LMFDB - Embedded newform 300.5.c.c.151.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.c (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:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 20x^14 - 108x^13 + 492x^12 - 2160x^11 + 7360x^10 - 39552x^9 + 234752x^8 - 632832x^7 + 1884160x^6 - 8847360x^5 + 32243712x^4 - 113246208x^3 + 335544320x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.14
Root			$3.79586 + 1.26152i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.c.151.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 + 15.8885i) q^{4} +(13.8039 - 15.5388i) q^{6} +74.3539i q^{7} +(-36.5704 + 52.5224i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 + 15.8885i) q^{4} +(13.8039 - 15.5388i) q^{6} +74.3539i q^{7} +(-36.5704 + 52.5224i) q^{8} -27.0000 q^{9} -107.360i q^{11} +(82.5592 - 9.79706i) q^{12} -30.7085 q^{13} +(-197.525 + 222.351i) q^{14} +(-248.890 + 59.9139i) q^{16} -292.805 q^{17} +(-80.7418 - 71.7269i) q^{18} +357.767i q^{19} +386.354 q^{21} +(285.207 - 321.053i) q^{22} -488.885i q^{23} +(272.915 + 190.025i) q^{24} +(-91.8318 - 81.5787i) q^{26} +140.296i q^{27} +(-1181.37 + 140.190i) q^{28} -1035.75 q^{29} -411.471i q^{31} +(-903.455 - 482.021i) q^{32} -557.858 q^{33} +(-875.616 - 777.852i) q^{34} +(-50.9070 - 428.990i) q^{36} +1506.64 q^{37} +(-950.428 + 1069.88i) q^{38} +159.566i q^{39} -2003.19 q^{41} +(1155.37 + 1026.37i) q^{42} +3279.91i q^{43} +(1705.79 - 202.421i) q^{44} +(1298.75 - 1461.98i) q^{46} +1602.96i q^{47} +(311.322 + 1293.27i) q^{48} -3127.50 q^{49} +1521.46i q^{51} +(-57.8991 - 487.912i) q^{52} -4381.56 q^{53} +(-372.704 + 419.547i) q^{54} +(-3905.25 - 2719.15i) q^{56} +1859.01 q^{57} +(-3097.35 - 2751.53i) q^{58} -851.518i q^{59} -5539.08 q^{61} +(1093.09 - 1230.48i) q^{62} -2007.55i q^{63} +(-1421.21 - 3841.53i) q^{64} +(-1668.24 - 1481.98i) q^{66} +4189.05i q^{67} +(-552.068 - 4652.24i) q^{68} -2540.32 q^{69} +6302.56i q^{71} +(987.401 - 1418.11i) q^{72} +7030.68 q^{73} +(4505.52 + 4002.48i) q^{74} +(-5684.40 + 674.551i) q^{76} +7982.62 q^{77} +(-423.895 + 477.172i) q^{78} -7014.54i q^{79} +729.000 q^{81} +(-5990.42 - 5321.58i) q^{82} -9127.59i q^{83} +(728.449 + 6138.59i) q^{84} +(-8713.26 + 9808.37i) q^{86} +5381.92i q^{87} +(5638.80 + 3926.19i) q^{88} +3180.88 q^{89} -2283.29i q^{91} +(7767.67 - 921.767i) q^{92} -2138.07 q^{93} +(-4258.35 + 4793.55i) q^{94} +(-2504.66 + 4694.49i) q^{96} +12299.4 q^{97} +(-9352.59 - 8308.37i) q^{98} +2898.72i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	2.99044	+	2.65655i	0.747610	+	0.664138i
