LMFDB - Embedded newform 36.5.d.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, 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("36.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.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:	$3.72131867102$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.5.d.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.302776 - 3.98852i) q^{2} +(-15.8167 - 2.41526i) q^{4} -34.8444 q^{5} -43.0318i q^{7} +(-14.4222 + 62.3538i) q^{8} +O(q^{10})$	\(q+(0.302776 - 3.98852i) q^{2} +(-15.8167 - 2.41526i) q^{4} -34.8444 q^{5} -43.0318i q^{7} +(-14.4222 + 62.3538i) q^{8} +(-10.5500 + 138.978i) q^{10} -65.2790i q^{11} -99.0665 q^{13} +(-171.633 - 13.0290i) q^{14} +(244.333 + 76.4025i) q^{16} +207.689 q^{17} -569.960i q^{19} +(551.122 + 84.1582i) q^{20} +(-260.367 - 19.7649i) q^{22} -371.198i q^{23} +589.133 q^{25} +(-29.9949 + 395.129i) q^{26} +(-103.933 + 680.619i) q^{28} -423.911 q^{29} +1174.18i q^{31} +(378.711 - 951.396i) q^{32} +(62.8831 - 828.372i) q^{34} +1499.42i q^{35} -1448.13 q^{37} +(-2273.30 - 172.570i) q^{38} +(502.533 - 2172.68i) q^{40} +265.822 q^{41} +699.900i q^{43} +(-157.665 + 1032.49i) q^{44} +(-1480.53 - 112.390i) q^{46} -1250.00i q^{47} +549.266 q^{49} +(178.375 - 2349.77i) q^{50} +(1566.90 + 239.271i) q^{52} -787.645 q^{53} +2274.61i q^{55} +(2683.20 + 620.613i) q^{56} +(-128.350 + 1690.78i) q^{58} +3012.53i q^{59} +4519.33 q^{61} +(4683.23 + 355.512i) q^{62} +(-3680.00 - 1798.56i) q^{64} +3451.91 q^{65} -5215.70i q^{67} +(-3284.94 - 501.622i) q^{68} +(5980.46 + 453.987i) q^{70} -4693.16i q^{71} -5404.92 q^{73} +(-438.459 + 5775.91i) q^{74} +(-1376.60 + 9014.86i) q^{76} -2809.07 q^{77} -7453.44i q^{79} +(-8513.64 - 2662.20i) q^{80} +(80.4843 - 1060.24i) q^{82} -8950.92i q^{83} -7236.79 q^{85} +(2791.57 + 211.913i) q^{86} +(4070.39 + 941.466i) q^{88} +616.496 q^{89} +4263.01i q^{91} +(-896.538 + 5871.11i) q^{92} +(-4985.66 - 378.470i) q^{94} +19859.9i q^{95} +13723.1 q^{97} +(166.304 - 2190.76i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5}+O(q^{10}) $ 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5	$ 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5} - 172 q^{10} + 296 q^{13} - 600 q^{14} + 112 q^{16} + 600 q^{17} + 1368 q^{20} - 1128 q^{22} + 972 q^{25} - 1692 q^{26} + 1488 q^{28} - 888 q^{29} + 2784 q^{32} - 484 q^{34} - 4408 q^{37} - 4680 q^{38} + 1664 q^{40} - 552 q^{41} + 3696 q^{44} - 384 q^{46} - 572 q^{49} + 1038 q^{50} + 6008 q^{52} - 5112 q^{53} - 1728 q^{56} - 124 q^{58} + 4232 q^{61} + 7224 q^{62} - 14720 q^{64} + 18192 q^{65} - 5496 q^{68} + 6096 q^{70} + 8840 q^{73} + 4116 q^{74} - 1872 q^{76} - 20928 q^{77} - 25632 q^{80} + 3740 q^{82} - 10256 q^{85} + 19560 q^{86} - 8640 q^{88} + 25080 q^{89} - 18816 q^{92} - 5232 q^{94} + 23048 q^{97} + 5850 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5 - 172 * q^10 + 296 * q^13 - 600 * q^14 + 112 * q^16 + 600 * q^17 + 1368 * q^20 - 1128 * q^22 + 972 * q^25 - 1692 * q^26 + 1488 * q^28 - 888 * q^29 + 2784 * q^32 - 484 * q^34 - 4408 * q^37 - 4680 * q^38 + 1664 * q^40 - 552 * q^41 + 3696 * q^44 - 384 * q^46 - 572 * q^49 + 1038 * q^50 + 6008 * q^52 - 5112 * q^53 - 1728 * q^56 - 124 * q^58 + 4232 * q^61 + 7224 * q^62 - 14720 * q^64 + 18192 * q^65 - 5496 * q^68 + 6096 * q^70 + 8840 * q^73 + 4116 * q^74 - 1872 * q^76 - 20928 * q^77 - 25632 * q^80 + 3740 * q^82 - 10256 * q^85 + 19560 * q^86 - 8640 * q^88 + 25080 * q^89 - 18816 * q^92 - 5232 * q^94 + 23048 * q^97 + 5850 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−15.8167	−	2.41526i	−0.988541	−	0.150954i
$5$	−34.8444			−1.39378			−0.696888	−	0.717180i	$-0.745433\pi$
$5$	−34.8444			−1.39378			−0.696888	+	0.717180i	$0.745433\pi$
$6$		0			0
$7$		−	43.0318i		−	0.878200i	−0.898438	−	0.439100i	$-0.855297\pi$
$7$		−	43.0318i		−	0.878200i	0.898438	−	0.439100i	$-0.144703\pi$
$8$	−14.4222	+	62.3538i	−0.225347	+	0.974279i
$9$		0			0
$10$	−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	$-0.0869403\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	244.333	+	76.4025i	0.954426	+	0.298447i
$17$	207.689			0.718646			0.359323	−	0.933213i	$-0.383008\pi$
$17$	207.689			0.718646			0.359323	+	0.933213i	$0.383008\pi$
$18$		0			0
$19$		−	569.960i		−	1.57884i	−0.613856	−	0.789418i	$-0.710382\pi$
$19$		−	569.960i		−	1.57884i	0.613856	−	0.789418i	$-0.289618\pi$
$20$	551.122	+	84.1582i	1.37780	+	0.210395i
$21$		0			0
$22$	−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	$-0.114107\pi$
$24$		0			0
$25$	589.133			0.942613
$26$	−29.9949	+	395.129i	−0.0443712	+	0.584510i
$27$		0			0
$28$	−103.933	+	680.619i	−0.132567	+	0.868136i
$29$	−423.911			−0.504056			−0.252028	−	0.967720i	$-0.581097\pi$
$29$	−423.911			−0.504056			−0.252028	+	0.967720i	$0.581097\pi$
$30$		0			0
$31$			1174.18i			1.22183i	0.791697	+	0.610914i	$0.209198\pi$
$31$			1174.18i			1.22183i	−0.791697	+	0.610914i	$0.790802\pi$
$32$	378.711	−	951.396i	0.369835	−	0.929097i
$33$		0			0
$34$	62.8831	−	828.372i	0.0543972	−	0.716585i
$35$			1499.42i			1.22401i
$36$		0			0
$37$	−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
$39$		0			0
$40$	502.533	−	2172.68i	0.314083	−	1.35793i
$41$	265.822			0.158133			0.0790666	−	0.996869i	$-0.474806\pi$
$41$	265.822			0.158133			0.0790666	+	0.996869i	$0.474806\pi$
$42$		0			0
$43$			699.900i			0.378529i	0.981926	+	0.189265i	$0.0606104\pi$
$43$			699.900i			0.378529i	−0.981926	+	0.189265i	$0.939390\pi$
$44$	−157.665	+	1032.49i	−0.0814387	+	0.533313i
$45$		0			0
$46$	−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	$-0.0913077\pi$
$48$		0			0
$49$	549.266			0.228765
$50$	178.375	−	2349.77i	0.0713500	−	0.939908i
$51$		0			0
