			1499.42i			1.22401i
$36$	427.050	−	65.2119i	0.329514	−	0.0503178i
$37$	−1448.13			−1.05780			−0.528902	−	0.848683i	$-0.677396\pi$
$37$	−1448.13			−1.05780			−0.528902	+	0.848683i	$0.677396\pi$
$38$	2273.30	−	172.570i	1.57431	−	0.119508i
$39$			514.764i			0.338438i
$40$	502.533	+	2172.68i	0.314083	+	1.35793i
$41$	−265.822			−0.158133			−0.0790666	−	0.996869i	$-0.525194\pi$
$41$	−265.822			−0.158133			−0.0790666	+	0.996869i	$0.525194\pi$
$42$	−67.7005	−	891.833i	−0.0383790	−	0.505574i
$43$		−	699.900i		−	0.378529i	−0.981926	−	0.189265i	$-0.939390\pi$
$43$		−	699.900i		−	0.378529i	0.981926	−	0.189265i	$-0.0606104\pi$
$44$	157.665	+	1032.49i	0.0814387	+	0.533313i
$45$	−940.799			−0.464592
$46$	−1480.53	+	112.390i	−0.699684	+	0.0531142i
$47$		−	1250.00i		−	0.565868i	−0.959139	−	0.282934i	$-0.908692\pi$
$47$		−	1250.00i		−	0.565868i	0.959139	−	0.282934i	$-0.0913077\pi$
$48$	−396.999	−	1269.59i	−0.172309	−	0.551038i
$49$	549.266			0.228765
$50$	−178.375	−	2349.77i	−0.0713500	−	0.939908i
$51$			1079.18i			0.414911i
$52$	1566.90	−	239.271i	0.579475	−	0.0884877i
$53$	787.645			0.280401			0.140200	−	0.990123i	$-0.455225\pi$
$53$	787.645			0.280401			0.140200	+	0.990123i	$0.455225\pi$
$54$	559.574	−	42.4782i	0.191898	−	0.0145673i
$55$		−	2274.61i		−	0.751936i
$56$	−2683.20	+	620.613i	−0.855611	+	0.197900i
$57$	2961.60			0.911541
$58$	−128.350	−	1690.78i	−0.0381539	−	0.502610i
$59$			3012.53i			0.865422i	0.901533	+	0.432711i	$0.142443\pi$
$59$			3012.53i			0.865422i	−0.901533	+	0.432711i	$0.857557\pi$
$60$	437.299	+	2863.71i	0.121472	+	0.795476i
$61$	4519.33			1.21455			0.607273	−	0.794493i	$-0.292263\pi$
$61$	4519.33			1.21455			0.607273	+	0.794493i	$0.292263\pi$
$62$	−4683.23	+	355.512i	−1.21832	+	0.0924849i
$63$		−	1161.86i		−	0.292733i
$64$	−3680.00	+	1798.56i	−0.898438	+	0.439101i
$65$	−3451.91			−0.817021
$66$	102.701	+	1352.91i	0.0235770	+	0.310584i
$67$			5215.70i			1.16189i	0.813945	+	0.580943i	$0.197316\pi$
$67$			5215.70i			1.16189i	−0.813945	+	0.580943i	$0.802684\pi$
$68$	3284.94	−	501.622i	0.710411	−	0.108482i
$69$	−1928.80			−0.405125
$70$	5980.46	−	453.987i	1.22050	−	0.0926504i
$71$		−	4693.16i		−	0.930998i	−0.885048	−	0.465499i	$-0.845875\pi$
$71$		−	4693.16i		−	0.930998i	0.885048	−	0.465499i	$-0.154125\pi$
$72$	−389.400	−	1683.55i	−0.0751157	−	0.324760i
$73$	−5404.92			−1.01425			−0.507124	−	0.861873i	$-0.669291\pi$
$73$	−5404.92			−1.01425			−0.507124	+	0.861873i	$0.669291\pi$
$74$	438.459	+	5775.91i	0.0800693	+	1.05477i
$75$		−	3061.22i		−	0.544218i
$76$	−1376.60	−	9014.86i	−0.238331	−	1.56074i
$77$	2809.07			0.473785
$78$	2053.15	−	155.858i	0.337467	−	0.0256177i
$79$			7453.44i			1.19427i	0.802141	+	0.597135i	$0.203694\pi$
$79$			7453.44i			1.19427i	−0.802141	+	0.597135i	$0.796306\pi$
$80$	8513.64	−	2662.20i	1.33026	−	0.415969i
$81$	729.000			0.111111
$82$	80.4843	+	1060.24i	0.0119697	+	0.157679i
$83$		−	8950.92i		−	1.29931i	−0.760231	−	0.649653i	$-0.774914\pi$
$83$		−	8950.92i		−	1.29931i	0.760231	−	0.649653i	$-0.225086\pi$
$84$	−3536.60	+	540.051i	−0.501219	+	0.0765378i
$85$	−7236.79			−1.00163
$86$	−2791.57	+	211.913i	−0.377443	+	0.0286523i
$87$		−	2202.71i		−	0.291017i
$88$	4070.39	−	941.466i	0.525619	−	0.121574i
$89$	−616.496			−0.0778305			−0.0389153	−	0.999243i	$-0.512390\pi$
$89$	−616.496			−0.0778305			−0.0389153	+	0.999243i	$0.512390\pi$
$90$	284.851	+	3752.40i	0.0351668	+	0.463259i
$91$		−	4263.01i		−	0.514794i
$92$	896.538	+	5871.11i	0.105924	+	0.693656i
$93$	−6101.20			−0.705422
$94$	−4985.66	+	378.470i	−0.564244	+	0.0428327i
$95$			19859.9i			2.20054i
$96$	−4943.60	+	1967.84i	−0.536415	+	0.213525i
$97$	13723.1			1.45850			0.729252	−	0.684246i	$-0.239868\pi$
$97$	13723.1			1.45850			0.729252	+	0.684246i	$0.239868\pi$
$98$	−166.304	−	2190.76i	−0.0173162	−	0.228109i
$99$			1762.53i			0.179832i
$100$	−9318.11	+	1422.91i	−0.931811	+	0.142291i
$101$	14758.8			1.44680			0.723401	−	0.690428i	$-0.242578\pi$
$101$	14758.8			1.44680			0.723401	+	0.690428i	$0.242578\pi$
$102$	4304.35	−	326.750i	0.413720	−	0.0314062i
$103$		−	1859.14i		−	0.175242i	−0.996154	−	0.0876210i	$-0.972074\pi$
$103$		−	1859.14i		−	0.175242i	0.996154	−	0.0876210i	$-0.0279264\pi$
$104$	−1428.76	−	6177.17i	−0.132097	−	0.571114i
$105$	7791.20			0.706685
$106$	−238.480	−	3141.54i	−0.0212246	−	0.279596i
$107$		−	10664.4i		−	0.931466i	−0.884925	−	0.465733i	$-0.845791\pi$
$107$		−	10664.4i		−	0.931466i	0.884925	−	0.465733i	$-0.154209\pi$
$108$	−338.851	−	2219.02i	−0.0290510	−	0.190245i
$109$	−4479.34			−0.377017			−0.188508	−	0.982072i	$-0.560365\pi$
$109$	−4479.34			−0.377017			−0.188508	+	0.982072i	$0.560365\pi$
$110$	−9072.32	+	688.695i	−0.749779	+	0.0569170i
$111$			7524.72i			0.610723i
$112$	3287.74	+	10514.1i	0.262096	+	0.838177i
$113$	−21225.5			−1.66227			−0.831135	−	0.556070i	$-0.812309\pi$
$113$	−21225.5			−1.66227			−0.831135	+	0.556070i	$0.812309\pi$
$114$	−896.700	−	11812.4i	−0.0689981	−	0.908926i
$115$		−	12934.2i		−	0.978009i
$116$	−6704.85	+	1023.85i	−0.498280	+	0.0760890i
$117$	2674.79			0.195397
$118$	12015.6	−	912.122i	0.862939	−	0.0655072i
$119$		−	8937.22i		−	0.631115i
$120$	11289.6	−	2611.24i	0.783999	−	0.181336i
$121$	10379.7			0.708945
$122$	−1368.34	−	18025.5i	−0.0919338	−	1.21106i
$123$			1381.25i			0.0912982i
$124$	2835.94	+	18571.5i	0.184439	+	1.20783i
$125$	−1249.77			−0.0799851
$126$	−4634.10	+	351.782i	−0.291893	+	0.0221581i
$127$			4676.78i			0.289961i	0.989435	+	0.144980i	$0.0463119\pi$
$127$			4676.78i			0.289961i	−0.989435	+	0.144980i	$0.953688\pi$
$128$	8287.81	+	14133.2i	0.505848	+	0.862623i
$129$	−3636.79			−0.218544
$130$	1045.15	+	13768.0i	0.0618435	+	0.814677i
$131$			29922.6i			1.74364i	0.489828	+	0.871819i	$0.337060\pi$
$131$			29922.6i			1.74364i	−0.489828	+	0.871819i	$0.662940\pi$
$132$	5365.00	−	819.253i	0.307909	−	0.0470187i
$133$	−24526.4			−1.38653
$134$	20803.0	−	1579.19i	1.15855	−	0.0879476i
$135$			4888.54i			0.268232i
$136$	−2995.33	−	12950.2i	−0.161945	−	0.700162i
$137$	−19273.3			−1.02687			−0.513434	−	0.858129i	$-0.671627\pi$
$137$	−19273.3			−1.02687			−0.513434	+	0.858129i	$0.671627\pi$
$138$	583.994	+	7693.07i	0.0306655	+	0.403963i
$139$		−	24086.9i		−	1.24667i	−0.781955	−	0.623335i	$-0.785778\pi$
$139$		−	24086.9i		−	1.24667i	0.781955	−	0.623335i	$-0.214222\pi$
$140$	−3621.48	−	23715.8i	−0.184769	−	1.20999i
$141$	−6495.20			−0.326704
$142$	−18718.8	+	1420.98i	−0.928327	+	0.0704709i
$143$			6466.95i			0.316248i
$144$	−6596.99	+	2062.87i	−0.318142	+	0.0994825i
$145$	14770.9			0.702541
$146$	1636.48	+	21557.7i	0.0767723	+	1.01134i
$147$		−	2854.07i		−	0.132078i
$148$	22904.6	−	3497.61i	1.04568	−	0.159679i
$149$	43993.2			1.98159			0.990794	−	0.135378i	$-0.0432248\pi$
$149$	43993.2			1.98159			0.990794	+	0.135378i	$0.0432248\pi$
$150$	−12209.8	+	926.864i	−0.542656	+	0.0411940i
$151$			1388.00i			0.0608746i	0.999537	+	0.0304373i	$0.00969000\pi$
$151$			1388.00i			0.0608746i	−0.999537	+	0.0304373i	$0.990310\pi$
$152$	−35539.2	+	8220.08i	−1.53823	+	0.355786i
$153$	5607.60			0.239549
$154$	−850.518	−	11204.0i	−0.0358626	−	0.472425i
$155$		−	40913.5i		−	1.70295i
$156$	−1243.29	−	8141.85i	−0.0510884	−	0.334560i
$157$	7464.93			0.302849			0.151425	−	0.988469i	$-0.451614\pi$
$157$	7464.93			0.302849			0.151425	+	0.988469i	$0.451614\pi$
$158$	29728.2	−	2256.72i	1.19084	−	0.0903989i
$159$		−	4092.72i		−	0.161889i