$2$	2.99044	+	2.65655i	0.747610	+	0.664138i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	1.88545	+	15.8885i	0.117840	+	0.993033i
$5$		0			0
$5$		0			0
$6$	13.8039	−	15.5388i	0.383440	−	0.431633i
$7$			74.3539i			1.51743i	0.651425	+	0.758713i	$0.274171\pi$
$7$			74.3539i			1.51743i	−0.651425	+	0.758713i	$0.725829\pi$
$8$	−36.5704	+	52.5224i	−0.571413	+	0.820663i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	107.360i		−	0.887271i	−0.896207	−	0.443636i	$-0.853688\pi$
$11$		−	107.360i		−	0.887271i	0.896207	−	0.443636i	$-0.146312\pi$
$12$	82.5592	−	9.79706i	0.573328	−	0.0680351i
$13$	−30.7085			−0.181707			−0.0908535	−	0.995864i	$-0.528959\pi$
$13$	−30.7085			−0.181707			−0.0908535	+	0.995864i	$0.528959\pi$
$14$	−197.525	+	222.351i	−1.00778	+	1.13444i
$15$		0			0
$16$	−248.890	+	59.9139i	−0.972227	+	0.234039i
$17$	−292.805			−1.01317			−0.506583	−	0.862191i	$-0.669092\pi$
$17$	−292.805			−1.01317			−0.506583	+	0.862191i	$0.669092\pi$
$18$	−80.7418	−	71.7269i	−0.249203	−	0.221379i
$19$			357.767i			0.991046i	0.868595	+	0.495523i	$0.165023\pi$
$19$			357.767i			0.991046i	−0.868595	+	0.495523i	$0.834977\pi$
$20$		0			0
$21$	386.354			0.876086
$22$	285.207	−	321.053i	0.589271	−	0.663333i
$23$		−	488.885i		−	0.924169i	−0.886836	−	0.462084i	$-0.847102\pi$
$23$		−	488.885i		−	0.924169i	0.886836	−	0.462084i	$-0.152898\pi$
$24$	272.915	+	190.025i	0.473810	+	0.329905i
$25$		0			0
$26$	−91.8318	−	81.5787i	−0.135846	−	0.120679i
$27$			140.296i			0.192450i
$28$	−1181.37	+	140.190i	−1.50685	+	0.178814i
$29$	−1035.75			−1.23157			−0.615785	−	0.787914i	$-0.711161\pi$
$29$	−1035.75			−1.23157			−0.615785	+	0.787914i	$0.711161\pi$
$30$		0			0
$31$		−	411.471i		−	0.428169i	−0.976815	−	0.214085i	$-0.931323\pi$
$31$		−	411.471i		−	0.428169i	0.976815	−	0.214085i	$-0.0686769\pi$
$32$	−903.455	−	482.021i	−0.882280	−	0.470724i
$33$	−557.858			−0.512266
$34$	−875.616	−	777.852i	−0.757453	−	0.672883i
$35$		0			0
$36$	−50.9070	−	428.990i	−0.0392801	−	0.331011i
$37$	1506.64			1.10054			0.550272	−	0.834986i	$-0.314524\pi$
$37$	1506.64			1.10054			0.550272	+	0.834986i	$0.314524\pi$
$38$	−950.428	+	1069.88i	−0.658191	+	0.740915i
$39$			159.566i			0.104909i
$40$		0			0
$41$	−2003.19			−1.19167			−0.595833	−	0.803108i	$-0.703178\pi$
$41$	−2003.19			−1.19167			−0.595833	+	0.803108i	$0.703178\pi$
$42$	1155.37	+	1026.37i	0.654971	+	0.581843i
$43$			3279.91i			1.77388i	0.461882	+	0.886942i	$0.347175\pi$