$52$	1566.90	+	239.271i	0.579475	+	0.0884877i
$53$	−787.645			−0.280401			−0.140200	−	0.990123i	$-0.544775\pi$
$53$	−787.645			−0.280401			−0.140200	+	0.990123i	$0.544775\pi$
$54$		0			0
$55$			2274.61i			0.751936i
$56$	2683.20	+	620.613i	0.855611	+	0.197900i
$57$		0			0
$58$	−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	$0.857557\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$	−3680.00	−	1798.56i	−0.898438	−	0.439101i
$65$	3451.91			0.817021
$66$		0			0
$67$		−	5215.70i		−	1.16189i	−0.813945	−	0.580943i	$-0.802684\pi$
$67$		−	5215.70i		−	1.16189i	0.813945	−	0.580943i	$-0.197316\pi$
$68$	−3284.94	−	501.622i	−0.710411	−	0.108482i
$69$		0			0
$70$	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	$-0.154125\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	−1376.60	+	9014.86i	−0.238331	+	1.56074i
$77$	−2809.07			−0.473785
$78$		0			0
$79$		−	7453.44i		−	1.19427i	−0.802141	−	0.597135i	$-0.796306\pi$
$79$		−	7453.44i		−	1.19427i	0.802141	−	0.597135i	$-0.203694\pi$
$80$	−8513.64	−	2662.20i	−1.33026	−	0.415969i
$81$		0			0
$82$	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	$-0.225086\pi$
$84$		0			0
$85$	−7236.79			−1.00163
$86$	2791.57	+	211.913i	0.377443	+	0.0286523i
$87$		0			0
$88$	4070.39	+	941.466i	0.525619	+	0.121574i
$89$	616.496			0.0778305			0.0389153	−	0.999243i	$-0.487610\pi$
$89$	616.496			0.0778305			0.0389153	+	0.999243i	$0.487610\pi$
$90$		0			0
$91$			4263.01i			0.514794i
$92$	−896.538	+	5871.11i	−0.105924	+	0.693656i
$93$		0			0
$94$	−4985.66	−	378.470i	−0.564244	−	0.0428327i
$95$			19859.9i			2.20054i
$96$		0			0
$97$	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
$99$		0			0
$100$	−9318.11	−	1422.91i	−0.931811	−	0.142291i
$101$	−14758.8			−1.44680			−0.723401	−	0.690428i	$-0.757422\pi$
$101$	−14758.8			−1.44680			−0.723401	+	0.690428i	$0.757422\pi$
$102$		0			0
$103$			1859.14i			0.175242i	0.996154	+	0.0876210i	$0.0279264\pi$
$103$			1859.14i			0.175242i	−0.996154	+	0.0876210i	$0.972074\pi$
$104$	1428.76	−	6177.17i	0.132097	−	0.571114i
$105$		0			0
$106$	−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	$-0.154209\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	3287.74	−	10514.1i	0.262096	−	0.838177i
$113$	21225.5			1.66227			0.831135	−	0.556070i	$-0.187691\pi$
$113$	21225.5			1.66227			0.831135	+	0.556070i	$0.187691\pi$
$114$		0			0
$115$			12934.2i			0.978009i
$116$	6704.85	+	1023.85i	0.498280	+	0.0760890i
$117$		0			0
$118$	12015.6	+	912.122i	0.862939	+	0.0655072i
$119$		−	8937.22i		−	0.631115i
$120$		0			0
$121$	10379.7			0.708945
$122$	1368.34	−	18025.5i	0.0919338	−	1.21106i
$123$		0			0
$124$	2835.94	−	18571.5i	0.184439	−	1.20783i
$125$	1249.77			0.0799851
$126$		0			0
$127$		−	4676.78i		−	0.289961i	−0.989435	−	0.144980i	$-0.953688\pi$
$127$		−	4676.78i		−	0.289961i	0.989435	−	0.144980i	$-0.0463119\pi$
$128$	−8287.81	+	14133.2i	−0.505848	+	0.862623i
$129$		0			0
$130$	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	$0.662940\pi$
$132$		0			0
$133$	−24526.4			−1.38653
$134$	−20803.0	−	1579.19i	−1.15855	−	0.0879476i
$135$		0			0
$136$	−2995.33	+	12950.2i	−0.161945	+	0.700162i
$137$	19273.3			1.02687			0.513434	−	0.858129i	$-0.328373\pi$
$137$	19273.3			1.02687			0.513434	+	0.858129i	$0.328373\pi$
$138$		0			0
$139$			24086.9i			1.24667i	0.781955	+	0.623335i	$0.214222\pi$
$139$			24086.9i			1.24667i	−0.781955	+	0.623335i	$0.785778\pi$
$140$	3621.48	−	23715.8i	0.184769	−	1.20999i
$141$		0			0
$142$	−18718.8	−	1420.98i	−0.928327	−	0.0704709i
$143$			6466.95i			0.316248i
$144$		0			0
$145$	14770.9			0.702541
$146$	−1636.48	+	21557.7i	−0.0767723	+	1.01134i
$147$		0			0
$148$	22904.6	+	3497.61i	1.04568	+	0.159679i
$149$	−43993.2			−1.98159			−0.990794	−	0.135378i	$-0.956775\pi$
$149$	−43993.2			−1.98159			−0.990794	+	0.135378i	$0.956775\pi$
$150$		0			0
$151$		−	1388.00i		−	0.0608746i	−0.999537	−	0.0304373i	$-0.990310\pi$
$151$		−	1388.00i		−	0.0608746i	0.999537	−	0.0304373i	$-0.00969000\pi$
$152$	35539.2	+	8220.08i	1.53823	+	0.355786i
$153$		0			0
$154$	−850.518	+	11204.0i	−0.0358626	+	0.472425i
$155$		−	40913.5i		−	1.70295i
$156$		0			0
$157$	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
$159$		0			0
$160$	−13196.0	+	33150.8i	−0.515468	+	1.29495i
$161$	−15973.3			−0.616230
$162$		0			0
$163$		−	47291.0i		−	1.77993i	−0.456029	−	0.889965i	$-0.650729\pi$
$163$		−	47291.0i		−	1.77993i	0.456029	−	0.889965i	$-0.349271\pi$
$164$	−4204.41	−	642.028i	−0.156321	−	0.0238707i
$165$		0			0
$166$	−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	$0.999485\pi$
$168$		0			0
$169$	−18746.8			−0.656379
$170$	−2191.13	+	28864.1i	−0.0758175	+	0.998759i
$171$		0			0
$172$	1690.44	−	11070.1i	0.0571403	−	0.374191i
$173$	1212.10			0.0404993			0.0202497	−	0.999795i	$-0.493554\pi$
$173$	1212.10			0.0404993			0.0202497	+	0.999795i	$0.493554\pi$
$174$		0			0
$175$		−	25351.4i		−	0.827802i
$176$	4987.48	−	15949.8i	0.161011	−	0.514909i
$177$		0			0
$178$	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	$0.895315\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	23145.6	+	5353.49i	0.683649	+	0.158125i
$185$	50459.3			1.47434
$186$		0			0
$187$		−	13557.7i		−	0.387706i
$188$	−3019.07	+	19770.8i	−0.0854197	+	0.559383i
$189$		0			0
$190$	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	$-0.169582\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−8687.55	−	1326.62i	−0.226144	−	0.0345329i
$197$	42137.6			1.08577			0.542885	−	0.839807i	$-0.317332\pi$
$197$	42137.6			1.08577			0.542885	+	0.839807i	$0.317332\pi$
$198$		0			0
$199$			68550.6i			1.73103i	0.500881	+	0.865516i	$0.333009\pi$
$199$			68550.6i			1.73103i	−0.500881	+	0.865516i	$0.666991\pi$