$160$	−13196.0	−	33150.8i	−0.515468	−	1.29495i
$161$	15973.3			0.616230
$162$	−220.723	−	2907.63i	−0.00841043	−	0.110792i
$163$			47291.0i			1.77993i	0.456029	+	0.889965i	$0.349271\pi$
$163$			47291.0i			1.77993i	−0.456029	+	0.889965i	$0.650729\pi$
$164$	4204.41	−	642.028i	0.156321	−	0.0238707i
$165$	−11819.2			−0.434130
$166$	−35701.0	+	2710.12i	−1.29558	+	0.0983496i
$167$			90.1917i			0.00323395i	0.999999	+	0.00161698i	$0.000514700\pi$
$167$			90.1917i			0.00323395i	−0.999999	+	0.00161698i	$0.999485\pi$
$168$	3224.80	+	13942.3i	0.114257	+	0.493987i
$169$	−18746.8			−0.656379
$170$	2191.13	+	28864.1i	0.0758175	+	0.998759i
$171$		−	15388.9i		−	0.526279i
$172$	1690.44	+	11070.1i	0.0571403	+	0.374191i
$173$	−1212.10			−0.0404993			−0.0202497	−	0.999795i	$-0.506446\pi$
$173$	−1212.10			−0.0404993			−0.0202497	+	0.999795i	$0.506446\pi$
$174$	−8785.54	+	666.926i	−0.290182	+	0.0220282i
$175$			25351.4i			0.827802i
$176$	−4987.48	−	15949.8i	−0.161011	−	0.514909i
$177$	15653.6			0.499652
$178$	186.660	+	2458.91i	0.00589130	+	0.0776072i
$179$			20697.3i			0.645964i	0.946405	+	0.322982i	$0.104685\pi$
$179$			20697.3i			0.645964i	−0.946405	+	0.322982i	$0.895315\pi$
$180$	14880.3	−	2272.27i	0.459268	−	0.0701318i
$181$	18722.8			0.571496			0.285748	−	0.958305i	$-0.407758\pi$
$181$	18722.8			0.571496			0.285748	+	0.958305i	$0.407758\pi$
$182$	−17003.1	+	1290.73i	−0.513317	+	0.0389667i
$183$		−	23483.1i		−	0.701219i
$184$	23145.6	−	5353.49i	0.683649	−	0.158125i
$185$	−50459.3			−1.47434
$186$	1847.29	+	24334.8i	0.0533962	+	0.703399i
$187$			13557.7i			0.387706i
$188$	3019.07	+	19770.8i	0.0854197	+	0.559383i
$189$	−6037.19			−0.169010
$190$	79211.8	−	6013.10i	2.19423	−	0.166568i
$191$		−	37058.2i		−	1.01582i	−0.861410	−	0.507910i	$-0.830418\pi$
$191$		−	37058.2i		−	1.01582i	0.861410	−	0.507910i	$-0.169582\pi$
$192$	9345.59	+	19121.8i	0.253515	+	0.518713i
$193$	−23019.8			−0.617999			−0.308999	−	0.951062i	$-0.599994\pi$
$193$	−23019.8			−0.617999			−0.308999	+	0.951062i	$0.599994\pi$
$194$	−4155.01	−	54734.7i	−0.110400	−	1.45432i
$195$			17936.7i			0.471707i
$196$	−8687.55	+	1326.62i	−0.226144	+	0.0345329i
$197$	−42137.6			−1.08577			−0.542885	−	0.839807i	$-0.682668\pi$
$197$	−42137.6			−1.08577			−0.542885	+	0.839807i	$0.682668\pi$
$198$	7029.90	−	533.652i	0.179316	−	0.0136122i
$199$		−	68550.6i		−	1.73103i	−0.500881	−	0.865516i	$-0.666991\pi$
$199$		−	68550.6i		−	1.73103i	0.500881	−	0.865516i	$-0.333009\pi$
$200$	8496.60	+	36734.7i	0.212415	+	0.918367i
$201$	27101.6			0.670815
$202$	−4468.62	−	58866.0i	−0.109514	−	1.44265i
$203$			18241.6i			0.442662i
$204$	−2606.50	−	17069.1i	−0.0626322	−	0.410156i
$205$	−9262.40			−0.220402
$206$	−7415.23	+	562.903i	−0.174739	+	0.0132647i
$207$			10022.3i			0.233899i
$208$	−24205.2	+	7568.93i	−0.559477	+	0.174948i
$209$	37206.4			0.851775
$210$	−2358.99	−	31075.4i	−0.0534917	−	0.704657i
$211$			37678.5i			0.846308i	0.906058	+	0.423154i	$0.139077\pi$
$211$			37678.5i			0.846308i	−0.906058	+	0.423154i	$0.860923\pi$
$212$	−12457.9	+	1902.36i	−0.277187	+	0.0423274i
$213$	−24386.4			−0.537512
$214$	−42535.0	+	3228.91i	−0.928794	+	0.0705063i
$215$		−	24387.6i		−	0.527585i
$216$	−8748.00	+	2023.38i	−0.187500	+	0.0433680i
$217$	50526.9			1.07301
$218$	1356.23	+	17866.0i	0.0285379	+	0.375935i
$219$			28084.8i			0.585576i
$220$	5493.76	+	35976.7i	0.113507	+	0.743320i
$221$	20575.0			0.421265
$222$	30012.5	−	2278.30i	0.608971	−	0.0462280i
$223$		−	9238.47i		−	0.185776i	−0.995677	−	0.0928882i	$-0.970390\pi$
$223$		−	9238.47i		−	0.185776i	0.995677	−	0.0928882i	$-0.0296099\pi$
$224$	40940.2	−	16296.6i	0.815933	−	0.324789i
$225$	−15906.6			−0.314204
$226$	6426.57	+	84658.6i	0.125824	+	1.65750i
$227$			48884.8i			0.948685i	0.880340	+	0.474342i	$0.157314\pi$
$227$			48884.8i			0.948685i	−0.880340	+	0.474342i	$0.842686\pi$
$228$	−46842.6	+	7153.02i	−0.901096	+	0.137600i
$229$	17654.5			0.336654			0.168327	−	0.985731i	$-0.446164\pi$
$229$	17654.5			0.336654			0.168327	+	0.985731i	$0.446164\pi$
$230$	−51588.3	+	3916.15i	−0.975203	+	0.0740293i
$231$		−	14596.4i		−	0.273540i
$232$	6113.73	+	26432.5i	0.113587	+	0.491091i
$233$	52029.9			0.958387			0.479193	−	0.877709i	$-0.340929\pi$
$233$	52029.9			0.958387			0.479193	+	0.877709i	$0.340929\pi$
$234$	−809.863	−	10668.5i	−0.0147904	−	0.194837i
$235$		−	43555.6i		−	0.788693i
$236$	−7276.04	−	47648.2i	−0.130638	−	0.855505i
$237$	38729.2			0.689512
$238$	−35646.3	+	2705.97i	−0.629304	+	0.0477716i
$239$			53899.3i			0.943598i	0.881706	+	0.471799i	$0.156395\pi$
$239$			53899.3i			0.943598i	−0.881706	+	0.471799i	$0.843605\pi$
$240$	−13833.2	−	44238.2i	−0.240160	−	0.768024i
$241$	−56311.0			−0.969526			−0.484763	−	0.874646i	$-0.661094\pi$
$241$	−56311.0			−0.969526			−0.484763	+	0.874646i	$0.661094\pi$
$242$	−3142.71	−	41399.5i	−0.0536628	−	0.706911i
$243$		−	3788.00i		−	0.0641500i
$244$	−71480.7	+	10915.3i	−1.20063	+	0.183340i
$245$	19138.8			0.318848
$246$	5509.15	−	418.209i	0.0910363	−	0.00691072i
$247$		−	56463.9i		−	0.925501i
$248$	73214.4	−	16934.2i	1.19040	−	0.275335i
$249$	−46510.3			−0.750155
$250$	378.399	+	4984.73i	0.00605438	+	0.0797556i
$251$		−	11951.6i		−	0.189705i	−0.995491	−	0.0948525i	$-0.969762\pi$
$251$		−	11951.6i		−	0.189705i	0.995491	−	0.0948525i	$-0.0302379\pi$
$252$	2806.18	+	18376.7i	0.0441891	+	0.289379i
$253$	−24231.4			−0.378562
$254$	18653.5	−	1416.02i	0.289129	−	0.0219483i
$255$			37603.5i			0.578293i
$256$	53861.3	−	37335.3i	0.821858	−	0.569692i
$257$	−15483.1			−0.234418			−0.117209	−	0.993107i	$-0.537395\pi$
$257$	−15483.1			−0.234418			−0.117209	+	0.993107i	$0.537395\pi$
$258$	1101.13	+	14505.4i	0.0165424	+	0.217917i
$259$		−	62315.7i		−	0.928963i
$260$	54597.7	−	8337.25i	0.807658	−	0.123332i
$261$	−11445.6			−0.168019
$262$	119347.	−	9059.83i	1.73864	−	0.131983i
$263$		−	16337.3i		−	0.236194i	−0.993002	−	0.118097i	$-0.962321\pi$
$263$		−	16337.3i		−	0.236194i	0.993002	−	0.118097i	$-0.0376793\pi$
$264$	−4892.00	−	21150.4i	−0.0701906	−	0.303466i
$265$	27445.0			0.390816
$266$	7425.99	+	97824.1i	0.104952	+	1.38256i
$267$			3203.41i			0.0449355i
$268$	−12597.3	−	82495.0i	−0.175391	−	1.14857i
$269$	−82062.5			−1.13407			−0.567035	−	0.823694i	$-0.691910\pi$
$269$	−82062.5			−1.13407			−0.567035	+	0.823694i	$0.691910\pi$
$270$	19498.0	−	1480.13i	0.267463	−	0.0203036i
$271$			75123.6i			1.02291i	0.859310	+	0.511456i	$0.170894\pi$
$271$			75123.6i			1.02291i	−0.859310	+	0.511456i	$0.829106\pi$
$272$	−50745.2	+	15868.0i	−0.685895	+	0.214478i
$273$	−22151.2			−0.297216
$274$	5835.48	+	76872.0i	0.0777277	+	1.02392i
$275$		−	38458.0i		−	0.508535i
$276$	30507.2	−	4658.55i	0.400483	−	0.0611551i
$277$	9651.88			0.125792			0.0628959	−	0.998020i	$-0.479966\pi$
$277$	9651.88			0.125792			0.0628959	+	0.998020i	$0.479966\pi$
$278$	−96071.2	+	7292.92i	−1.24309	+	0.0943653i
$279$			31702.8i			0.407276i
$280$	−93494.4	+	21624.9i	−1.19253	+	0.275828i
$281$	−90483.6			−1.14593			−0.572964	−	0.819581i	$-0.694206\pi$
$281$	−90483.6			−1.14593			−0.572964	+	0.819581i	$0.694206\pi$
$282$	1966.59	+	25906.3i	0.0247295	+	0.325767i
$283$			44901.3i			0.560643i	0.959906	+	0.280321i	$0.0904410\pi$
$283$			44901.3i			0.560643i	−0.959906	+	0.280321i	$0.909559\pi$
$284$	11335.2	+	74230.1i	0.140537	+	0.920330i
$285$	103195.			1.27048
$286$	25793.6	−	1958.04i	0.315341	−	0.0239380i
$287$		−	11438.8i		−	0.138872i