$43$			3279.91i			1.77388i	−0.461882	+	0.886942i	$0.652825\pi$
$44$	1705.79	−	202.421i	0.881089	−	0.104556i
$45$		0			0
$46$	1298.75	−	1461.98i	0.613776	−	0.690918i
$47$			1602.96i			0.725650i	0.931857	+	0.362825i	$0.118188\pi$
$47$			1602.96i			0.725650i	−0.931857	+	0.362825i	$0.881812\pi$
$48$	311.322	+	1293.27i	0.135122	+	0.561316i
$49$	−3127.50			−1.30258
$50$		0			0
$51$			1521.46i			0.584952i
$52$	−57.8991	−	487.912i	−0.0214124	−	0.180441i
$53$	−4381.56			−1.55983			−0.779915	−	0.625885i	$-0.784738\pi$
$53$	−4381.56			−1.55983			−0.779915	+	0.625885i	$0.784738\pi$
$54$	−372.704	+	419.547i	−0.127813	+	0.143878i
$55$		0			0
$56$	−3905.25	−	2719.15i	−1.24530	−	0.867076i
$57$	1859.01			0.572180
$58$	−3097.35	−	2751.53i	−0.920734	−	0.817933i
$59$		−	851.518i		−	0.244619i	−0.992492	−	0.122309i	$-0.960970\pi$
$59$		−	851.518i		−	0.244619i	0.992492	−	0.122309i	$-0.0390300\pi$
$60$		0			0
$61$	−5539.08			−1.48860			−0.744300	−	0.667845i	$-0.767217\pi$
$61$	−5539.08			−1.48860			−0.744300	+	0.667845i	$0.767217\pi$
$62$	1093.09	−	1230.48i	0.284364	−	0.320104i
$63$		−	2007.55i		−	0.505809i
$64$	−1421.21	−	3841.53i	−0.346975	−	0.937874i
$65$		0			0
$66$	−1668.24	−	1481.98i	−0.382975	−	0.340216i
$67$			4189.05i			0.933181i	0.884473	+	0.466590i	$0.154518\pi$
$67$			4189.05i			0.933181i	−0.884473	+	0.466590i	$0.845482\pi$
$68$	−552.068	−	4652.24i	−0.119392	−	1.00611i
$69$	−2540.32			−0.533569
$70$		0			0
$71$			6302.56i			1.25026i	0.780521	+	0.625130i	$0.214954\pi$
$71$			6302.56i			1.25026i	−0.780521	+	0.625130i	$0.785046\pi$
$72$	987.401	−	1418.11i	0.190471	−	0.273554i
$73$	7030.68			1.31933			0.659663	−	0.751562i	$-0.270699\pi$
$73$	7030.68			1.31933			0.659663	+	0.751562i	$0.270699\pi$
$74$	4505.52	+	4002.48i	0.822777	+	0.730913i
$75$		0			0
$76$	−5684.40	+	674.551i	−0.984140	+	0.116785i
$77$	7982.62			1.34637
$78$	−423.895	+	477.172i	−0.0696738	+	0.0784306i
$79$		−	7014.54i		−	1.12395i	−0.827156	−	0.561973i	$-0.810043\pi$
$79$		−	7014.54i		−	1.12395i	0.827156	−	0.561973i	$-0.189957\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−5990.42	−	5321.58i	−0.890901	−	0.791431i
$83$		−	9127.59i		−	1.32495i	−0.749083	−	0.662476i	$-0.769506\pi$
$83$		−	9127.59i		−	1.32495i	0.749083	−	0.662476i	$-0.230494\pi$
$84$	728.449	+	6138.59i	0.103238	+	0.869982i
$85$		0			0
$86$	−8713.26	+	9808.37i	−1.17810	+	1.32617i
$87$			5381.92i			0.711048i
$88$	5638.80	+	3926.19i	0.728151	+	0.506998i
$89$	3180.88			0.401575			0.200788	−	0.979635i	$-0.435650\pi$