$200$	−8496.60	+	36734.7i	−0.212415	+	0.918367i
$201$		0			0
$202$	−4468.62	+	58866.0i	−0.109514	+	1.44265i
$203$			18241.6i			0.442662i
$204$		0			0
$205$	−9262.40			−0.220402
$206$	7415.23	+	562.903i	0.174739	+	0.0132647i
$207$		0			0
$208$	−24205.2	−	7568.93i	−0.559477	−	0.174948i
$209$	−37206.4			−0.851775
$210$		0			0
$211$		−	37678.5i		−	0.846308i	−0.906058	−	0.423154i	$-0.860923\pi$
$211$		−	37678.5i		−	0.846308i	0.906058	−	0.423154i	$-0.139077\pi$
$212$	12457.9	+	1902.36i	0.277187	+	0.0423274i
$213$		0			0
$214$	−42535.0	−	3228.91i	−0.928794	−	0.0705063i
$215$		−	24387.6i		−	0.527585i
$216$		0			0
$217$	50526.9			1.07301
$218$	−1356.23	+	17866.0i	−0.0285379	+	0.375935i
$219$		0			0
$220$	5493.76	−	35976.7i	0.113507	−	0.743320i
$221$	−20575.0			−0.421265
$222$		0			0
$223$			9238.47i			0.185776i	0.995677	+	0.0928882i	$0.0296099\pi$
$223$			9238.47i			0.185776i	−0.995677	+	0.0928882i	$0.970390\pi$
$224$	−40940.2	−	16296.6i	−0.815933	−	0.324789i
$225$		0			0
$226$	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	$0.842686\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	6113.73	−	26432.5i	0.113587	−	0.491091i
$233$	−52029.9			−0.958387			−0.479193	−	0.877709i	$-0.659071\pi$
$233$	−52029.9			−0.958387			−0.479193	+	0.877709i	$0.659071\pi$
$234$		0			0
$235$			43555.6i			0.788693i
$236$	7276.04	−	47648.2i	0.130638	−	0.855505i
$237$		0			0
$238$	−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	$0.843605\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−71480.7	−	10915.3i	−1.20063	−	0.183340i
$245$	−19138.8			−0.318848
$246$		0			0
$247$			56463.9i			0.925501i
$248$	−73214.4	−	16934.2i	−1.19040	−	0.275335i
$249$		0			0
$250$	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	$-0.0302379\pi$
$252$		0			0
$253$	−24231.4			−0.378562
$254$	−18653.5	−	1416.02i	−0.289129	−	0.0219483i
$255$		0			0
$256$	53861.3	+	37335.3i	0.821858	+	0.569692i
$257$	15483.1			0.234418			0.117209	−	0.993107i	$-0.462605\pi$
$257$	15483.1			0.234418			0.117209	+	0.993107i	$0.462605\pi$
$258$		0			0
$259$			62315.7i			0.928963i
$260$	−54597.7	−	8337.25i	−0.807658	−	0.123332i
$261$		0			0
$262$	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	$-0.0376793\pi$
$264$		0			0
$265$	27445.0			0.390816
$266$	−7425.99	+	97824.1i	−0.104952	+	1.38256i
$267$		0			0
$268$	−12597.3	+	82495.0i	−0.175391	+	1.14857i
$269$	82062.5			1.13407			0.567035	−	0.823694i	$-0.308090\pi$
$269$	82062.5			1.13407			0.567035	+	0.823694i	$0.308090\pi$
$270$		0			0
$271$		−	75123.6i		−	1.02291i	−0.859310	−	0.511456i	$-0.829106\pi$
$271$		−	75123.6i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$272$	50745.2	+	15868.0i	0.685895	+	0.214478i
$273$		0			0
$274$	5835.48	−	76872.0i	0.0777277	−	1.02392i
$275$		−	38458.0i		−	0.508535i
$276$		0			0
$277$	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
$279$		0			0
$280$	−93494.4	−	21624.9i	−1.19253	−	0.275828i
$281$	90483.6			1.14593			0.572964	−	0.819581i	$-0.305794\pi$
$281$	90483.6			1.14593			0.572964	+	0.819581i	$0.305794\pi$
$282$		0			0
$283$		−	44901.3i		−	0.560643i	−0.959906	−	0.280321i	$-0.909559\pi$
$283$		−	44901.3i		−	0.560643i	0.959906	−	0.280321i	$-0.0904410\pi$
$284$	−11335.2	+	74230.1i	−0.140537	+	0.920330i
$285$		0			0
$286$	25793.6	+	1958.04i	0.315341	+	0.0239380i
$287$		−	11438.8i		−	0.138872i
$288$		0			0
$289$	−40386.4			−0.483547
$290$	4472.28	−	58914.2i	0.0531781	−	0.700525i
$291$		0			0
$292$	85487.8	+	13054.3i	1.00262	+	0.153104i
$293$	−30326.7			−0.353257			−0.176628	−	0.984278i	$-0.556519\pi$
$293$	−30326.7			−0.353257			−0.176628	+	0.984278i	$0.556519\pi$
$294$		0			0
$295$		−	104970.i		−	1.20620i
$296$	20885.3	−	90296.6i	0.238373	−	1.03060i
$297$		0			0
$298$	−13320.1	+	175468.i	−0.149994	+	1.97590i
$299$			36773.3i			0.411329i
$300$		0			0
$301$	30118.0			0.332424
$302$	−5536.08	−	420.253i	−0.0607000	−	0.00460784i
$303$		0			0
$304$	43546.4	−	139260.i	0.471200	−	1.50688i
$305$	−157473.			−1.69281
$306$		0			0
$307$		−	35547.6i		−	0.377167i	−0.982057	−	0.188583i	$-0.939610\pi$
$307$		−	35547.6i		−	0.377167i	0.982057	−	0.188583i	$-0.0603896\pi$
$308$	44430.1	+	6784.62i	0.468356	+	0.0715195i
$309$		0			0
$310$	−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	$-0.121757\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−18002.0	+	117888.i	−0.180279	+	1.18058i
$317$	64556.9			0.642428			0.321214	−	0.947007i	$-0.395909\pi$
$317$	64556.9			0.642428			0.321214	+	0.947007i	$0.395909\pi$
$318$		0			0
$319$			27672.5i			0.271936i
$320$	128227.	+	62669.7i	1.25222	+	0.612009i
$321$		0			0
$322$	−4836.33	+	63709.9i	−0.0466449	+	0.614462i
$323$		−	118374.i		−	1.13462i
$324$		0			0
$325$	−58363.3			−0.552552
$326$	−188621.	−	14318.6i	−1.77482	−	0.134730i
$327$		0			0
$328$	−3833.74	+	16575.0i	−0.0356348	+	0.154066i
$329$	−53789.8			−0.496945
$330$		0			0
$331$		−	11544.1i		−	0.105367i	−0.998611	−	0.0526833i	$-0.983223\pi$
$331$		−	11544.1i		−	0.105367i	0.998611	−	0.0526833i	$-0.0167774\pi$
$332$	−21618.8	+	141574.i	−0.196135	+	1.28442i
$333$		0			0
$334$	359.732	+	27.3078i	0.00322467	+	0.000244790i
$335$			181738.i			1.61941i
$336$		0			0
$337$	−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
$339$		0			0
$340$	114462.	+	17478.7i	0.990155	+	0.151200i
$341$	76649.0			0.659170
$342$		0			0
$343$		−	126955.i		−	1.07910i
$344$	−43641.5	−	10094.1i	−0.368793	−	0.0853004i
$345$		0			0
$346$	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	$-0.233628\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−62106.1	−	24721.9i	−0.501244	−	0.199525i
$353$	−186762.			−1.49878			−0.749391	−	0.662128i	$-0.769653\pi$
$353$	−186762.			−1.49878			−0.749391	+	0.662128i	$0.769653\pi$