$288$	10225.2	+	25687.7i	0.123278	+	0.309699i
$289$	−40386.4			−0.483547
$290$	−4472.28	−	58914.2i	−0.0531781	−	0.700525i
$291$		−	71307.1i		−	0.842067i
$292$	85487.8	−	13054.3i	1.00262	−	0.153104i
$293$	30326.7			0.353257			0.176628	−	0.984278i	$-0.443481\pi$
$293$	30326.7			0.353257			0.176628	+	0.984278i	$0.443481\pi$
$294$	−11383.5	+	864.143i	−0.131699	+	0.00999748i
$295$			104970.i			1.20620i
$296$	−20885.3	−	90296.6i	−0.238373	−	1.03060i
$297$	9158.38			0.103826
$298$	−13320.1	−	175468.i	−0.149994	−	1.97590i
$299$			36773.3i			0.411329i
$300$	7393.64	+	48418.3i	0.0821516	+	0.537981i
$301$	30118.0			0.332424
$302$	5536.08	−	420.253i	0.0607000	−	0.00460784i
$303$		−	76689.2i		−	0.835312i
$304$	43546.4	+	139260.i	0.471200	+	1.50688i
$305$	157473.			1.69281
$306$	−1697.84	−	22366.0i	−0.0181324	−	0.238862i
$307$			35547.6i			0.377167i	0.982057	+	0.188583i	$0.0603896\pi$
$307$			35547.6i			0.377167i	−0.982057	+	0.188583i	$0.939610\pi$
$308$	−44430.1	+	6784.62i	−0.468356	+	0.0715195i
$309$	−9660.38			−0.101176
$310$	−163184.	+	12387.6i	−1.69807	+	0.128903i
$311$		−	72202.2i		−	0.746500i	−0.927731	−	0.373250i	$-0.878243\pi$
$311$		−	72202.2i		−	0.746500i	0.927731	−	0.373250i	$-0.121757\pi$
$312$	−32097.5	+	7424.04i	−0.329733	+	0.0762660i
$313$	162750.			1.66124			0.830618	−	0.556842i	$-0.187987\pi$
$313$	162750.			1.66124			0.830618	+	0.556842i	$0.187987\pi$
$314$	−2260.20	−	29774.1i	−0.0229238	−	0.301980i
$315$		−	40484.3i		−	0.408005i
$316$	−18002.0	−	117888.i	−0.180279	−	1.18058i
$317$	−64556.9			−0.642428			−0.321214	−	0.947007i	$-0.604091\pi$
$317$	−64556.9			−0.642428			−0.321214	+	0.947007i	$0.604091\pi$
$318$	−16323.9	+	1239.18i	−0.161425	+	0.0122540i
$319$		−	27672.5i		−	0.271936i
$320$	−128227.	+	62669.7i	−1.25222	+	0.612009i
$321$	−55413.6			−0.537782
$322$	−4836.33	−	63709.9i	−0.0466449	−	0.614462i
$323$		−	118374.i		−	1.13462i
$324$	−11530.3	+	1760.72i	−0.109838	+	0.0167726i
$325$	−58363.3			−0.552552
$326$	188621.	−	14318.6i	1.77482	−	0.134730i
$327$			23275.3i			0.217671i
$328$	−3833.74	−	16575.0i	−0.0356348	−	0.154066i
$329$	53789.8			0.496945
$330$	3578.57	+	47141.2i	0.0328610	+	0.432885i
$331$			11544.1i			0.105367i	0.998611	+	0.0526833i	$0.0167774\pi$
$331$			11544.1i			0.105367i	−0.998611	+	0.0526833i	$0.983223\pi$
$332$	21618.8	+	141574.i	0.196135	+	1.28442i
$333$	39099.6			0.352601
$334$	359.732	−	27.3078i	0.00322467	−	0.000244790i
$335$			181738.i			1.61941i
$336$	54632.8	−	17083.6i	0.483921	−	0.151321i
$337$	−209011.			−1.84039			−0.920195	−	0.391461i	$-0.871970\pi$
$337$	−209011.			−1.84039			−0.920195	+	0.391461i	$0.871970\pi$
$338$	5676.09	+	74772.2i	0.0496839	+	0.654496i
$339$			110291.i			0.959712i
$340$	114462.	−	17478.7i	0.990155	−	0.151200i
$341$	−76649.0			−0.659170
$342$	−61379.1	+	4659.39i	−0.524769	+	0.0398361i
$343$			126955.i			1.07910i
$344$	43641.5	−	10094.1i	0.368793	−	0.0853004i
$345$	−67207.9			−0.564654
$346$	366.996	+	4834.51i	0.00306555	+	0.0403831i
$347$		−	161304.i		−	1.33964i	−0.742525	−	0.669819i	$-0.766372\pi$
$347$		−	161304.i		−	1.33964i	0.742525	−	0.669819i	$-0.233628\pi$
$348$	5320.10	+	34839.4i	0.0439300	+	0.287682i
$349$	88041.4			0.722830			0.361415	−	0.932405i	$-0.382294\pi$
$349$	88041.4			0.722830			0.361415	+	0.932405i	$0.382294\pi$
$350$	101115.	−	7675.80i	0.825427	−	0.0626596i
$351$		−	13898.6i		−	0.112813i
$352$	−62106.1	+	24721.9i	−0.501244	+	0.199525i
$353$	186762.			1.49878			0.749391	−	0.662128i	$-0.230347\pi$
$353$	186762.			1.49878			0.749391	+	0.662128i	$0.230347\pi$
$354$	−4739.52	−	62434.7i	−0.0378206	−	0.498218i
$355$		−	163530.i		−	1.29760i
$356$	9750.90	−	1488.99i	0.0769387	−	0.0117488i
$357$	−46439.2			−0.364374
$358$	82551.8	−	6266.65i	0.644111	−	0.0488955i
$359$			226517.i			1.75756i	0.477224	+	0.878782i	$0.341643\pi$
$359$			226517.i			1.75756i	−0.477224	+	0.878782i	$0.658357\pi$
$360$	−13568.4	−	58662.4i	−0.104694	−	0.452642i
$361$	−194533.			−1.49272
$362$	−5668.80	−	74676.3i	−0.0432588	−	0.569857i
$363$		−	53934.3i		−	0.409309i
$364$	10296.3	+	67426.5i	0.0777099	+	0.508895i
$365$	−188331.			−1.41363
$366$	−93663.0	+	7110.12i	−0.699207	+	0.0530780i
$367$		−	106652.i		−	0.791839i	−0.918285	−	0.395920i	$-0.870426\pi$
$367$		−	106652.i		−	0.791839i	0.918285	−	0.395920i	$-0.129574\pi$
$368$	−28360.5	−	90695.9i	−0.209420	−	0.669718i
$369$	7177.19			0.0527110
$370$	15277.9	+	201258.i	0.111599	+	1.47011i
$371$			33893.8i			0.246248i
$372$	96500.5	−	14736.0i	0.697339	−	0.106486i
$373$	129184.			0.928518			0.464259	−	0.885699i	$-0.346321\pi$
$373$	129184.			0.928518			0.464259	+	0.885699i	$0.346321\pi$
$374$	54075.3	−	4104.94i	0.386594	−	0.0293470i
$375$			6493.98i			0.0461794i
$376$	77942.4	−	18027.8i	0.551313	−	0.127517i
$377$	−41995.3			−0.295473
$378$	1827.91	+	24079.5i	0.0127930	+	0.168525i
$379$		−	156156.i		−	1.08713i	−0.839368	−	0.543563i	$-0.817075\pi$
$379$		−	156156.i		−	1.08713i	0.839368	−	0.543563i	$-0.182925\pi$
$380$	−47966.8	−	314117.i	−0.332180	−	2.17533i
$381$	24301.3			0.167409
$382$	−147807.	+	11220.3i	−1.01291	+	0.0768915i
$383$		−	261403.i		−	1.78202i	−0.453980	−	0.891012i	$-0.649996\pi$
$383$		−	261403.i		−	1.78202i	0.453980	−	0.891012i	$-0.350004\pi$
$384$	73438.3	−	43064.7i	0.498035	−	0.292051i
$385$	97880.4			0.660350
$386$	6969.85	+	91815.2i	0.0467787	+	0.616226i
$387$			18897.3i			0.126176i
$388$	−217053.	+	33144.7i	−1.44179	+	0.220166i
$389$	−1046.60			−0.00691644			−0.00345822	−	0.999994i	$-0.501101\pi$
$389$	−1046.60			−0.00691644			−0.00345822	+	0.999994i	$0.501101\pi$
$390$	71540.8	−	5430.78i	0.470354	−	0.0357054i
$391$			77093.6i			0.504272i
$392$	7921.62	+	34248.8i	0.0515516	+	0.222881i
$393$	155482.			1.00669
$394$	12758.3	+	168067.i	0.0821862	+	1.08265i
$395$			259711.i			1.66454i
$396$	−4256.97	−	27877.4i	−0.0271462	−	0.177771i
$397$	181472.			1.15140			0.575702	−	0.817659i	$-0.304729\pi$
$397$	181472.			1.15140			0.575702	+	0.817659i	$0.304729\pi$
$398$	−273416.	+	20755.5i	−1.72607	+	0.131029i
$399$			127443.i			0.800515i
$400$	143945.	−	45011.3i	0.899654	−	0.281320i
$401$	144404.			0.898029			0.449015	−	0.893524i	$-0.351775\pi$
$401$	144404.			0.898029			0.449015	+	0.893524i	$0.351775\pi$
$402$	−8205.70	−	108095.i	−0.0507766	−	0.668890i
$403$			116321.i			0.716226i
$404$	−233435.	+	35646.4i	−1.43022	+	0.218400i
$405$	25401.6			0.154864
$406$	72757.2	−	5523.12i	0.441392	−	0.0335068i
$407$			94532.6i			0.570680i
$408$	−67291.2	+	15564.2i	−0.404239	+	0.0934989i
$409$	1867.96			0.0111666			0.00558330	−	0.999984i	$-0.498223\pi$
$409$	1867.96			0.0111666			0.00558330	+	0.999984i	$0.498223\pi$
$410$	2804.43	+	36943.3i	0.0166831	+	0.219770i
$411$			100147.i			0.592863i
$412$	4490.30	+	29405.4i	0.0264534	+	0.173234i
$413$	−129635.			−0.760013
$414$	39974.4	−	3034.52i	0.233228	−	0.0177047i
$415$		−	311889.i		−	1.81094i
$416$	37517.6	+	94251.4i	0.216795	+	0.544629i
$417$	−125159.			−0.719765
$418$	−11265.2	−	148399.i	−0.0644742	−	0.849331i
$419$		−	112803.i		−	0.642531i	−0.946989	−	0.321266i	$-0.895892\pi$
$419$		−	112803.i		−	0.642531i	0.946989	−	0.321266i	$-0.104108\pi$
$420$	−123231.	+	18817.7i	−0.698587	+	0.106677i
$421$	−77595.0			−0.437794			−0.218897	−	0.975748i	$-0.570246\pi$
$421$	−77595.0			−0.437794			−0.218897	+	0.975748i	$0.570246\pi$
$422$	150282.	−	11408.1i	0.843881	−	0.0640604i
$423$			33750.0i			0.188623i
$424$	11359.6	+	49112.7i	0.0631874	+	0.273188i