$89$	3180.88			0.401575			0.200788	+	0.979635i	$0.435650\pi$
$90$		0			0
$91$		−	2283.29i		−	0.275727i
$92$	7767.67	−	921.767i	0.917730	−	0.108904i
$93$	−2138.07			−0.247204
$94$	−4258.35	+	4793.55i	−0.481932	+	0.542503i
$95$		0			0
$96$	−2504.66	+	4694.49i	−0.271773	+	0.509385i
$97$	12299.4			1.30720			0.653600	−	0.756840i	$-0.273258\pi$
$97$	12299.4			1.30720			0.653600	+	0.756840i	$0.273258\pi$
$98$	−9352.59	−	8308.37i	−0.973822	−	0.865094i
$99$			2898.72i			0.295757i
$100$		0			0
$101$	8454.27			0.828769			0.414385	−	0.910102i	$-0.363997\pi$
$101$	8454.27			0.828769			0.414385	+	0.910102i	$0.363997\pi$
$102$	−4041.84	+	4549.83i	−0.388489	+	0.437316i
$103$			12655.1i			1.19287i	0.802662	+	0.596435i	$0.203416\pi$
$103$			12655.1i			1.19287i	−0.802662	+	0.596435i	$0.796584\pi$
$104$	1123.02	−	1612.88i	0.103830	−	0.149120i
$105$		0			0
$106$	−13102.8	−	11639.9i	−1.16614	−	1.03594i
$107$			6961.91i			0.608080i	0.952659	+	0.304040i	$0.0983357\pi$
$107$			6961.91i			0.608080i	−0.952659	+	0.304040i	$0.901664\pi$
$108$	−2229.10	+	264.521i	−0.191109	+	0.0226784i
$109$	−10686.8			−0.899489			−0.449744	−	0.893157i	$-0.648485\pi$
$109$	−10686.8			−0.899489			−0.449744	+	0.893157i	$0.648485\pi$
$110$		0			0
$111$		−	7828.75i		−	0.635399i
$112$	−4454.83	−	18505.9i	−0.355136	−	1.47528i
$113$	18780.7			1.47080			0.735402	−	0.677632i	$-0.236994\pi$
$113$	18780.7			1.47080			0.735402	+	0.677632i	$0.236994\pi$
$114$	5559.27	+	4938.57i	0.427768	+	0.380007i
$115$		0			0
$116$	−1952.85	−	16456.5i	−0.145129	−	1.22299i
$117$	829.129			0.0605690
$118$	2262.10	−	2546.41i	0.162461	−	0.182879i
$119$		−	21771.2i		−	1.53740i
$120$		0			0
$121$	3114.87			0.212750
$122$	−16564.3	−	14714.9i	−1.11289	−	0.988637i
$123$			10408.9i			0.688009i
$124$	6537.66	−	775.806i	0.425186	−	0.0504556i
$125$		0			0
$126$	5333.18	−	6003.47i	0.335927	−	0.378147i
$127$		−	4370.53i		−	0.270974i	−0.990779	−	0.135487i	$-0.956740\pi$
$127$		−	4370.53i		−	0.270974i	0.990779	−	0.135487i	$-0.0432598\pi$
$128$	5955.19	−	15263.4i	0.363476	−	0.931604i
$129$	17042.9			1.02415
$130$		0			0
$131$			20280.0i			1.18175i	0.806763	+	0.590875i	$0.201217\pi$
$131$			20280.0i			1.18175i	−0.806763	+	0.590875i	$0.798783\pi$
$132$	−1051.81	−	8863.54i	−0.0603656	−	0.508697i
$133$	−26601.4			−1.50384
$134$	−11128.4	+	12527.1i	−0.619761	+	0.697655i
$135$		0			0
$136$	10708.0	−	15378.8i	0.578936	−	0.831468i
$137$	25989.4			1.38470			0.692349	−	0.721563i	$-0.256576\pi$
$137$	25989.4			1.38470			0.692349	+	0.721563i	$0.256576\pi$