$354$		0			0
$355$			163530.i			1.29760i
$356$	−9750.90	−	1488.99i	−0.0769387	−	0.0117488i
$357$		0			0
$358$	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	$0.658357\pi$
$360$		0			0
$361$	−194533.			−1.49272
$362$	5668.80	−	74676.3i	0.0432588	−	0.569857i
$363$		0			0
$364$	10296.3	−	67426.5i	0.0777099	−	0.508895i
$365$	188331.			1.41363
$366$		0			0
$367$			106652.i			0.791839i	0.918285	+	0.395920i	$0.129574\pi$
$367$			106652.i			0.791839i	−0.918285	+	0.395920i	$0.870426\pi$
$368$	28360.5	−	90695.9i	0.209420	−	0.669718i
$369$		0			0
$370$	15277.9	−	201258.i	0.111599	−	1.47011i
$371$			33893.8i			0.246248i
$372$		0			0
$373$	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
$375$		0			0
$376$	77942.4	+	18027.8i	0.551313	+	0.127517i
$377$	41995.3			0.295473
$378$		0			0
$379$			156156.i			1.08713i	0.839368	+	0.543563i	$0.182925\pi$
$379$			156156.i			1.08713i	−0.839368	+	0.543563i	$0.817075\pi$
$380$	47966.8	−	314117.i	0.332180	−	2.17533i
$381$		0			0
$382$	−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	$-0.350004\pi$
$384$		0			0
$385$	97880.4			0.660350
$386$	−6969.85	+	91815.2i	−0.0467787	+	0.616226i
$387$		0			0
$388$	−217053.	−	33144.7i	−1.44179	−	0.220166i
$389$	1046.60			0.00691644			0.00345822	−	0.999994i	$-0.498899\pi$
$389$	1046.60			0.00691644			0.00345822	+	0.999994i	$0.498899\pi$
$390$		0			0
$391$		−	77093.6i		−	0.504272i
$392$	−7921.62	+	34248.8i	−0.0515516	+	0.222881i
$393$		0			0
$394$	12758.3	−	168067.i	0.0821862	−	1.08265i
$395$			259711.i			1.66454i
$396$		0			0
$397$	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
$399$		0			0
$400$	143945.	+	45011.3i	0.899654	+	0.281320i
$401$	−144404.			−0.898029			−0.449015	−	0.893524i	$-0.648225\pi$
$401$	−144404.			−0.898029			−0.449015	+	0.893524i	$0.648225\pi$
$402$		0			0
$403$		−	116321.i		−	0.716226i
$404$	233435.	+	35646.4i	1.43022	+	0.218400i
$405$		0			0
$406$	72757.2	+	5523.12i	0.441392	+	0.0335068i
$407$			94532.6i			0.570680i
$408$		0			0
$409$	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
$411$		0			0
$412$	4490.30	−	29405.4i	0.0264534	−	0.173234i
$413$	129635.			0.760013
$414$		0			0
$415$			311889.i			1.81094i
$416$	−37517.6	+	94251.4i	−0.216795	+	0.544629i
$417$		0			0
$418$	−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	$-0.104108\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	11359.6	−	49112.7i	0.0631874	−	0.273188i
$425$	122356.			0.677405
$426$		0			0
$427$		−	194475.i		−	1.06661i
$428$	−25757.2	+	168674.i	−0.140608	+	0.920792i
$429$		0			0
$430$	−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	$-0.138619\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	70848.1	+	10818.7i	0.372697	+	0.0569120i
$437$	−211568.			−1.10786
$438$		0			0
$439$			154804.i			0.803252i	0.915804	+	0.401626i	$0.131555\pi$
$439$			154804.i			0.803252i	−0.915804	+	0.401626i	$0.868445\pi$
$440$	−141830.	−	32804.8i	−0.732595	−	0.169447i
$441$		0			0
$442$	−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	$0.779006\pi$
$444$		0			0
$445$	−21481.4			−0.108478
$446$	36847.9	+	2797.18i	0.185243	+	0.0140621i
$447$		0			0
$448$	−77395.2	+	158357.i	−0.385619	+	0.789007i
$449$	31888.6			0.158177			0.0790884	−	0.996868i	$-0.474799\pi$
$449$	31888.6			0.158177			0.0790884	+	0.996868i	$0.474799\pi$
$450$		0			0
$451$		−	17352.6i		−	0.0853121i
$452$	−335717.	−	51265.1i	−1.64322	−	0.250926i
$453$		0			0
$454$	194978.	+	14801.1i	0.945963	+	0.0718096i
$455$		−	148542.i		−	0.717507i
$456$		0			0
$457$	−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
$459$		0			0
$460$	31239.3	−	204575.i	0.147634	−	0.966802i
$461$	130544.			0.614266			0.307133	−	0.951667i	$-0.400630\pi$
$461$	130544.			0.614266			0.307133	+	0.951667i	$0.400630\pi$
$462$		0			0
$463$		−	273167.i		−	1.27428i	−0.770746	−	0.637142i	$-0.780116\pi$
$463$		−	273167.i		−	1.27428i	0.770746	−	0.637142i	$-0.219884\pi$
$464$	−103575.	−	32387.9i	−0.481084	−	0.150434i
$465$		0			0
$466$	−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	$-0.0410320\pi$
$468$		0			0
$469$	−224441.			−1.02037
$470$	173722.	+	13187.6i	0.786430	+	0.0596993i
$471$		0			0
$472$	−187843.	−	43447.4i	−0.843162	−	0.195020i
$473$	45688.8			0.204215
$474$		0			0
$475$		−	335782.i		−	1.48823i
$476$	−21585.7	+	141357.i	−0.0952690	+	0.623883i
$477$		0			0
$478$	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	$-0.113664\pi$
$480$		0			0
$481$	143461.			0.620076
$482$	−17049.6	+	224598.i	−0.0733872	+	0.966745i
$483$		0			0
$484$	−164171.	−	25069.5i	−0.700821	−	0.107018i
$485$	−478172.			−2.03283
$486$		0			0
$487$		−	314133.i		−	1.32451i	−0.749278	−	0.662256i	$-0.769599\pi$
$487$		−	314133.i		−	1.32451i	0.749278	−	0.662256i	$-0.230401\pi$
$488$	−65178.7	+	281797.i	−0.273694	+	1.18331i
$489$		0			0
$490$	−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	$0.961735\pi$
$492$		0			0
$493$	−88041.5			−0.362238
$494$	225208.	+	17095.9i	0.922846	+	0.0700548i
$495$		0			0
$496$	−89710.0	+	286890.i	−0.364651	+	1.16614i
$497$	−201955.			−0.817602
$498$		0			0
$499$			276054.i			1.10865i	0.832301	+	0.554324i	$0.187023\pi$
$499$			276054.i			1.10865i	−0.832301	+	0.554324i	$0.812977\pi$
$500$	−19767.1	−	3018.51i	−0.0790685	−	0.0120740i
$501$		0			0
$502$	−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	$-0.0789524\pi$
$504$		0			0
$505$	514263.			2.01652
$506$	−7336.68	+	96647.6i	−0.0286549	+	0.377476i
$507$		0			0
$508$	−11295.6	+	73971.0i	−0.0437706	+	0.286638i
$509$	335116.			1.29348			0.646739	−	0.762711i	$-0.276132\pi$
$509$	335116.			1.29348			0.646739	+	0.762711i	$0.276132\pi$
$510$		0			0
$511$			232584.i			0.890712i
$512$	165221.	−	203523.i	0.630267	−	0.776378i