$425$	−122356.			−0.677405
$426$	7383.60	+	97265.7i	0.0406864	+	0.535970i
$427$			194475.i			1.06661i
$428$	25757.2	+	168674.i	0.140608	+	0.920792i
$429$	33603.3			0.182586
$430$	−97270.6	+	7383.97i	−0.526071	+	0.0399350i
$431$		−	156726.i		−	0.843699i	−0.906666	−	0.421850i	$-0.861381\pi$
$431$		−	156726.i		−	0.843699i	0.906666	−	0.421850i	$-0.138619\pi$
$432$	10719.0	+	34279.0i	0.0574362	+	0.183679i
$433$	−41267.2			−0.220105			−0.110052	−	0.993926i	$-0.535102\pi$
$433$	−41267.2			−0.220105			−0.110052	+	0.993926i	$0.535102\pi$
$434$	−15298.3	−	201528.i	−0.0812202	−	1.06993i
$435$		−	76752.0i		−	0.405612i
$436$	70848.1	−	10818.7i	0.372697	−	0.0569120i
$437$	211568.			1.10786
$438$	112017.	−	8503.40i	0.583896	−	0.0443245i
$439$		−	154804.i		−	0.803252i	−0.915804	−	0.401626i	$-0.868445\pi$
$439$		−	154804.i		−	0.803252i	0.915804	−	0.401626i	$-0.131555\pi$
$440$	141830.	−	32804.8i	0.732595	−	0.169447i
$441$	−14830.2			−0.0762551
$442$	−6229.61	−	82063.9i	−0.0318872	−	0.420056i
$443$			251131.i			1.27966i	0.768518	+	0.639828i	$0.220994\pi$
$443$			251131.i			1.27966i	−0.768518	+	0.639828i	$0.779006\pi$
$444$	−18174.1	−	119016.i	−0.0921908	−	0.603725i
$445$	−21481.4			−0.108478
$446$	−36847.9	+	2797.18i	−0.185243	+	0.0140621i
$447$		−	228596.i		−	1.14407i
$448$	−77395.2	−	158357.i	−0.385619	−	0.789007i
$449$	−31888.6			−0.158177			−0.0790884	−	0.996868i	$-0.525201\pi$
$449$	−31888.6			−0.158177			−0.0790884	+	0.996868i	$0.525201\pi$
$450$	4816.13	+	63443.8i	0.0237833	+	0.313303i
$451$			17352.6i			0.0853121i
$452$	335717.	−	51265.1i	1.64322	−	0.250926i
$453$	7212.27			0.0351460
$454$	194978.	−	14801.1i	0.945963	−	0.0718096i
$455$		−	148542.i		−	0.717507i
$456$	42712.8	+	184667.i	0.205413	+	0.888095i
$457$	−166922.			−0.799247			−0.399624	−	0.916679i	$-0.630859\pi$
$457$	−166922.			−0.799247			−0.399624	+	0.916679i	$0.630859\pi$
$458$	−5345.35	−	70415.3i	−0.0254827	−	0.335688i
$459$		−	29137.9i		−	0.138304i
$460$	31239.3	+	204575.i	0.147634	+	0.966802i
$461$	−130544.			−0.614266			−0.307133	−	0.951667i	$-0.599370\pi$
$461$	−130544.			−0.614266			−0.307133	+	0.951667i	$0.599370\pi$
$462$	−58217.9	+	4419.42i	−0.272755	+	0.0207053i
$463$			273167.i			1.27428i	0.770746	+	0.637142i	$0.219884\pi$
$463$			273167.i			1.27428i	−0.770746	+	0.637142i	$0.780116\pi$
$464$	103575.	−	32387.9i	0.481084	−	0.150434i
$465$	−212593.			−0.983201
$466$	−15753.4	−	207522.i	−0.0725440	−	0.955637i
$467$		−	56070.3i		−	0.257098i	−0.991703	−	0.128549i	$-0.958968\pi$
$467$		−	56070.3i		−	0.257098i	0.991703	−	0.128549i	$-0.0410320\pi$
$468$	−42306.3	+	6460.31i	−0.193158	+	0.0294959i
$469$	−224441.			−1.02037
$470$	−173722.	+	13187.6i	−0.786430	+	0.0596993i
$471$		−	38788.9i		−	0.174850i
$472$	−187843.	+	43447.4i	−0.843162	+	0.195020i
$473$	−45688.8			−0.204215
$474$	−11726.3	−	154472.i	−0.0521918	−	0.687534i
$475$			335782.i			1.48823i
$476$	21585.7	+	141357.i	0.0952690	+	0.623883i
$477$	−21266.4			−0.0934668
$478$	214978.	−	16319.4i	0.940891	−	0.0714246i
$479$		−	160400.i		−	0.699091i	−0.936919	−	0.349546i	$-0.886336\pi$
$479$		−	160400.i		−	0.699091i	0.936919	−	0.349546i	$-0.113664\pi$
$480$	−172257.	+	68568.3i	−0.747642	+	0.297606i
$481$	143461.			0.620076
$482$	17049.6	+	224598.i	0.0733872	+	0.966745i
$483$		−	82999.7i		−	0.355781i
$484$	−164171.	+	25069.5i	−0.700821	+	0.107018i
$485$	478172.			2.03283
$486$	−15108.5	+	1146.91i	−0.0639660	+	0.00485577i
$487$			314133.i			1.32451i	0.749278	+	0.662256i	$0.230401\pi$
$487$			314133.i			1.32451i	−0.749278	+	0.662256i	$0.769599\pi$
$488$	65178.7	+	281797.i	0.273694	+	1.18331i
$489$	245731.			1.02764
$490$	−5794.78	−	76335.7i	−0.0241348	−	0.317933i
$491$			57822.1i			0.239845i	0.992783	+	0.119923i	$0.0382646\pi$
$491$			57822.1i			0.239845i	−0.992783	+	0.119923i	$0.961735\pi$
$492$	−3336.07	−	21846.8i	−0.0137818	−	0.0902520i
$493$	−88041.5			−0.362238
$494$	−225208.	+	17095.9i	−0.922846	+	0.0700548i
$495$			61414.4i			0.250645i
$496$	−89710.0	−	286890.i	−0.364651	−	1.16614i
$497$	201955.			0.817602
$498$	14082.2	+	185508.i	0.0567821	+	0.748003i
$499$		−	276054.i		−	1.10865i	−0.832301	−	0.554324i	$-0.812977\pi$
$499$		−	276054.i		−	1.10865i	0.832301	−	0.554324i	$-0.187023\pi$
$500$	19767.1	−	3018.51i	0.0790685	−	0.0120740i
$501$	468.650			0.00186712
$502$	−47669.3	+	3618.66i	−0.189161	+	0.0143595i
$503$		−	124228.i		−	0.491002i	−0.969396	−	0.245501i	$-0.921048\pi$
$503$		−	124228.i		−	0.491002i	0.969396	−	0.245501i	$-0.0789524\pi$
$504$	72446.3	−	16756.6i	0.285204	−	0.0659665i
$505$	514263.			2.01652
$506$	7336.68	+	96647.6i	0.0286549	+	0.377476i
$507$			97411.4i			0.378961i
$508$	−11295.6	−	73971.0i	−0.0437706	−	0.286638i
$509$	−335116.			−1.29348			−0.646739	−	0.762711i	$-0.723868\pi$
$509$	−335116.			−1.29348			−0.646739	+	0.762711i	$0.723868\pi$
$510$	149982.	−	11385.4i	0.576634	−	0.0437732i
$511$		−	232584.i		−	0.890712i
$512$	−165221.	−	203523.i	−0.630267	−	0.776378i
$513$	−79963.2			−0.303847
$514$	4687.91	+	61754.7i	0.0177440	+	0.233746i
$515$		−	64780.7i		−	0.244248i
$516$	57521.8	−	8783.77i	0.216040	−	0.0329900i
$517$	−81598.8			−0.305283
$518$	−248548.	+	18867.7i	−0.926297	+	0.0703168i
$519$			6298.28i			0.0233823i
$520$	−49784.2	−	215240.i	−0.184113	−	0.796006i
$521$	−320361.			−1.18022			−0.590111	−	0.807322i	$-0.700916\pi$
$521$	−320361.			−1.18022			−0.590111	+	0.807322i	$0.700916\pi$
$522$	3465.45	+	45651.0i	0.0127180	+	0.167537i
$523$			202708.i			0.741085i	0.928816	+	0.370542i	$0.120828\pi$
$523$			202708.i			0.741085i	−0.928816	+	0.370542i	$0.879172\pi$
$524$	−72270.7	−	473275.i	−0.263208	−	1.72366i
$525$	131730.			0.477932
$526$	−65161.7	+	4946.53i	−0.235516	+	0.0178784i
$527$			243863.i			0.878062i
$528$	−82877.6	+	25915.7i	−0.297283	+	0.0929598i
$529$	142053.			0.507621
$530$	−8309.69	−	109465.i	−0.0295824	−	0.389694i
$531$		−	81338.4i		−	0.288474i
$532$	387925.	−	59237.5i	1.37064	−	0.209302i
$533$	26334.0			0.0926964
$534$	12776.9	−	969.913i	0.0448066	−	0.00340134i
$535$		−	371593.i		−	1.29826i
$536$	−325219.	+	75221.9i	−1.13200	+	0.261827i
$537$	107546.			0.372947
$538$	24846.5	+	327308.i	0.0858422	+	1.13082i
$539$		−	35855.5i		−	0.123418i
$540$	−11807.1	−	77320.3i	−0.0404906	−	0.265159i
$541$	195927.			0.669421			0.334710	−	0.942321i	$-0.391361\pi$
$541$	195927.			0.669421			0.334710	+	0.942321i	$0.391361\pi$
$542$	299632.	−	22745.6i	1.01998	−	0.0774282i
$543$		−	97286.5i		−	0.329954i
$544$	78654.1	+	197594.i	0.265781	+	0.667692i
$545$	−156080.			−0.525477
$546$	6706.85	+	88350.7i	0.0224975	+	0.296364i
$547$		−	71049.9i		−	0.237459i	−0.992927	−	0.118730i	$-0.962118\pi$
$547$		−	71049.9i		−	0.237459i	0.992927	−	0.118730i	$-0.0378822\pi$
$548$	304839.	−	46549.9i	1.01510	−	0.155009i
$549$	−122022.			−0.404849
$550$	−153391.	+	11644.1i	−0.507076	+	0.0384930i
$551$			241612.i			0.795821i
$552$	−27817.6	−	120268.i	−0.0912937	−	0.394705i
$553$	−320735.			−1.04881
$554$	−2922.35	−	38496.7i	−0.00952167	−	0.125431i
$555$			262194.i			0.851211i
$556$	58176.0	+	380974.i	0.188189	+	1.23238i
$557$	152777.			0.492432			0.246216	−	0.969215i	$-0.420813\pi$
$557$	152777.			0.492432			0.246216	+	0.969215i	$0.420813\pi$
$558$	126447.	−	9598.82i	0.406107	−	0.0308283i
$559$			69336.6i			0.221891i
$560$	114559.	+	366357.i	0.365304	+	1.16823i
$561$	70447.9			0.223842
$562$	27396.2	+	360896.i	0.0867398	+	1.14264i