$138$	−7596.68	−	6748.50i	−0.398901	−	0.354364i
$139$		−	21049.3i		−	1.08945i	−0.838614	−	0.544726i	$-0.816634\pi$
$139$		−	21049.3i		−	1.08945i	0.838614	−	0.544726i	$-0.183366\pi$
$140$		0			0
$141$	8329.22			0.418954
$142$	−16743.1	+	18847.4i	−0.830346	+	0.934707i
$143$			3296.86i			0.161223i
$144$	6720.04	−	1617.67i	0.324076	−	0.0780128i
$145$		0			0
$146$	21024.8	+	18677.4i	0.986340	+	0.876214i
$147$			16251.0i			0.752046i
$148$	2840.69	+	23938.3i	0.129688	+	1.09288i
$149$	−19502.4			−0.878447			−0.439223	−	0.898378i	$-0.644746\pi$
$149$	−19502.4			−0.878447			−0.439223	+	0.898378i	$0.644746\pi$
$150$		0			0
$151$			33284.1i			1.45977i	0.683572	+	0.729883i	$0.260426\pi$
$151$			33284.1i			1.45977i	−0.683572	+	0.729883i	$0.739574\pi$
$152$	−18790.8	−	13083.7i	−0.813314	−	0.566296i
$153$	7905.74			0.337722
$154$	23871.5	+	21206.3i	1.00656	+	0.894175i
$155$		0			0
$156$	−2535.27	+	300.853i	−0.104178	+	0.0123625i
$157$	−10857.6			−0.440487			−0.220243	−	0.975445i	$-0.570685\pi$
$157$	−10857.6			−0.440487			−0.220243	+	0.975445i	$0.570685\pi$
$158$	18634.5	−	20976.6i	0.746455	−	0.840272i
$159$			22767.3i			0.900568i
$160$		0			0
$161$	36350.5			1.40236
$162$	2180.03	+	1936.63i	0.0830677	+	0.0737932i
$163$			28923.6i			1.08862i	0.838883	+	0.544311i	$0.183209\pi$
$163$			28923.6i			1.08862i	−0.838883	+	0.544311i	$0.816791\pi$
$164$	−3776.91	−	31827.7i	−0.140426	−	1.18336i
$165$		0			0
$166$	24247.9	−	27295.5i	0.879951	−	0.990546i
$167$			31156.8i			1.11717i	0.829447	+	0.558585i	$0.188656\pi$
$167$			31156.8i			1.11717i	−0.829447	+	0.558585i	$0.811344\pi$
$168$	−14129.1	+	20292.3i	−0.500607	+	0.718972i
$169$	−27618.0			−0.966983
$170$		0			0
$171$		−	9659.72i		−	0.330349i
$172$	−52112.9	+	6184.09i	−1.76152	+	0.209035i
$173$	11118.3			0.371489			0.185744	−	0.982598i	$-0.440530\pi$
$173$	11118.3			0.371489			0.185744	+	0.982598i	$0.440530\pi$
$174$	−14297.4	+	16094.3i	−0.472234	+	0.531586i
$175$		0			0
$176$	6432.34	+	26720.8i	0.207656	+	0.862629i
$177$	−4424.62			−0.141231
$178$	9512.22	+	8450.18i	0.300222	+	0.266702i
$179$		−	8347.18i		−	0.260515i	−0.991480	−	0.130258i	$-0.958420\pi$
$179$		−	8347.18i		−	0.260515i	0.991480	−	0.130258i	$-0.0415805\pi$
$180$		0			0
$181$	54703.3			1.66977			0.834885	−	0.550425i	$-0.185534\pi$
$181$	54703.3			1.66977			0.834885	+	0.550425i	$0.185534\pi$
$182$	6065.69	−	6828.05i	0.183121	−	0.206136i
$183$			28781.9i			0.859444i
$184$	25677.4	+	17878.7i	0.758431	+	0.528082i
$185$		0			0