$513$		0			0
$514$	4687.91	−	61754.7i	0.0177440	−	0.233746i
$515$		−	64780.7i		−	0.244248i
$516$		0			0
$517$	−81598.8			−0.305283
$518$	248548.	+	18867.7i	0.926297	+	0.0703168i
$519$		0			0
$520$	−49784.2	+	215240.i	−0.184113	+	0.796006i
$521$	320361.			1.18022			0.590111	−	0.807322i	$-0.299084\pi$
$521$	320361.			1.18022			0.590111	+	0.807322i	$0.299084\pi$
$522$		0			0
$523$		−	202708.i		−	0.741085i	−0.928816	−	0.370542i	$-0.879172\pi$
$523$		−	202708.i		−	0.741085i	0.928816	−	0.370542i	$-0.120828\pi$
$524$	72270.7	−	473275.i	0.263208	−	1.72366i
$525$		0			0
$526$	−65161.7	−	4946.53i	−0.235516	−	0.0178784i
$527$			243863.i			0.878062i
$528$		0			0
$529$	142053.			0.507621
$530$	8309.69	−	109465.i	0.0295824	−	0.389694i
$531$		0			0
$532$	387925.	+	59237.5i	1.37064	+	0.209302i
$533$	−26334.0			−0.0926964
$534$		0			0
$535$			371593.i			1.29826i
$536$	325219.	+	75221.9i	1.13200	+	0.261827i
$537$		0			0
$538$	24846.5	−	327308.i	0.0858422	−	1.13082i
$539$		−	35855.5i		−	0.123418i
$540$		0			0
$541$	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
$543$		0			0
$544$	78654.1	−	197594.i	0.265781	−	0.667692i
$545$	156080.			0.525477
$546$		0			0
$547$			71049.9i			0.237459i	0.992927	+	0.118730i	$0.0378822\pi$
$547$			71049.9i			0.237459i	−0.992927	+	0.118730i	$0.962118\pi$
$548$	−304839.	−	46549.9i	−1.01510	−	0.155009i
$549$		0			0
$550$	−153391.	−	11644.1i	−0.507076	−	0.0384930i
$551$			241612.i			0.795821i
$552$		0			0
$553$	−320735.			−1.04881
$554$	2922.35	−	38496.7i	0.00952167	−	0.125431i
$555$		0			0
$556$	58176.0	−	380974.i	0.188189	−	1.23238i
$557$	−152777.			−0.492432			−0.246216	−	0.969215i	$-0.579187\pi$
$557$	−152777.			−0.492432			−0.246216	+	0.969215i	$0.579187\pi$
$558$		0			0
$559$		−	69336.6i		−	0.221891i
$560$	−114559.	+	366357.i	−0.365304	+	1.16823i
$561$		0			0
$562$	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	$0.934966\pi$
$564$		0			0
$565$	−739591.			−2.31683
$566$	−179090.	−	13595.0i	−0.559034	−	0.0424372i
$567$		0			0
$568$	292637.	+	67685.7i	0.907052	+	0.209798i
$569$	353147.			1.09076			0.545382	−	0.838188i	$-0.316385\pi$
$569$	353147.			1.09076			0.545382	+	0.838188i	$0.316385\pi$
$570$		0			0
$571$		−	9607.19i		−	0.0294662i	−0.999891	−	0.0147331i	$-0.995310\pi$
$571$		−	9607.19i		−	0.0294662i	0.999891	−	0.0147331i	$-0.00468986\pi$
$572$	15619.4	−	102286.i	0.0477387	−	0.312624i
$573$		0			0
$574$	−45623.9	−	3463.38i	−0.138474	−	0.0105118i
$575$		−	218685.i		−	0.661429i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−233627.	−	35675.6i	−0.694490	−	0.106051i
$581$	−385174.			−1.14105
$582$		0			0
$583$			51416.6i			0.151275i
$584$	77950.9	−	337018.i	0.228558	−	0.988159i
$585$		0			0
$586$	−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	$-0.195150\pi$
$588$		0			0
$589$	669233.			1.92907
$590$	−418675.	−	31782.3i	−1.20274	−	0.0913023i
$591$		0			0
$592$	−353827.	−	110641.i	−1.00960	−	0.315699i
$593$	199308.			0.566780			0.283390	−	0.959005i	$-0.408541\pi$
$593$	199308.			0.566780			0.283390	+	0.959005i	$0.408541\pi$
$594$		0			0
$595$			311412.i			0.879633i
$596$	695826.	+	106255.i	1.95888	+	0.299128i
$597$		0			0
$598$	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	$0.687390\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−3352.38	+	21953.6i	−0.00918924	+	0.0601771i
$605$	−361673.			−0.988110
$606$		0			0
$607$			204299.i			0.554485i	0.960800	+	0.277243i	$0.0894205\pi$
$607$			204299.i			0.554485i	−0.960800	+	0.277243i	$0.910579\pi$
$608$	−542257.	−	215850.i	−1.46689	−	0.583910i
$609$		0			0
$610$	−47679.1	+	628086.i	−0.128135	+	1.68795i
$611$			123833.i			0.331707i
$612$		0			0
$613$	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
$615$		0			0
$616$	40513.0	−	175156.i	0.106766	−	0.461598i
$617$	−387966.			−1.01911			−0.509557	−	0.860437i	$-0.670191\pi$
$617$	−387966.			−1.01911			−0.509557	+	0.860437i	$0.670191\pi$
$618$		0			0
$619$			676575.i			1.76577i	0.469587	+	0.882886i	$0.344403\pi$
$619$			676575.i			1.76577i	−0.469587	+	0.882886i	$0.655597\pi$
$620$	−98816.5	+	647114.i	−0.257067	+	1.68344i
$621$		0			0
$622$	−287980.	−	21861.1i	−0.744358	−	0.0565055i
$623$		−	26528.9i		−	0.0683507i
$624$		0			0
$625$	−411755.			−1.05409
$626$	49276.6	−	649131.i	0.125745	−	1.65647i
$627$		0			0
$628$	−118070.	−	18029.7i	−0.299379	−	0.0457162i
$629$	−300761.			−0.760187
$630$		0			0
$631$		−	383055.i		−	0.962059i	−0.876704	−	0.481030i	$-0.840263\pi$
$631$		−	383055.i		−	0.962059i	0.876704	−	0.481030i	$-0.159737\pi$
$632$	464750.	+	107495.i	1.16355	+	0.269125i
$633$		0			0
$634$	19546.3	−	257487.i	0.0486279	−	0.640585i
$635$			162960.i			0.404141i
$636$		0			0
$637$	−54413.8			−0.134100
$638$	110372.	+	8378.55i	0.271156	+	0.0205839i
$639$		0			0
$640$	288784.	−	492463.i	0.705039	−	1.20230i
$641$	−218038.			−0.530660			−0.265330	−	0.964158i	$-0.585481\pi$
$641$	−218038.			−0.530660			−0.265330	+	0.964158i	$0.585481\pi$
$642$		0			0
$643$		−	329758.i		−	0.797579i	−0.917043	−	0.398789i	$-0.869430\pi$
$643$		−	329758.i		−	0.797579i	0.917043	−	0.398789i	$-0.130570\pi$
$644$	252644.	+	38579.6i	0.609169	+	0.0930221i
$645$		0			0
$646$	−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	$0.936174\pi$
$648$		0			0
$649$	196655.			0.466891
$650$	−17671.0	+	232784.i	−0.0418248	+	0.550967i
$651$		0			0
$652$	−114220.	+	747985.i	−0.268687	+	1.75953i
$653$	684629.			1.60557			0.802785	−	0.596269i	$-0.203351\pi$
$653$	684629.			1.60557			0.802785	+	0.596269i	$0.203351\pi$
$654$		0			0
$655$		−	1.04263e6i		−	2.43024i
$656$	64949.0	+	20309.5i	0.150926	+	0.0471944i
$657$		0			0
$658$	−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	$-0.233062\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	558124.	+	129092.i	1.26589	+	0.292795i