$563$			128620.i			0.405782i	0.979201	+	0.202891i	$0.0650337\pi$
$563$			128620.i			0.405782i	−0.979201	+	0.202891i	$0.934966\pi$
$564$	102732.	−	15687.6i	0.322960	−	0.0493171i
$565$	−739591.			−2.31683
$566$	179090.	−	13595.0i	0.559034	−	0.0424372i
$567$			31370.2i			0.0975777i
$568$	292637.	−	67685.7i	0.907052	−	0.209798i
$569$	−353147.			−1.09076			−0.545382	−	0.838188i	$-0.683615\pi$
$569$	−353147.			−1.09076			−0.545382	+	0.838188i	$0.683615\pi$
$570$	−31245.0	−	411596.i	−0.0961680	−	1.26684i
$571$			9607.19i			0.0294662i	0.999891	+	0.0147331i	$0.00468986\pi$
$571$			9607.19i			0.0294662i	−0.999891	+	0.0147331i	$0.995310\pi$
$572$	−15619.4	−	102286.i	−0.0477387	−	0.312624i
$573$	−192560.			−0.586484
$574$	−45623.9	+	3463.38i	−0.138474	+	0.0105118i
$575$		−	218685.i		−	0.661429i
$576$	99360.0	−	48561.1i	0.299479	−	0.146367i
$577$	−35488.3			−0.106594			−0.0532971	−	0.998579i	$-0.516973\pi$
$577$	−35488.3			−0.106594			−0.0532971	+	0.998579i	$0.516973\pi$
$578$	12228.0	+	161082.i	0.0366016	+	0.482160i
$579$			119615.i			0.356802i
$580$	−233627.	+	35675.6i	−0.694490	+	0.106051i
$581$	385174.			1.14105
$582$	−284410.	+	21590.1i	−0.839651	+	0.0637394i
$583$		−	51416.6i		−	0.151275i
$584$	−77950.9	−	337018.i	−0.228558	−	0.988159i
$585$	93201.6			0.272340
$586$	−9182.20	−	120959.i	−0.0267394	−	0.352243i
$587$		−	396523.i		−	1.15078i	−0.817879	−	0.575390i	$-0.804850\pi$
$587$		−	396523.i		−	1.15078i	0.817879	−	0.575390i	$-0.195150\pi$
$588$	6893.31	+	45141.8i	0.0199376	+	0.130564i
$589$	669233.			1.92907
$590$	418675.	−	31782.3i	1.20274	−	0.0913023i
$591$			218954.i			0.626869i
$592$	−353827.	+	110641.i	−1.00960	+	0.315699i
$593$	−199308.			−0.566780			−0.283390	−	0.959005i	$-0.591459\pi$
$593$	−199308.			−0.566780			−0.283390	+	0.959005i	$0.591459\pi$
$594$	−2772.94	−	36528.4i	−0.00785899	−	0.103528i
$595$		−	311412.i		−	0.879633i
$596$	−695826.	+	106255.i	−1.95888	+	0.299128i
$597$	−356199.			−0.999412
$598$	146671.	−	11134.0i	0.410149	−	0.0311351i
$599$			596802.i			1.66332i	0.555284	+	0.831661i	$0.312610\pi$
$599$			596802.i			1.66332i	−0.555284	+	0.831661i	$0.687390\pi$
$600$	190879.	−	44149.6i	0.530220	−	0.122638i
$601$	171774.			0.475563			0.237782	−	0.971319i	$-0.423580\pi$
$601$	171774.			0.475563			0.237782	+	0.971319i	$0.423580\pi$
$602$	−9118.98	−	120126.i	−0.0251625	−	0.331470i
$603$		−	140824.i		−	0.387295i
$604$	−3352.38	−	21953.6i	−0.00918924	−	0.0601771i
$605$	361673.			0.988110
$606$	−305877.	+	23219.6i	−0.832916	+	0.0632280i
$607$		−	204299.i		−	0.554485i	−0.960800	−	0.277243i	$-0.910579\pi$
$607$		−	204299.i		−	0.554485i	0.960800	−	0.277243i	$-0.0894205\pi$
$608$	542257.	−	215850.i	1.46689	−	0.583910i
$609$	94786.3			0.255571
$610$	−47679.1	−	628086.i	−0.128135	−	1.68795i
$611$			123833.i			0.331707i
$612$	−88693.4	+	13543.8i	−0.236804	+	0.0361607i
$613$	72753.9			0.193613			0.0968066	−	0.995303i	$-0.469137\pi$
$613$	72753.9			0.193613			0.0968066	+	0.995303i	$0.469137\pi$
$614$	141782.	−	10762.9i	0.376085	−	0.0285492i
$615$			48128.9i			0.127249i
$616$	40513.0	+	175156.i	0.106766	+	0.461598i
$617$	387966.			1.01911			0.509557	−	0.860437i	$-0.329809\pi$
$617$	387966.			1.01911			0.509557	+	0.860437i	$0.329809\pi$
$618$	2924.93	+	38530.7i	0.00765841	+	0.100886i
$619$		−	676575.i		−	1.76577i	−0.469587	−	0.882886i	$-0.655597\pi$
$619$		−	676575.i		−	1.76577i	0.469587	−	0.882886i	$-0.344403\pi$
$620$	98816.5	+	647114.i	0.257067	+	1.68344i
$621$	52077.6			0.135042
$622$	−287980.	+	21861.1i	−0.744358	+	0.0565055i
$623$		−	26528.9i		−	0.0683507i
$624$	39329.3	+	125774.i	0.101006	+	0.323014i
$625$	−411755.			−1.05409
$626$	−49276.6	−	649131.i	−0.125745	−	1.65647i
$627$		−	193330.i		−	0.491772i
$628$	−118070.	+	18029.7i	−0.299379	+	0.0457162i
$629$	300761.			0.760187
$630$	−161472.	+	12257.6i	−0.406834	+	0.0308835i
$631$			383055.i			0.962059i	0.876704	+	0.481030i	$0.159737\pi$
$631$			383055.i			0.962059i	−0.876704	+	0.481030i	$0.840263\pi$
$632$	−464750.	+	107495.i	−1.16355	+	0.269125i
$633$	195783.			0.488616
$634$	19546.3	+	257487.i	0.0486279	+	0.640585i
$635$			162960.i			0.404141i
$636$	9884.98	+	64733.2i	0.0244378	+	0.160034i
$637$	−54413.8			−0.134100
$638$	−110372.	+	8378.55i	−0.271156	+	0.0205839i
$639$			126715.i			0.310333i
$640$	288784.	+	492463.i	0.705039	+	1.20230i
$641$	218038.			0.530660			0.265330	−	0.964158i	$-0.414519\pi$
$641$	218038.			0.530660			0.265330	+	0.964158i	$0.414519\pi$
$642$	16777.9	+	221019.i	0.0407068	+	0.536239i
$643$			329758.i			0.797579i	0.917043	+	0.398789i	$0.130570\pi$
$643$			329758.i			0.797579i	−0.917043	+	0.398789i	$0.869430\pi$
$644$	−252644.	+	38579.6i	−0.609169	+	0.0930221i
$645$	−126722.			−0.304601
$646$	−472139.	+	35840.8i	−1.13137	+	0.0858842i
$647$			166751.i			0.398346i	0.979964	+	0.199173i	$0.0638256\pi$
$647$			166751.i			0.398346i	−0.979964	+	0.199173i	$0.936174\pi$
$648$	10513.8	+	45455.9i	0.0250386	+	0.108253i
$649$	196655.			0.466891
$650$	17671.0	+	232784.i	0.0418248	+	0.550967i
$651$		−	262545.i		−	0.619502i
$652$	−114220.	−	747985.i	−0.268687	−	1.75953i
$653$	−684629.			−1.60557			−0.802785	−	0.596269i	$-0.796649\pi$
$653$	−684629.			−1.60557			−0.802785	+	0.596269i	$0.796649\pi$
$654$	92834.2	−	7047.20i	0.217046	−	0.0164764i
$655$			1.04263e6i			2.43024i
$656$	−64949.0	+	20309.5i	−0.150926	+	0.0471944i
$657$	145933.			0.338082
$658$	−16286.2	−	214542.i	−0.0376157	−	0.495519i
$659$		−	580631.i		−	1.33699i	−0.743714	−	0.668497i	$-0.766938\pi$
$659$		−	580631.i		−	1.33699i	0.743714	−	0.668497i	$-0.233062\pi$
$660$	186940.	−	28546.4i	0.429156	−	0.0655335i
$661$	324617.			0.742964			0.371482	−	0.928440i	$-0.378850\pi$
$661$	324617.			0.742964			0.371482	+	0.928440i	$0.378850\pi$
$662$	46043.8	−	3495.26i	0.105064	−	0.00797561i
$663$		−	106911.i		−	0.243217i
$664$	558124.	−	129092.i	1.26589	−	0.292795i
$665$	−854607.			−1.93252
$666$	−11838.4	−	155950.i	−0.0266898	−	0.351590i
$667$		−	157355.i		−	0.353695i
$668$	−217.836	−	1426.53i	−0.000488176	−	0.00319689i
$669$	−48004.5			−0.107258
$670$	724867.	−	55025.9i	1.61476	−	0.122579i
$671$		−	295017.i		−	0.655243i
$672$	−84679.8	−	212732.i	−0.187517	−	0.471079i
$673$	46209.4			0.102024			0.0510118	−	0.998698i	$-0.483755\pi$
$673$	46209.4			0.102024			0.0510118	+	0.998698i	$0.483755\pi$
$674$	63283.5	+	833646.i	0.139306	+	1.83511i
$675$			82653.1i			0.181406i
$676$	296512.	−	45278.4i	0.648857	−	0.0990827i
$677$	−98225.8			−0.214313			−0.107156	−	0.994242i	$-0.534175\pi$
$677$	−98225.8			−0.214313			−0.107156	+	0.994242i	$0.534175\pi$
$678$	439899.	−	33393.5i	0.956959	−	0.0726444i
$679$			590528.i			1.28086i
$680$	−104371.	−	451242.i	−0.225715	−	0.975869i
$681$	254013.			0.547723
$682$	23207.4	+	305716.i	0.0498952	+	0.657279i
$683$		−	454709.i		−	0.974747i	−0.873194	−	0.487373i	$-0.837955\pi$
$683$		−	454709.i		−	0.974747i	0.873194	−	0.487373i	$-0.162045\pi$
$684$	37168.2	+	243401.i	0.0794436	+	0.520248i
$685$	−671567.			−1.43123
$686$	506364.	−	38438.9i	1.07601	−	0.0816814i
$687$		−	91735.4i		−	0.194367i
$688$	−53474.2	−	171009.i	−0.112971	−	0.361278i
$689$	−78029.2			−0.164369
$690$	20348.9	+	268060.i	0.0427409	+	0.563034i
$691$			190359.i			0.398673i	0.979931	+	0.199337i	$0.0638787\pi$
$691$			190359.i			0.398673i	−0.979931	+	0.199337i	$0.936121\pi$
$692$	19171.4	−	2927.54i	0.0400352	−	0.00611352i
$693$	−75844.9			−0.157928