$186$	−6393.75	−	5679.88i	−0.184812	−	0.164178i
$187$			31435.5i			0.898953i
$188$	−25468.7	+	3022.29i	−0.720594	+	0.0855108i
$189$	−10431.6			−0.292029
$190$		0			0
$191$		−	170.614i		−	0.00467678i	−0.999997	−	0.00233839i	$-0.999256\pi$
$191$		−	170.614i		−	0.00467678i	0.999997	−	0.00233839i	$-0.000744333\pi$
$192$	−19961.2	+	7384.83i	−0.541482	+	0.200326i
$193$	38429.3			1.03169			0.515843	−	0.856683i	$-0.327479\pi$
$193$	38429.3			1.03169			0.515843	+	0.856683i	$0.327479\pi$
$194$	36780.7	+	32674.1i	0.977276	+	0.868162i
$195$		0			0
$196$	−5896.73	−	49691.3i	−0.153497	−	1.29351i
$197$	−47014.6			−1.21143			−0.605717	−	0.795680i	$-0.707114\pi$
$197$	−47014.6			−1.21143			−0.605717	+	0.795680i	$0.707114\pi$
$198$	−7700.59	+	8668.43i	−0.196424	+	0.221111i
$199$			49175.8i			1.24178i	0.783897	+	0.620891i	$0.213229\pi$
$199$			49175.8i			1.24178i	−0.783897	+	0.620891i	$0.786771\pi$
$200$		0			0
$201$	21766.9			0.538772
$202$	25282.0	+	22459.2i	0.619596	+	0.550417i
$203$		−	77012.1i		−	1.86882i
$204$	−24173.7	+	2868.63i	−0.580876	+	0.0689309i
$205$		0			0
$206$	−33619.1	+	37844.4i	−0.792230	+	0.891800i
$207$			13199.9i			0.308056i
$208$	7643.04	−	1839.86i	0.176660	−	0.0425264i
$209$	38409.8			0.879326
$210$		0			0
$211$			4500.34i			0.101084i	0.998722	+	0.0505418i	$0.0160948\pi$
$211$			4500.34i			0.101084i	−0.998722	+	0.0505418i	$0.983905\pi$
$212$	−8261.20	−	69616.6i	−0.183811	−	1.54896i
$213$	32749.1			0.721838
$214$	−18494.7	+	20819.2i	−0.403849	+	0.454607i
$215$		0			0
$216$	−7368.69	−	5130.69i	−0.157937	−	0.109968i
$217$	30594.4			0.649715
$218$	−31958.3	−	28390.1i	−0.672466	−	0.597385i
$219$		−	36532.5i		−	0.761713i
$220$		0			0
$221$	8991.60			0.184099
$222$	20797.5	−	23411.4i	0.421993	−	0.475030i
$223$		−	480.278i		−	0.00965790i	−0.999988	−	0.00482895i	$-0.998463\pi$
$223$		−	480.278i		−	0.00965790i	0.999988	−	0.00482895i	$-0.00153711\pi$
$224$	35840.2	−	67175.4i	0.714289	−	1.33880i
$225$		0			0
$226$	56162.5	+	49891.9i	1.09959	+	0.976817i
$227$		−	38994.8i		−	0.756754i	−0.925652	−	0.378377i	$-0.876482\pi$
$227$		−	38994.8i		−	0.756754i	0.925652	−	0.378377i	$-0.123518\pi$
$228$	3505.07	+	29537.0i	0.0674259	+	0.568194i
$229$	27569.4			0.525723			0.262861	−	0.964834i	$-0.415334\pi$
$229$	27569.4			0.525723			0.262861	+	0.964834i	$0.415334\pi$
$230$		0			0
$231$		−	41478.9i		−	0.777326i
$232$	37877.8	−	54400.1i	0.703735	−	1.01070i
$233$	42015.1			0.773915			0.386957	−	0.922098i	$-0.373526\pi$
$233$	42015.1			0.773915			0.386957	+	0.922098i	$0.373526\pi$