$665$	854607.			1.93252
$666$		0			0
$667$			157355.i			0.353695i
$668$	217.836	−	1426.53i	0.000488176	−	0.00319689i
$669$		0			0
$670$	724867.	+	55025.9i	1.61476	+	0.122579i
$671$		−	295017.i		−	0.655243i
$672$		0			0
$673$	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
$675$		0			0
$676$	296512.	+	45278.4i	0.648857	+	0.0990827i
$677$	98225.8			0.214313			0.107156	−	0.994242i	$-0.465825\pi$
$677$	98225.8			0.214313			0.107156	+	0.994242i	$0.465825\pi$
$678$		0			0
$679$		−	590528.i		−	1.28086i
$680$	104371.	−	451242.i	0.225715	−	0.975869i
$681$		0			0
$682$	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	$-0.162045\pi$
$684$		0			0
$685$	−671567.			−1.43123
$686$	−506364.	−	38438.9i	−1.07601	−	0.0816814i
$687$		0			0
$688$	−53474.2	+	171009.i	−0.112971	+	0.361278i
$689$	78029.2			0.164369
$690$		0			0
$691$		−	190359.i		−	0.398673i	−0.979931	−	0.199337i	$-0.936121\pi$
$691$		−	190359.i		−	0.398673i	0.979931	−	0.199337i	$-0.0638787\pi$
$692$	−19171.4	−	2927.54i	−0.0400352	−	0.00611352i
$693$		0			0
$694$	−643366.	−	48839.0i	−1.33579	−	0.101402i
$695$		−	839294.i		−	1.73758i
$696$		0			0
$697$	55208.2			0.113642
$698$	26656.8	−	351155.i	0.0547138	−	0.720756i
$699$		0			0
$700$	−61230.2	+	400975.i	−0.124960	+	0.818316i
$701$	−504089.			−1.02582			−0.512910	−	0.858442i	$-0.671433\pi$
$701$	−504089.			−1.02582			−0.512910	+	0.858442i	$0.671433\pi$
$702$		0			0
$703$			825378.i			1.67010i
$704$	−117408.	+	240227.i	−0.236893	+	0.484703i
$705$		0			0
$706$	−56546.9	+	744903.i	−0.113449	+	1.49448i
$707$			635099.i			1.27058i
$708$		0			0
$709$	−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
$711$		0			0
$712$	−8891.23	+	38440.9i	−0.0175389	+	0.0758286i
$713$	435852.			0.857353
$714$		0			0
$715$		−	225337.i		−	0.440779i
$716$	49989.3	−	327362.i	0.0975105	−	0.638562i
$717$		0			0
$718$	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	$0.651514\pi$
$720$		0			0
$721$	80002.2			0.153897
$722$	−58899.9	+	775900.i	−0.112990	+	1.48844i
$723$		0			0
$724$	−296132.	−	45220.3i	−0.564947	−	0.0862694i
$725$	−249740.			−0.475129
$726$		0			0
$727$			339605.i			0.642548i	0.946986	+	0.321274i	$0.104111\pi$
$727$			339605.i			0.642548i	−0.946986	+	0.321274i	$0.895889\pi$
$728$	−265815.	−	61482.0i	−0.501552	−	0.116007i
$729$		0			0
$730$	57022.2	−	751164.i	0.107003	−	1.40958i
$731$			145361.i			0.272029i
$732$		0			0
$733$	−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
$735$		0			0
$736$	−353156.	−	140577.i	−0.651945	−	0.259513i
$737$	−340476.			−0.626832
$738$		0			0
$739$		−	561855.i		−	1.02881i	−0.857547	−	0.514405i	$-0.828013\pi$
$739$		−	561855.i		−	1.02881i	0.857547	−	0.514405i	$-0.171987\pi$
$740$	−798098.	−	121872.i	−1.45745	−	0.222557i
$741$		0			0
$742$	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	$0.974123\pi$
$744$		0			0
$745$	1.53292e6			2.76189
$746$	39113.7	−	515253.i	0.0702832	−	0.925854i
$747$		0			0
$748$	−32745.3	+	214438.i	−0.0585257	+	0.383264i
$749$	−458906.			−0.818013
$750$		0			0
$751$			58229.8i			0.103244i	0.998667	+	0.0516221i	$0.0164391\pi$
$751$			58229.8i			0.103244i	−0.998667	+	0.0516221i	$0.983561\pi$
$752$	95503.3	−	305417.i	0.168882	−	0.540079i
$753$		0			0
$754$	12715.2	−	167499.i	0.0223655	−	0.294626i
$755$			48364.1i			0.0848456i
$756$		0			0
$757$	−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
$759$		0			0
$760$	−1.23834e6	−	286424.i	−2.14394	−	0.495886i
$761$	−241107.			−0.416332			−0.208166	−	0.978094i	$-0.566749\pi$
$761$	−241107.			−0.416332			−0.208166	+	0.978094i	$0.566749\pi$
$762$		0			0
$763$			192754.i			0.331096i
$764$	−89505.0	+	586136.i	−0.153342	+	1.00418i
$765$		0			0
$766$	−1.04261e6	−	79146.5i	−1.77691	−	0.134888i
$767$		−	298441.i		−	0.507303i
$768$		0			0
$769$	−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
$771$		0			0
$772$	364097.	+	55598.8i	0.610917	+	0.0932891i
$773$	−431024.			−0.721344			−0.360672	−	0.932693i	$-0.617453\pi$
$773$	−431024.			−0.721344			−0.360672	+	0.932693i	$0.617453\pi$
$774$		0			0
$775$			691746.i			1.15171i
$776$	−197917.	+	855685.i	−0.328669	+	1.42099i
$777$		0			0
$778$	316.886	−	4174.40i	0.000523532	−	0.00689660i
$779$		−	151508.i		−	0.249666i
$780$		0			0
$781$	−306365.			−0.502269
$782$	−307490.	−	23342.1i	−0.502826	−	0.0381703i
$783$		0			0
$784$	134204.	+	41965.3i	0.218340	+	0.0682745i
$785$	−260111.			−0.422104
$786$		0			0
$787$			347948.i			0.561778i	0.959740	+	0.280889i	$0.0906293\pi$
$787$			347948.i			0.561778i	−0.959740	+	0.280889i	$0.909371\pi$
$788$	−666476.	−	101773.i	−1.07333	−	0.163901i
$789$		0			0
$790$	1.03586e6	+	78634.0i	1.65977	+	0.125996i
$791$		−	913373.i		−	1.45981i
$792$		0			0
$793$	−447714.			−0.711958
$794$	54945.2	−	723804.i	0.0871543	−	1.14810i
$795$		0			0
$796$	165567.	−	1.08424e6i	0.261305	−	1.71120i
$797$	460443.			0.724868			0.362434	−	0.932009i	$-0.381946\pi$
$797$	460443.			0.724868			0.362434	+	0.932009i	$0.381946\pi$
$798$		0			0
$799$		−	259611.i		−	0.406659i
$800$	223111.	−	560498.i	0.348612	−	0.875779i
$801$		0			0
$802$	−43722.0	+	575959.i	−0.0679753	+	0.895453i
$803$			352828.i			0.547182i
$804$		0			0
$805$	556580.			0.858887
$806$	−463951.	−	35219.3i	−0.714171	−	0.0542139i
$807$		0			0
$808$	212855.	−	920270.i	0.326033	−	1.40959i
$809$	621711.			0.949930			0.474965	−	0.880005i	$-0.342461\pi$
$809$	621711.			0.949930			0.474965	+	0.880005i	$0.342461\pi$
$810$		0			0
$811$		−	25991.9i		−	0.0395181i	−0.999805	−	0.0197591i	$-0.993710\pi$
$811$		−	25991.9i		−	0.0395181i	0.999805	−	0.0197591i	$-0.00628991\pi$
$812$	44058.2	−	288522.i	0.0668213	−	0.437589i
$813$		0			0