$694$	−643366.	+	48839.0i	−1.33579	+	0.101402i
$695$		−	839294.i		−	1.73758i
$696$	137347.	−	31767.9i	0.283531	−	0.0655797i
$697$	55208.2			0.113642
$698$	−26656.8	−	351155.i	−0.0547138	−	0.720756i
$699$		−	270355.i		−	0.553325i
$700$	−61230.2	−	400975.i	−0.124960	−	0.818316i
$701$	504089.			1.02582			0.512910	−	0.858442i	$-0.328567\pi$
$701$	504089.			1.02582			0.512910	+	0.858442i	$0.328567\pi$
$702$	−55435.1	+	4208.17i	−0.112489	+	0.00853924i
$703$		−	825378.i		−	1.67010i
$704$	117408.	+	240227.i	0.236893	+	0.484703i
$705$	−226321.			−0.455352
$706$	−56546.9	−	744903.i	−0.113449	−	1.49448i
$707$			635099.i			1.27058i
$708$	−247587.	+	37807.4i	−0.493926	+	0.0754241i
$709$	−160106.			−0.318504			−0.159252	−	0.987238i	$-0.550908\pi$
$709$	−160106.			−0.318504			−0.159252	+	0.987238i	$0.550908\pi$
$710$	−652245.	+	49513.0i	−1.29388	+	0.0982207i
$711$		−	201243.i		−	0.398090i
$712$	−8891.23	−	38440.9i	−0.0175389	−	0.0758286i
$713$	−435852.			−0.857353
$714$	14060.6	+	185224.i	0.0275809	+	0.363329i
$715$			225337.i			0.440779i
$716$	−49989.3	−	327362.i	−0.0975105	−	0.638562i
$717$	280069.			0.544786
$718$	903467.	−	68583.7i	1.75252	−	0.133037i
$719$			918988.i			1.77767i	0.458224	+	0.888836i	$0.348486\pi$
$719$			918988.i			1.77767i	−0.458224	+	0.888836i	$0.651514\pi$
$720$	−229868.	+	71879.4i	−0.443419	+	0.138656i
$721$	80002.2			0.153897
$722$	58899.9	+	775900.i	0.112990	+	1.48844i
$723$			292601.i			0.559756i
$724$	−296132.	+	45220.3i	−0.564947	+	0.0862694i
$725$	249740.			0.475129
$726$	−215118.	+	16330.0i	−0.408135	+	0.0309822i
$727$		−	339605.i		−	0.642548i	−0.946986	−	0.321274i	$-0.895889\pi$
$727$		−	339605.i		−	0.642548i	0.946986	−	0.321274i	$-0.104111\pi$
$728$	265815.	−	61482.0i	0.501552	−	0.116007i
$729$	−19683.0			−0.0370370
$730$	57022.2	+	751164.i	0.107003	+	1.40958i
$731$			145361.i			0.272029i
$732$	56717.8	+	371424.i	0.105851	+	0.693184i
$733$	−310186.			−0.577317			−0.288659	−	0.957432i	$-0.593209\pi$
$733$	−310186.			−0.577317			−0.288659	+	0.957432i	$0.593209\pi$
$734$	−425384.	+	32291.6i	−0.789567	+	0.0599374i
$735$		−	99448.4i		−	0.184087i
$736$	−353156.	+	140577.i	−0.651945	+	0.259513i
$737$	340476.			0.626832
$738$	−2173.08	−	28626.4i	−0.00398990	−	0.0525598i
$739$			561855.i			1.02881i	0.857547	+	0.514405i	$0.171987\pi$
$739$			561855.i			1.02881i	−0.857547	+	0.514405i	$0.828013\pi$
$740$	798098.	−	121872.i	1.45745	−	0.222557i
$741$	−293395.			−0.534338
$742$	135186.	−	10262.2i	0.245541	−	0.0186394i
$743$			89658.6i			0.162411i	0.996697	+	0.0812053i	$0.0258769\pi$
$743$			89658.6i			0.162411i	−0.996697	+	0.0812053i	$0.974123\pi$
$744$	−87992.7	−	380433.i	−0.158965	−	0.687278i
$745$	1.53292e6			2.76189
$746$	−39113.7	−	515253.i	−0.0702832	−	0.925854i
$747$			241675.i			0.433102i
$748$	−32745.3	−	214438.i	−0.0585257	−	0.383264i
$749$	458906.			0.818013
$750$	25901.4	−	1966.22i	0.0460469	−	0.00349550i
$751$		−	58229.8i		−	0.103244i	−0.998667	−	0.0516221i	$-0.983561\pi$
$751$		−	58229.8i		−	0.103244i	0.998667	−	0.0516221i	$-0.0164391\pi$
$752$	−95503.3	−	305417.i	−0.168882	−	0.540079i
$753$	−62102.4			−0.109526
$754$	12715.2	+	167499.i	0.0223655	+	0.294626i
$755$			48364.1i			0.0848456i
$756$	95488.2	−	14581.4i	0.167073	−	0.0255126i
$757$	−77925.2			−0.135983			−0.0679917	−	0.997686i	$-0.521659\pi$
$757$	−77925.2			−0.135983			−0.0679917	+	0.997686i	$0.521659\pi$
$758$	−622832.	+	47280.2i	−1.08401	+	0.0822889i
$759$			125910.i			0.218563i
$760$	−1.23834e6	+	286424.i	−2.14394	+	0.495886i
$761$	241107.			0.416332			0.208166	−	0.978094i	$-0.433251\pi$
$761$	241107.			0.416332			0.208166	+	0.978094i	$0.433251\pi$
$762$	−7357.83	−	96926.2i	−0.0126718	−	0.166929i
$763$		−	192754.i		−	0.331096i
$764$	89505.0	+	586136.i	0.153342	+	1.00418i
$765$	195393.			0.333877
$766$	−1.04261e6	+	79146.5i	−1.77691	+	0.134888i
$767$		−	298441.i		−	0.507303i
$768$	−194000.	−	279872.i	−0.328912	−	0.474500i
$769$	−805186.			−1.36158			−0.680791	−	0.732478i	$-0.738364\pi$
$769$	−805186.			−1.36158			−0.680791	+	0.732478i	$0.738364\pi$
$770$	−29635.8	−	390398.i	−0.0499845	−	0.658455i
$771$			80452.5i			0.135342i
$772$	364097.	−	55598.8i	0.610917	−	0.0932891i
$773$	431024.			0.721344			0.360672	−	0.932693i	$-0.382547\pi$
$773$	431024.			0.721344			0.360672	+	0.932693i	$0.382547\pi$
$774$	75372.4	−	5721.64i	0.125814	−	0.00955078i
$775$		−	691746.i		−	1.15171i
$776$	197917.	+	855685.i	0.328669	+	1.42099i
$777$	−323802.			−0.536337
$778$	316.886	+	4174.40i	0.000523532	+	0.00689660i
$779$		−	151508.i		−	0.249666i
$780$	−43321.6	−	283698.i	−0.0712058	−	0.466302i
$781$	−306365.			−0.502269
$782$	307490.	−	23342.1i	0.502826	−	0.0381703i
$783$			59473.0i			0.0970056i
$784$	134204.	−	41965.3i	0.218340	−	0.0682745i
$785$	260111.			0.422104
$786$	−47076.2	−	620145.i	−0.0762003	−	1.00380i
$787$		−	347948.i		−	0.561778i	−0.959740	−	0.280889i	$-0.909371\pi$
$787$		−	347948.i		−	0.561778i	0.959740	−	0.280889i	$-0.0906293\pi$
$788$	666476.	−	101773.i	1.07333	−	0.163901i
$789$	−84891.0			−0.136367
$790$	1.03586e6	−	78634.0i	1.65977	−	0.125996i
$791$		−	913373.i		−	1.45981i
$792$	−109901.	+	25419.6i	−0.175206	+	0.0405246i
$793$	−447714.			−0.711958
$794$	−54945.2	−	723804.i	−0.0871543	−	1.14810i
$795$		−	142609.i		−	0.225637i
$796$	165567.	+	1.08424e6i	0.261305	+	1.71120i
$797$	−460443.			−0.724868			−0.362434	−	0.932009i	$-0.618054\pi$
$797$	−460443.			−0.724868			−0.362434	+	0.932009i	$0.618054\pi$
$798$	508309.	−	38586.6i	0.798219	−	0.0605941i
$799$			259611.i			0.406659i
$800$	−223111.	−	560498.i	−0.348612	−	0.875779i
$801$	16645.4			0.0259435
$802$	−43722.0	−	575959.i	−0.0679753	−	0.895453i
$803$			352828.i			0.547182i
$804$	−428656.	+	65457.3i	−0.663128	+	0.101262i
$805$	556580.			0.858887
$806$	463951.	−	35219.3i	0.714171	−	0.0542139i
$807$			426409.i			0.654756i
$808$	212855.	+	920270.i	0.326033	+	1.40959i
$809$	−621711.			−0.949930			−0.474965	−	0.880005i	$-0.657539\pi$
$809$	−621711.			−0.949930			−0.474965	+	0.880005i	$0.657539\pi$
$810$	−7690.98	−	101315.i	−0.0117223	−	0.154420i
$811$			25991.9i			0.0395181i	0.999805	+	0.0197591i	$0.00628991\pi$
$811$			25991.9i			0.0395181i	−0.999805	+	0.0197591i	$0.993710\pi$
$812$	−44058.2	−	288522.i	−0.0668213	−	0.437589i
$813$	390354.			0.590578
$814$	377046.	−	28622.2i	0.569043	−	0.0431970i
$815$			1.64783e6i			2.48082i
$816$	82452.3	+	263680.i	0.123829	+	0.396002i
$817$	398915.			0.597635
$818$	−565.573	−	7450.41i	−0.000845244	−	0.0111346i
$819$			115101.i			0.171598i
$820$	146500.	−	22371.1i	0.217877	−	0.0332705i
$821$	−917945.			−1.36185			−0.680927	−	0.732352i	$-0.738423\pi$
$821$	−917945.			−1.36185			−0.680927	+	0.732352i	$0.738423\pi$
$822$	399439.	−	30322.1i	0.591162	−	0.0448761i
$823$		−	1.22951e6i		−	1.81523i	−0.419807	−	0.907613i	$-0.637902\pi$
$823$		−	1.22951e6i		−	1.81523i	0.419807	−	0.907613i	$-0.362098\pi$
$824$	115925.	−	26812.9i	0.170734	−	0.0394902i
$825$	−199834.			−0.293603
$826$	39250.2	+	517051.i	0.0575284	+	0.757833i
$827$			254347.i			0.371891i	0.982560	+	0.185946i	$0.0595348\pi$
$827$			254347.i			0.371891i	−0.982560	+	0.185946i	$0.940465\pi$
$828$	−24206.5	−	158520.i	−0.0353079	−	0.231219i
$829$	−456708.			−0.664552			−0.332276	−	0.943182i	$-0.607817\pi$
$829$	−456708.			−0.664552			−0.332276	+	0.943182i	$0.607817\pi$
$830$	−1.24398e6	+	94432.5i	−1.80575	+	0.137077i
$831$		−	50152.6i		−	0.0726259i