$234$	2479.46	+	2202.63i	0.0452820	+	0.0402262i
$235$		0			0
$236$	13529.4	−	1605.49i	0.242914	−	0.0288260i
$237$	−36448.6			−0.648910
$238$	57836.3	−	65105.4i	1.02105	−	1.14938i
$239$		−	93158.6i		−	1.63090i	−0.578828	−	0.815450i	$-0.696490\pi$
$239$		−	93158.6i		−	1.63090i	0.578828	−	0.815450i	$-0.303510\pi$
$240$		0			0
$241$	−108882.			−1.87466			−0.937328	−	0.348447i	$-0.886709\pi$
$241$	−108882.			−1.87466			−0.937328	+	0.348447i	$0.886709\pi$
$242$	9314.82	+	8274.81i	0.159054	+	0.141295i
$243$		−	3788.00i		−	0.0641500i
$244$	−10443.6	−	88007.8i	−0.175417	−	1.47823i
$245$		0			0
$246$	−27651.8	+	31127.1i	−0.456933	+	0.514362i
$247$		−	10986.5i		−	0.180080i
$248$	21611.4	+	15047.7i	0.351383	+	0.244661i
$249$	−47428.3			−0.764961
$250$		0			0
$251$			31606.9i			0.501689i	0.968027	+	0.250845i	$0.0807083\pi$
$251$			31606.9i			0.501689i	−0.968027	+	0.250845i	$0.919292\pi$
$252$	31897.1	−	3785.13i	0.502284	−	0.0596047i
$253$	−52486.6			−0.819989
$254$	11610.6	−	13069.8i	0.179964	−	0.202582i
$255$		0			0
$256$	58356.7	−	29823.9i	0.890452	−	0.455077i
$257$	−20019.5			−0.303101			−0.151550	−	0.988450i	$-0.548427\pi$
$257$	−20019.5			−0.303101			−0.151550	+	0.988450i	$0.548427\pi$
$258$	50965.8	+	45275.4i	0.765666	+	0.680179i
$259$			112025.i			1.66999i
$260$		0			0
$261$	27965.3			0.410523
$262$	−53875.0	+	60646.2i	−0.784846	+	0.883488i
$263$		−	62700.2i		−	0.906478i	−0.891389	−	0.453239i	$-0.850268\pi$
$263$		−	62700.2i		−	0.906478i	0.891389	−	0.453239i	$-0.149732\pi$
$264$	20401.1	−	29300.1i	0.292715	−	0.420398i
$265$		0			0
$266$	−79549.8	−	70668.0i	−1.12428	−	0.998757i
$267$		−	16528.3i		−	0.231850i
$268$	−66557.8	+	7898.22i	−0.926679	+	0.109966i
$269$	33804.6			0.467166			0.233583	−	0.972337i	$-0.424955\pi$
$269$	33804.6			0.467166			0.233583	+	0.972337i	$0.424955\pi$
$270$		0			0
$271$			56181.7i			0.764991i	0.923957	+	0.382496i	$0.124935\pi$
$271$			56181.7i			0.764991i	−0.923957	+	0.382496i	$0.875065\pi$
$272$	72876.3	−	17543.1i	0.985028	−	0.237120i
$273$	−11864.3			−0.159191
$274$	77719.7	+	69042.2i	1.03521	+	0.919631i
$275$		0			0
$276$	−4789.64	−	40362.0i	−0.0628760	−	0.529852i
$277$	121560.			1.58428			0.792141	−	0.610338i	$-0.208966\pi$
$277$	121560.			1.58428			0.792141	+	0.610338i	$0.208966\pi$
$278$	55918.6	−	62946.7i	0.723547	−	0.814485i
$279$			11109.7i			0.142723i
$280$		0			0
$281$	−51790.9			−0.655905			−0.327952	−	0.944694i	$-0.606359\pi$
$281$	−51790.9			−0.655905			−0.327952	+	0.944694i	$0.606359\pi$