$814$	377046.	+	28622.2i	0.569043	+	0.0431970i
$815$			1.64783e6i			2.48082i
$816$		0			0
$817$	398915.			0.597635
$818$	565.573	−	7450.41i	0.000845244	−	0.0111346i
$819$		0			0
$820$	146500.	+	22371.1i	0.217877	+	0.0332705i
$821$	917945.			1.36185			0.680927	−	0.732352i	$-0.261577\pi$
$821$	917945.			1.36185			0.680927	+	0.732352i	$0.261577\pi$
$822$		0			0
$823$			1.22951e6i			1.81523i	0.419807	+	0.907613i	$0.362098\pi$
$823$			1.22951e6i			1.81523i	−0.419807	+	0.907613i	$0.637902\pi$
$824$	−115925.	−	26812.9i	−0.170734	−	0.0394902i
$825$		0			0
$826$	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	$0.940465\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	364565.	+	178177.i	0.526657	+	0.257398i
$833$	114076.			0.164401
$834$		0			0
$835$		−	3142.68i		−	0.00450740i
$836$	588480.	+	89862.9i	0.842014	+	0.128578i
$837$		0			0
$838$	−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	$-0.0911916\pi$
$840$		0			0
$841$	−527581.			−0.745928
$842$	−23493.9	+	309490.i	−0.0331383	+	0.436538i
$843$		0			0
$844$	−91003.2	+	595948.i	−0.127753	+	0.836611i
$845$	653222.			0.914845
$846$		0			0
$847$		−	446655.i		−	0.622595i
$848$	−192448.	−	60178.1i	−0.267622	−	0.0836848i
$849$		0			0
$850$	37046.5	−	488021.i	0.0512755	−	0.675462i
$851$			537544.i			0.742258i
$852$		0			0
$853$	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
$855$		0			0
$856$	664964.	+	153804.i	0.907508	+	0.209903i
$857$	116155.			0.158152			0.0790760	−	0.996869i	$-0.474803\pi$
$857$	116155.			0.158152			0.0790760	+	0.996869i	$0.474803\pi$
$858$		0			0
$859$			169632.i			0.229890i	0.993372	+	0.114945i	$0.0366692\pi$
$859$			169632.i			0.229890i	−0.993372	+	0.114945i	$0.963331\pi$
$860$	−58902.3	+	385730.i	−0.0796408	+	0.521539i
$861$		0			0
$862$	−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	$-0.144064\pi$
$864$		0			0
$865$	−42235.1			−0.0564470
$866$	−12494.7	+	164595.i	−0.0166606	+	0.219473i
$867$		0			0
$868$	−799166.	−	122035.i	−1.06071	−	0.161974i
$869$	−486552.			−0.644303
$870$		0			0
$871$			516701.i			0.681088i
$872$	64601.9	−	279304.i	0.0849596	−	0.367320i
$873$		0			0
$874$	−64057.6	+	843844.i	−0.0838586	+	1.10469i
$875$		−	53779.7i		−	0.0702429i
$876$		0			0
$877$	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
$879$		0			0
$880$	−173786.	+	555762.i	−0.224413	+	0.717667i
$881$	−976763.			−1.25845			−0.629227	−	0.777222i	$-0.716628\pi$
$881$	−976763.			−1.25845			−0.629227	+	0.777222i	$0.716628\pi$
$882$		0			0
$883$		−	1.29155e6i		−	1.65650i	−0.560362	−	0.828248i	$-0.689338\pi$
$883$		−	1.29155e6i		−	1.65650i	0.560362	−	0.828248i	$-0.310662\pi$
$884$	325428.	+	49693.9i	0.416438	+	0.0635914i
$885$		0			0
$886$	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	$-0.351923\pi$
$888$		0			0
$889$	−201250.			−0.254644
$890$	−6504.05	+	85679.2i	−0.00821115	+	0.108167i
$891$		0			0
$892$	22313.3	−	146122.i	0.0280436	−	0.183648i
$893$	−712451.			−0.893412
$894$		0			0
$895$		−	721186.i		−	0.900329i
$896$	608177.	+	356639.i	0.757555	+	0.444235i
$897$		0			0
$898$	9655.09	−	127188.i	0.0119730	−	0.157723i
$899$		−	497746.i		−	0.615869i
$900$		0			0
$901$	−163585.			−0.201509
$902$	−69211.1	−	5253.93i	−0.0850673	−	0.00645761i
$903$		0			0
$904$	−306119.	+	1.32349e6i	−0.374588	+	1.61951i
$905$	−652385.			−0.796538
$906$		0			0
$907$		−	373379.i		−	0.453874i	−0.973909	−	0.226937i	$-0.927129\pi$
$907$		−	373379.i		−	0.453874i	0.973909	−	0.226937i	$-0.0728712\pi$
$908$	118069.	−	773193.i	0.143207	−	0.937813i
$909$		0			0
$910$	−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	$0.987986\pi$
$912$		0			0
$913$	−584307.			−0.700970
$914$	−50539.9	+	665772.i	−0.0604981	+	0.796954i
$915$		0			0
$916$	−279235.	−	42640.1i	−0.332796	−	0.0508191i
$917$	1.28762e6			1.53126
$918$		0			0
$919$		−	829993.i		−	0.982751i	−0.870948	−	0.491375i	$-0.836494\pi$
$919$		−	829993.i		−	0.982751i	0.870948	−	0.491375i	$-0.163506\pi$
$920$	−806495.	−	186539.i	−0.952853	−	0.220391i
$921$		0			0
$922$	39525.7	−	520679.i	0.0464962	−	0.612503i
$923$			464935.i			0.545744i
$924$		0			0
$925$	−853143.			−0.997099
$926$	−1.08953e6	−	82708.3i	−1.27063	−	0.0964556i
$927$		0			0
$928$	−160540.	+	403307.i	−0.186418	+	0.468317i
$929$	−1.22106e6			−1.41483			−0.707416	−	0.706798i	$-0.750139\pi$
$929$	−1.22106e6			−1.41483			−0.707416	+	0.706798i	$0.750139\pi$
$930$		0			0
$931$		−	313059.i		−	0.361183i
$932$	822938.	+	125665.i	0.947404	+	0.144672i
$933$		0			0
$934$	−223638.	−	16976.7i	−0.256361	−	0.0194608i
$935$			472410.i			0.540376i
$936$		0			0
$937$	−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
$939$		0			0
$940$	105198.	−	688903.i	0.119056	−	0.779655i
$941$	1.17958e6			1.33214			0.666070	−	0.745889i	$-0.267975\pi$
$941$	1.17958e6			1.33214			0.666070	+	0.745889i	$0.267975\pi$
$942$		0			0
$943$		−	98672.5i		−	0.110962i
$944$	−230165.	+	736062.i	−0.258283	+	0.825981i
$945$		0			0
$946$	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	$0.835395\pi$
$948$		0			0
$949$	535447.			0.594544
$950$	−1.33928e6	−	101667.i	−1.48396	−	0.112650i
$951$		0			0
$952$	557270.	+	128894.i	0.614882	+	0.142220i
$953$	−1.72385e6			−1.89807			−0.949037	−	0.315166i	$-0.897940\pi$
$953$	−1.72385e6			−1.89807			−0.949037	+	0.315166i	$0.897940\pi$
$954$		0			0
$955$			1.29127e6i			1.41583i
$956$	130181.	−	852506.i	0.142439	−	0.932785i
$957$		0			0
$958$	−639760.	−	48565.3i	−0.697086	−	0.0529169i
$959$		−	829364.i		−	0.901796i
$960$		0			0
$961$	−455168.			−0.492862
$962$	43436.6	−	572199.i	0.0469360	−	0.618297i
$963$		0			0
$964$	890652.	+	136006.i	0.958416	+	0.146353i
$965$	802113.			0.861352
$966$		0			0
$967$		−	652513.i		−	0.697808i	−0.937158	−	0.348904i	$-0.886554\pi$