$832$	364565.	−	178177.i	0.526657	−	0.257398i
$833$	−114076.			−0.164401
$834$	37895.1	+	499200.i	0.0544818	+	0.717700i
$835$			3142.68i			0.00450740i
$836$	−588480.	+	89862.9i	−0.842014	+	0.128578i
$837$	164732.			0.235141
$838$	−449919.	+	34154.1i	−0.640688	+	0.0486357i
$839$		−	397834.i		−	0.565168i	−0.959243	−	0.282584i	$-0.908808\pi$
$839$		−	397834.i		−	0.565168i	0.959243	−	0.282584i	$-0.0911916\pi$
$840$	112366.	+	485811.i	0.159249	+	0.688508i
$841$	−527581.			−0.745928
$842$	23493.9	+	309490.i	0.0331383	+	0.436538i
$843$			470167.i			0.661602i
$844$	−91003.2	−	595948.i	−0.127753	−	0.836611i
$845$	−653222.			−0.914845
$846$	134613.	−	10218.7i	0.188081	−	0.0142776i
$847$			446655.i			0.622595i
$848$	192448.	−	60178.1i	0.267622	−	0.0836848i
$849$	233314.			0.323687
$850$	37046.5	+	488021.i	0.0512755	+	0.675462i
$851$			537544.i			0.742258i
$852$	385711.	−	58899.4i	0.531353	−	0.0811393i
$853$	683508.			0.939389			0.469694	−	0.882829i	$-0.344364\pi$
$853$	683508.			0.939389			0.469694	+	0.882829i	$0.344364\pi$
$854$	775667.	−	58882.2i	1.06355	−	0.0807362i
$855$		−	536218.i		−	0.733515i
$856$	664964.	−	153804.i	0.907508	−	0.209903i
$857$	−116155.			−0.158152			−0.0790760	−	0.996869i	$-0.525197\pi$
$857$	−116155.			−0.158152			−0.0790760	+	0.996869i	$0.525197\pi$
$858$	−10174.3	−	134028.i	−0.0138206	−	0.182062i
$859$		−	169632.i		−	0.229890i	−0.993372	−	0.114945i	$-0.963331\pi$
$859$		−	169632.i		−	0.229890i	0.993372	−	0.114945i	$-0.0366692\pi$
$860$	58902.3	+	385730.i	0.0796408	+	0.521539i
$861$	−59437.7			−0.0801780
$862$	−625107.	+	47452.9i	−0.841279	+	0.0638629i
$863$		−	651371.i		−	0.874595i	−0.899317	−	0.437298i	$-0.855936\pi$
$863$		−	651371.i		−	0.874595i	0.899317	−	0.437298i	$-0.144064\pi$
$864$	133477.	−	53131.8i	0.178805	−	0.0711749i
$865$	−42235.1			−0.0564470
$866$	12494.7	+	164595.i	0.0166606	+	0.219473i
$867$			209854.i			0.279176i
$868$	−799166.	+	122035.i	−1.06071	+	0.161974i
$869$	486552.			0.644303
$870$	−306127.	+	23238.6i	−0.404449	+	0.0307024i
$871$		−	516701.i		−	0.681088i
$872$	−64601.9	−	279304.i	−0.0849596	−	0.367320i
$873$	−370523.			−0.486168
$874$	−64057.6	−	843844.i	−0.0838586	−	1.10469i
$875$		−	53779.7i		−	0.0702429i
$876$	−67832.0	−	444208.i	−0.0883947	−	0.578866i
$877$	1.36009e6			1.76836			0.884178	−	0.467151i	$-0.154720\pi$
$877$	1.36009e6			1.76836			0.884178	+	0.467151i	$0.154720\pi$
$878$	−617438.	+	46870.7i	−0.800947	+	0.0608013i
$879$		−	157582.i		−	0.203953i
$880$	−173786.	−	555762.i	−0.224413	−	0.717667i
$881$	976763.			1.25845			0.629227	−	0.777222i	$-0.283372\pi$
$881$	976763.			1.25845			0.629227	+	0.777222i	$0.283372\pi$
$882$	4490.22	+	59150.5i	0.00577205	+	0.0760364i
$883$			1.29155e6i			1.65650i	0.560362	+	0.828248i	$0.310662\pi$
$883$			1.29155e6i			1.65650i	−0.560362	+	0.828248i	$0.689338\pi$
$884$	−325428.	+	49693.9i	−0.416438	+	0.0635914i
$885$	545440.			0.696403
$886$	1.00164e6	−	76036.4i	1.27598	−	0.0968621i
$887$		−	1.40632e6i		−	1.78747i	−0.448599	−	0.893733i	$-0.648077\pi$
$887$		−	1.40632e6i		−	1.78747i	0.448599	−	0.893733i	$-0.351923\pi$
$888$	−469195.	+	108523.i	−0.595014	+	0.137625i
$889$	−201250.			−0.254644
$890$	6504.05	+	85679.2i	0.00821115	+	0.108167i
$891$		−	47588.4i		−	0.0599439i
$892$	22313.3	+	146122.i	0.0280436	+	0.183648i
$893$	712451.			0.893412
$894$	−911759.	+	69213.2i	−1.14079	+	0.0865992i
$895$			721186.i			0.900329i
$896$	−608177.	+	356639.i	−0.757555	+	0.444235i
$897$	191079.			0.237481
$898$	9655.09	+	127188.i	0.0119730	+	0.157723i
$899$		−	497746.i		−	0.615869i
$900$	251589.	−	38418.5i	0.310604	−	0.0474302i
$901$	−163585.			−0.201509
$902$	69211.1	−	5253.93i	0.0850673	−	0.00645761i
$903$		−	156497.i		−	0.191925i
$904$	−306119.	−	1.32349e6i	−0.374588	−	1.61951i
$905$	652385.			0.796538
$906$	−2183.70	−	28766.3i	−0.00266034	−	0.0350452i
$907$			373379.i			0.453874i	0.973909	+	0.226937i	$0.0728712\pi$
$907$			373379.i			0.453874i	−0.973909	+	0.226937i	$0.927129\pi$
$908$	−118069.	−	773193.i	−0.143207	−	0.937813i
$909$	−398489.			−0.482268
$910$	−592463.	+	44974.9i	−0.715449	+	0.0543109i
$911$			62632.1i			0.0754675i	0.999288	+	0.0377338i	$0.0120139\pi$
$911$			62632.1i			0.0754675i	−0.999288	+	0.0377338i	$0.987986\pi$
$912$	723616.	−	226274.i	0.869999	−	0.272047i
$913$	−584307.			−0.700970
$914$	50539.9	+	665772.i	0.0604981	+	0.796954i
$915$		−	818256.i		−	0.977343i
$916$	−279235.	+	42640.1i	−0.332796	+	0.0508191i
$917$	−1.28762e6			−1.53126
$918$	−116217.	+	8822.26i	−0.137907	+	0.0104687i
$919$			829993.i			0.982751i	0.870948	+	0.491375i	$0.163506\pi$
$919$			829993.i			0.982751i	−0.870948	+	0.491375i	$0.836494\pi$
$920$	806495.	−	186539.i	0.952853	−	0.220391i
$921$	184711.			0.217757
$922$	39525.7	+	520679.i	0.0464962	+	0.612503i
$923$			464935.i			0.545744i
$924$	35253.9	+	230865.i	0.0412918	+	0.270405i
$925$	−853143.			−0.997099
$926$	1.08953e6	−	82708.3i	1.27063	−	0.0964556i
$927$			50196.8i			0.0584140i
$928$	−160540.	−	403307.i	−0.186418	−	0.468317i
$929$	1.22106e6			1.41483			0.707416	−	0.706798i	$-0.249861\pi$
$929$	1.22106e6			1.41483			0.707416	+	0.706798i	$0.249861\pi$
$930$	64367.9	+	847931.i	0.0744223	+	0.980380i
$931$			313059.i			0.361183i
$932$	−822938.	+	125665.i	−0.947404	+	0.144672i
$933$	−375174.			−0.430992
$934$	−223638.	+	16976.7i	−0.256361	+	0.0194608i
$935$			472410.i			0.540376i
$936$	38576.4	+	166784.i	0.0440322	+	0.190371i
$937$	−238403.			−0.271539			−0.135770	−	0.990740i	$-0.543351\pi$
$937$	−238403.			−0.271539			−0.135770	+	0.990740i	$0.543351\pi$
$938$	67955.3	+	895188.i	0.0772356	+	1.01744i
$939$		−	845672.i		−	0.959115i
$940$	105198.	+	688903.i	0.119056	+	0.779655i
$941$	−1.17958e6			−1.33214			−0.666070	−	0.745889i	$-0.732025\pi$
$941$	−1.17958e6			−1.33214			−0.666070	+	0.745889i	$0.732025\pi$
$942$	−154711.	+	11744.3i	−0.174348	+	0.0132351i
$943$			98672.5i			0.110962i
$944$	230165.	+	736062.i	0.258283	+	0.825981i
$945$	−210362.			−0.235562
$946$	13833.4	+	182231.i	0.0154578	+	0.203629i
$947$			886731.i			0.988762i	0.869245	+	0.494381i	$0.164605\pi$
$947$			886731.i			0.988762i	−0.869245	+	0.494381i	$0.835395\pi$
$948$	−612566.	+	93540.9i	−0.681611	+	0.104084i
$949$	535447.			0.594544
$950$	1.33928e6	−	101667.i	1.48396	−	0.112650i
$951$			335448.i			0.370906i
$952$	557270.	−	128894.i	0.614882	−	0.142220i
$953$	1.72385e6			1.89807			0.949037	−	0.315166i	$-0.102060\pi$
$953$	1.72385e6			1.89807			0.949037	+	0.315166i	$0.102060\pi$
$954$	6438.95	+	84821.6i	0.00707487	+	0.0931987i
$955$		−	1.29127e6i		−	1.41583i
$956$	−130181.	−	852506.i	−0.142439	−	0.932785i
$957$	−143790.			−0.157002
$958$	−639760.	+	48565.3i	−0.697086	+	0.0529169i
$959$		−	829364.i		−	0.901796i
$960$	325642.	+	666289.i	0.353344	+	0.722970i
$961$	−455168.			−0.492862
$962$	−43436.6	−	572199.i	−0.0469360	−	0.618297i
$963$			287938.i			0.310489i
$964$	890652.	−	136006.i	0.958416	−	0.146353i
$965$	−802113.			−0.861352
$966$	−331046.	+	25130.3i	−0.354760	+	0.0269304i
$967$			652513.i			0.697808i	0.937158	+	0.348904i	$0.113446\pi$
$967$			652513.i			0.697808i	−0.937158	+	0.348904i	$0.886554\pi$
$968$	149698.	+	647211.i	0.159759	+	0.690710i
$969$	−615091.			−0.655076
$970$	−144779.	−	1.90720e6i	−0.153873	−	2.02700i
$971$		−	399968.i		−	0.424216i	−0.977246	−	0.212108i	$-0.931967\pi$
$971$		−	399968.i		−	0.424216i	0.977246	−	0.212108i	$-0.0680328\pi$
$972$	9148.98	+	59913.4i	0.00968367	+	0.0634149i
$973$	1.03650e6			1.09482
$974$	1.25293e6	−	95111.8i	1.32071	−	0.100257i
$975$			303265.i			0.319016i
$976$	1.10422e6	−	345288.i	1.15920	−	0.362478i
$977$	−1.43718e6			−1.50564			−0.752820	−	0.658227i	$-0.771307\pi$
$977$	−1.43718e6			−1.50564			−0.752820	+	0.658227i	$0.771307\pi$
$978$	−74401.4	−	980104.i	−0.0777863	−	1.02470i
$979$			40244.2i			0.0419892i
$980$	−302712.	+	46225.2i	−0.315194	+	0.0481312i
$981$	120942.			0.125672
$982$	230625.	−	17507.1i	0.239157	−	0.0181548i
$983$			1.64352e6i			1.70086i	0.526092	+	0.850428i	$0.323657\pi$
$983$			1.64352e6i			1.70086i	−0.526092	+	0.850428i	$0.676343\pi$
$984$	−86126.2	+	19920.7i	−0.0889499	+	0.0205738i
$985$	−1.46826e6			−1.51332
$986$	26656.8	+	351156.i	0.0274192	+	0.361199i
$987$		−	279500.i		−	0.286911i
$988$	136375.	+	893070.i	0.139708	+	0.914896i
$989$	−259801.			−0.265613
$990$	244953.	−	18594.8i	0.249926	−	0.0189723i
$991$		−	713551.i		−	0.726570i	−0.931678	−	0.363285i	$-0.881655\pi$
$991$		−	713551.i		−	0.726570i	0.931678	−	0.363285i	$-0.118345\pi$
$992$	−1.11711e6	+	444674.i	−1.13520	+	0.451875i
$993$	59984.8			0.0608334
$994$	−61147.1	−	805503.i	−0.0618875	−	0.815257i
$995$		−	2.38861e6i		−	2.41267i
$996$	735638.	−	112334.i	0.741559	−	0.113238i
$997$	−1.13252e6			−1.13935			−0.569673	−	0.821871i	$-0.692930\pi$
$997$	−1.13252e6			−1.13935			−0.569673	+	0.821871i	$0.692930\pi$
$998$	−1.10105e6	+	83582.5i	−1.10547	+	0.0839179i
$999$		−	203167.i		−	0.203574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.5.d.a.7.1	✓	4
3.2	odd	2		36.5.d.b.19.4		4
4.3	odd	2	inner	12.5.d.a.7.2	yes	4
5.2	odd	4		300.5.f.a.199.7		8
5.3	odd	4		300.5.f.a.199.2		8
5.4	even	2		300.5.c.a.151.4		4
8.3	odd	2		192.5.g.d.127.1		4
8.5	even	2		192.5.g.d.127.3		4
12.11	even	2		36.5.d.b.19.3		4
16.3	odd	4		768.5.b.g.127.1		8
16.5	even	4		768.5.b.g.127.4		8
16.11	odd	4		768.5.b.g.127.8		8
16.13	even	4		768.5.b.g.127.5		8
20.3	even	4		300.5.f.a.199.8		8
20.7	even	4		300.5.f.a.199.1		8
20.19	odd	2		300.5.c.a.151.3		4
24.5	odd	2		576.5.g.m.127.4		4
24.11	even	2		576.5.g.m.127.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.1	✓	4	1.1	even	1	trivial
12.5.d.a.7.2	yes	4	4.3	odd	2	inner
36.5.d.b.19.3		4	12.11	even	2
36.5.d.b.19.4		4	3.2	odd	2
192.5.g.d.127.1		4	8.3	odd	2
192.5.g.d.127.3		4	8.5	even	2
300.5.c.a.151.3		4	20.19	odd	2
300.5.c.a.151.4		4	5.4	even	2
300.5.f.a.199.1		8	20.7	even	4
300.5.f.a.199.2		8	5.3	odd	4
300.5.f.a.199.7		8	5.2	odd	4
300.5.f.a.199.8		8	20.3	even	4
576.5.g.m.127.3		4	24.11	even	2
576.5.g.m.127.4		4	24.5	odd	2
768.5.b.g.127.1		8	16.3	odd	4
768.5.b.g.127.4		8	16.5	even	4
768.5.b.g.127.5		8	16.13	even	4
768.5.b.g.127.8		8	16.11	odd	4

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.302776 - 3.98852i) q^{2} -5.19615i q^{3} +(-15.8167 + 2.41526i) q^{4} +34.8444 q^{5} +(-20.7250 + 1.57327i) q^{6} +43.0318i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-0.302776 - 3.98852i) q^{2} -5.19615i q^{3} +(-15.8167 + 2.41526i) q^{4} +34.8444 q^{5} +(-20.7250 + 1.57327i) q^{6} +43.0318i q^{7} +(14.4222 + 62.3538i) q^{8} -27.0000 q^{9} +(-10.5500 - 138.978i) q^{10} -65.2790i q^{11} +(12.5500 + 82.1857i) q^{12} -99.0665 q^{13} +(171.633 - 13.0290i) q^{14} -181.057i q^{15} +(244.333 - 76.4025i) q^{16} -207.689 q^{17} +(8.17494 + 107.690i) q^{18} +569.960i q^{19} +(-551.122 + 84.1582i) q^{20} +223.600 q^{21} +(-260.367 + 19.7649i) q^{22} -371.198i q^{23} +(324.000 - 74.9400i) q^{24} +589.133 q^{25} +(29.9949 + 395.129i) q^{26} +140.296i q^{27} +(-103.933 - 680.619i) q^{28} +423.911 q^{29} +(-722.150 + 54.8196i) q^{30} -1174.18i q^{31} +(-378.711 - 951.396i) q^{32} -339.199 q^{33} +(62.8831 + 828.372i) q^{34} +1499.42i q^{35} +(427.050 - 65.2119i) q^{36} -1448.13 q^{37} +(2273.30 - 172.570i) q^{38} +514.764i q^{39} +(502.533 + 2172.68i) q^{40} -265.822 q^{41} +(-67.7005 - 891.833i) q^{42} -699.900i q^{43} +(157.665 + 1032.49i) q^{44} -940.799 q^{45} +(-1480.53 + 112.390i) q^{46} -1250.00i q^{47} +(-396.999 - 1269.59i) q^{48} +549.266 q^{49} +(-178.375 - 2349.77i) q^{50} +1079.18i q^{51} +(1566.90 - 239.271i) q^{52} +787.645 q^{53} +(559.574 - 42.4782i) q^{54} -2274.61i q^{55} +(-2683.20 + 620.613i) q^{56} +2961.60 q^{57} +(-128.350 - 1690.78i) q^{58} +3012.53i q^{59} +(437.299 + 2863.71i) q^{60} +4519.33 q^{61} +(-4683.23 + 355.512i) q^{62} -1161.86i q^{63} +(-3680.00 + 1798.56i) q^{64} -3451.91 q^{65} +(102.701 + 1352.91i) q^{66} +5215.70i q^{67} +(3284.94 - 501.622i) q^{68} -1928.80 q^{69} +(5980.46 - 453.987i) q^{70} -4693.16i q^{71} +(-389.400 - 1683.55i) q^{72} -5404.92 q^{73} +(438.459 + 5775.91i) q^{74} -3061.22i q^{75} +(-1376.60 - 9014.86i) q^{76} +2809.07 q^{77} +(2053.15 - 155.858i) q^{78} +7453.44i q^{79} +(8513.64 - 2662.20i) q^{80} +729.000 q^{81} +(80.4843 + 1060.24i) q^{82} -8950.92i q^{83} +(-3536.60 + 540.051i) q^{84} -7236.79 q^{85} +(-2791.57 + 211.913i) q^{86} -2202.71i q^{87} +(4070.39 - 941.466i) q^{88} -616.496 q^{89} +(284.851 + 3752.40i) q^{90} -4263.01i q^{91} +(896.538 + 5871.11i) q^{92} -6101.20 q^{93} +(-4985.66 + 378.470i) q^{94} +19859.9i q^{95} +(-4943.60 + 1967.84i) q^{96} +13723.1 q^{97} +(-166.304 - 2190.76i) q^{98} +1762.53i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 - 20 * q^4 + 24 * q^5 - 18 * q^6 - 108 * q^9	\( 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9} - 172 q^{10} + 180 q^{12} + 296 q^{13} + 600 q^{14} + 112 q^{16} - 600 q^{17} - 162 q^{18} - 1368 q^{20} - 144 q^{21} - 1128 q^{22} + 1296 q^{24} + 972 q^{25} + 1692 q^{26} + 1488 q^{28} + 888 q^{29} - 1980 q^{30} - 2784 q^{32} + 720 q^{33} - 484 q^{34} + 540 q^{36} - 4408 q^{37} + 4680 q^{38} + 1664 q^{40} + 552 q^{41} - 2088 q^{42} - 3696 q^{44} - 648 q^{45} - 384 q^{46} + 1008 q^{48} - 572 q^{49} - 1038 q^{50} + 6008 q^{52} + 5112 q^{53} + 486 q^{54} + 1728 q^{56} + 5616 q^{57} - 124 q^{58} - 2664 q^{60} + 4232 q^{61} - 7224 q^{62} - 14720 q^{64} - 18192 q^{65} + 4824 q^{66} + 5496 q^{68} - 9792 q^{69} + 6096 q^{70} + 8840 q^{73} - 4116 q^{74} - 1872 q^{76} + 20928 q^{77} + 9900 q^{78} + 25632 q^{80} + 2916 q^{81} + 3740 q^{82} - 10512 q^{84} - 10256 q^{85} - 19560 q^{86} - 8640 q^{88} - 25080 q^{89} + 4644 q^{90} + 18816 q^{92} - 17136 q^{93} - 5232 q^{94} - 8352 q^{96} + 23048 q^{97} - 5850 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 - 20 * q^4 + 24 * q^5 - 18 * q^6 - 108 * q^9 - 172 * q^10 + 180 * q^12 + 296 * q^13 + 600 * q^14 + 112 * q^16 - 600 * q^17 - 162 * q^18 - 1368 * q^20 - 144 * q^21 - 1128 * q^22 + 1296 * q^24 + 972 * q^25 + 1692 * q^26 + 1488 * q^28 + 888 * q^29 - 1980 * q^30 - 2784 * q^32 + 720 * q^33 - 484 * q^34 + 540 * q^36 - 4408 * q^37 + 4680 * q^38 + 1664 * q^40 + 552 * q^41 - 2088 * q^42 - 3696 * q^44 - 648 * q^45 - 384 * q^46 + 1008 * q^48 - 572 * q^49 - 1038 * q^50 + 6008 * q^52 + 5112 * q^53 + 486 * q^54 + 1728 * q^56 + 5616 * q^57 - 124 * q^58 - 2664 * q^60 + 4232 * q^61 - 7224 * q^62 - 14720 * q^64 - 18192 * q^65 + 4824 * q^66 + 5496 * q^68 - 9792 * q^69 + 6096 * q^70 + 8840 * q^73 - 4116 * q^74 - 1872 * q^76 + 20928 * q^77 + 9900 * q^78 + 25632 * q^80 + 2916 * q^81 + 3740 * q^82 - 10512 * q^84 - 10256 * q^85 - 19560 * q^86 - 8640 * q^88 - 25080 * q^89 + 4644 * q^90 + 18816 * q^92 - 17136 * q^93 - 5232 * q^94 - 8352 * q^96 + 23048 * q^97 - 5850 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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