$967$		−	652513.i		−	0.697808i	0.937158	−	0.348904i	$-0.113446\pi$
$968$	−149698.	+	647211.i	−0.159759	+	0.690710i
$969$		0			0
$970$	−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	$-0.0680328\pi$
$972$		0			0
$973$	1.03650e6			1.09482
$974$	−1.25293e6	−	95111.8i	−1.32071	−	0.100257i
$975$		0			0
$976$	1.10422e6	+	345288.i	1.15920	+	0.362478i
$977$	1.43718e6			1.50564			0.752820	−	0.658227i	$-0.228693\pi$
$977$	1.43718e6			1.50564			0.752820	+	0.658227i	$0.228693\pi$
$978$		0			0
$979$		−	40244.2i		−	0.0419892i
$980$	302712.	+	46225.2i	0.315194	+	0.0481312i
$981$		0			0
$982$	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	$0.676343\pi$
$984$		0			0
$985$	−1.46826e6			−1.51332
$986$	−26656.8	+	351156.i	−0.0274192	+	0.361199i
$987$		0			0
$988$	136375.	−	893070.i	0.139708	−	0.914896i
$989$	259801.			0.265613
$990$		0			0
$991$			713551.i			0.726570i	0.931678	+	0.363285i	$0.118345\pi$
$991$			713551.i			0.726570i	−0.931678	+	0.363285i	$0.881655\pi$
$992$	1.11711e6	+	444674.i	1.13520	+	0.451875i
$993$		0			0
$994$	−61147.1	+	805503.i	−0.0618875	+	0.815257i
$995$		−	2.38861e6i		−	2.41267i
$996$		0			0
$997$	−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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.d.b.19.3		4
3.2	odd	2		12.5.d.a.7.2	yes	4
4.3	odd	2	inner	36.5.d.b.19.4		4
8.3	odd	2		576.5.g.m.127.4		4
8.5	even	2		576.5.g.m.127.3		4
12.11	even	2		12.5.d.a.7.1	✓	4
15.2	even	4		300.5.f.a.199.1		8
15.8	even	4		300.5.f.a.199.8		8
15.14	odd	2		300.5.c.a.151.3		4
24.5	odd	2		192.5.g.d.127.1		4
24.11	even	2		192.5.g.d.127.3		4
48.5	odd	4		768.5.b.g.127.8		8
48.11	even	4		768.5.b.g.127.4		8
48.29	odd	4		768.5.b.g.127.1		8
48.35	even	4		768.5.b.g.127.5		8
60.23	odd	4		300.5.f.a.199.2		8
60.47	odd	4		300.5.f.a.199.7		8
60.59	even	2		300.5.c.a.151.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.5.d.a.7.1	✓	4	12.11	even	2
12.5.d.a.7.2	yes	4	3.2	odd	2
36.5.d.b.19.3		4	1.1	even	1	trivial
36.5.d.b.19.4		4	4.3	odd	2	inner
192.5.g.d.127.1		4	24.5	odd	2
192.5.g.d.127.3		4	24.11	even	2
300.5.c.a.151.3		4	15.14	odd	2
300.5.c.a.151.4		4	60.59	even	2
300.5.f.a.199.1		8	15.2	even	4
300.5.f.a.199.2		8	60.23	odd	4
300.5.f.a.199.7		8	60.47	odd	4
300.5.f.a.199.8		8	15.8	even	4
576.5.g.m.127.3		4	8.5	even	2
576.5.g.m.127.4		4	8.3	odd	2
768.5.b.g.127.1		8	48.29	odd	4
768.5.b.g.127.4		8	48.11	even	4
768.5.b.g.127.5		8	48.35	even	4
768.5.b.g.127.8		8	48.5	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.302776 - 3.98852i) q^{2} +(-15.8167 - 2.41526i) q^{4} -34.8444 q^{5} -43.0318i q^{7} +(-14.4222 + 62.3538i) q^{8} +O(q^{10})\)	\(q+(0.302776 - 3.98852i) q^{2} +(-15.8167 - 2.41526i) q^{4} -34.8444 q^{5} -43.0318i q^{7} +(-14.4222 + 62.3538i) q^{8} +(-10.5500 + 138.978i) q^{10} -65.2790i q^{11} -99.0665 q^{13} +(-171.633 - 13.0290i) q^{14} +(244.333 + 76.4025i) q^{16} +207.689 q^{17} -569.960i q^{19} +(551.122 + 84.1582i) q^{20} +(-260.367 - 19.7649i) q^{22} -371.198i q^{23} +589.133 q^{25} +(-29.9949 + 395.129i) q^{26} +(-103.933 + 680.619i) q^{28} -423.911 q^{29} +1174.18i q^{31} +(378.711 - 951.396i) q^{32} +(62.8831 - 828.372i) q^{34} +1499.42i q^{35} -1448.13 q^{37} +(-2273.30 - 172.570i) q^{38} +(502.533 - 2172.68i) q^{40} +265.822 q^{41} +699.900i q^{43} +(-157.665 + 1032.49i) q^{44} +(-1480.53 - 112.390i) q^{46} -1250.00i q^{47} +549.266 q^{49} +(178.375 - 2349.77i) q^{50} +(1566.90 + 239.271i) q^{52} -787.645 q^{53} +2274.61i q^{55} +(2683.20 + 620.613i) q^{56} +(-128.350 + 1690.78i) q^{58} +3012.53i q^{59} +4519.33 q^{61} +(4683.23 + 355.512i) q^{62} +(-3680.00 - 1798.56i) q^{64} +3451.91 q^{65} -5215.70i q^{67} +(-3284.94 - 501.622i) q^{68} +(5980.46 + 453.987i) q^{70} -4693.16i q^{71} -5404.92 q^{73} +(-438.459 + 5775.91i) q^{74} +(-1376.60 + 9014.86i) q^{76} -2809.07 q^{77} -7453.44i q^{79} +(-8513.64 - 2662.20i) q^{80} +(80.4843 - 1060.24i) q^{82} -8950.92i q^{83} -7236.79 q^{85} +(2791.57 + 211.913i) q^{86} +(4070.39 + 941.466i) q^{88} +616.496 q^{89} +4263.01i q^{91} +(-896.538 + 5871.11i) q^{92} +(-4985.66 - 378.470i) q^{94} +19859.9i q^{95} +13723.1 q^{97} +(166.304 - 2190.76i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5}+O(q^{10}) \) 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5	\( 4 q - 6 q^{2} - 20 q^{4} - 24 q^{5} - 172 q^{10} + 296 q^{13} - 600 q^{14} + 112 q^{16} + 600 q^{17} + 1368 q^{20} - 1128 q^{22} + 972 q^{25} - 1692 q^{26} + 1488 q^{28} - 888 q^{29} + 2784 q^{32} - 484 q^{34} - 4408 q^{37} - 4680 q^{38} + 1664 q^{40} - 552 q^{41} + 3696 q^{44} - 384 q^{46} - 572 q^{49} + 1038 q^{50} + 6008 q^{52} - 5112 q^{53} - 1728 q^{56} - 124 q^{58} + 4232 q^{61} + 7224 q^{62} - 14720 q^{64} + 18192 q^{65} - 5496 q^{68} + 6096 q^{70} + 8840 q^{73} + 4116 q^{74} - 1872 q^{76} - 20928 q^{77} - 25632 q^{80} + 3740 q^{82} - 10256 q^{85} + 19560 q^{86} - 8640 q^{88} + 25080 q^{89} - 18816 q^{92} - 5232 q^{94} + 23048 q^{97} + 5850 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 20 * q^4 - 24 * q^5 - 172 * q^10 + 296 * q^13 - 600 * q^14 + 112 * q^16 + 600 * q^17 + 1368 * q^20 - 1128 * q^22 + 972 * q^25 - 1692 * q^26 + 1488 * q^28 - 888 * q^29 + 2784 * q^32 - 484 * q^34 - 4408 * q^37 - 4680 * q^38 + 1664 * q^40 - 552 * q^41 + 3696 * q^44 - 384 * q^46 - 572 * q^49 + 1038 * q^50 + 6008 * q^52 - 5112 * q^53 - 1728 * q^56 - 124 * q^58 + 4232 * q^61 + 7224 * q^62 - 14720 * q^64 + 18192 * q^65 - 5496 * q^68 + 6096 * q^70 + 8840 * q^73 + 4116 * q^74 - 1872 * q^76 - 20928 * q^77 - 25632 * q^80 + 3740 * q^82 - 10256 * q^85 + 19560 * q^86 - 8640 * q^88 + 25080 * q^89 - 18816 * q^92 - 5232 * q^94 + 23048 * q^97 + 5850 * q^98

Introduction

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