$282$	24908.0	+	22127.0i	0.313214	+	0.278243i
$283$			126660.i			1.58149i	0.612149	+	0.790743i	$0.290305\pi$
$283$			126660.i			1.58149i	−0.612149	+	0.790743i	$0.709695\pi$
$284$	−100138.	+	11883.1i	−1.24155	+	0.147331i
$285$		0			0
$286$	−8758.28	+	9859.05i	−0.107075	+	0.120532i
$287$		−	148945.i		−	1.80826i
$288$	24393.3	+	13014.6i	0.294093	+	0.156908i
$289$	2213.80			0.0265059
$290$		0			0
$291$		−	63909.8i		−	0.754712i
$292$	13256.0	+	111707.i	0.155470	+	1.31013i
$293$	−5958.17			−0.0694029			−0.0347014	−	0.999398i	$-0.511048\pi$
$293$	−5958.17			−0.0694029			−0.0347014	+	0.999398i	$0.511048\pi$
$294$	−43171.5	+	48597.5i	−0.499462	+	0.562237i
$295$		0			0
$296$	−55098.6	+	79132.6i	−0.628864	+	0.903175i
$297$	15062.2			0.170755
$298$	−58320.7	−	51809.2i	−0.656735	−	0.583410i
$299$			15012.9i			0.167928i
$300$		0			0
$301$	−243874.			−2.69174
$302$	−88421.1	+	99534.1i	−0.969487	+	1.09134i
$303$		−	43929.7i		−	0.478490i
$304$	−21435.2	−	89044.8i	−0.231943	−	0.963522i
$305$		0			0
$306$	23641.6	+	21002.0i	0.252484	+	0.224294i
$307$		−	78071.0i		−	0.828348i	−0.910198	−	0.414174i	$-0.864070\pi$
$307$		−	78071.0i		−	0.828348i	0.910198	−	0.414174i	$-0.135930\pi$
$308$	15050.8	+	126832.i	0.158656	+	1.33699i
$309$	65758.1			0.688703
$310$		0			0
$311$		−	36755.5i		−	0.380016i	−0.981783	−	0.190008i	$-0.939149\pi$
$311$		−	36755.5i		−	0.380016i	0.981783	−	0.190008i	$-0.0608514\pi$
$312$	−8380.79	−	5835.39i	−0.0860946	−	0.0599461i
$313$	−169020.			−1.72524			−0.862619	−	0.505854i	$-0.831177\pi$
$313$	−169020.			−1.72524			−0.862619	+	0.505854i	$0.831177\pi$
$314$	−32468.8	−	28843.7i	−0.329312	−	0.292544i
$315$		0			0
$316$	111451.	−	13225.5i	1.11611	−	0.132446i
$317$	−129820.			−1.29188			−0.645939	−	0.763389i	$-0.723534\pi$
$317$	−129820.			−1.29188			−0.645939	+	0.763389i	$0.723534\pi$
$318$	−60482.5	+	68084.1i	−0.598102	+	0.673274i
$319$			111198.i			1.09274i
$320$		0			0
$321$	36175.1			0.351075
$322$	108704.	+	96567.1i	1.04842	+	0.931360i
$323$		−	104756.i		−	1.00409i
$324$	1374.49	+	11582.7i	0.0130934	+	0.110337i
$325$		0			0
$326$	−76837.1	+	86494.3i	−0.722996	+	0.813865i
$327$			55530.4i			0.519320i
$328$	73257.5	−	105212.i	0.680933	−	0.977956i
$329$	−119186.			−1.10112
$330$		0			0
$331$		−	58912.8i		−	0.537717i	−0.963180	−	0.268858i	$-0.913354\pi$
$331$		−	58912.8i		−	0.537717i	0.963180	−	0.268858i	$-0.0866463\pi$
$332$	145024.	−	17209.6i	1.31572	−	0.156133i
$333$	−40679.4			−0.366848
$334$	−82769.6	+	93172.4i	−0.741956	+	0.835208i
$335$		0			0
$336$	−96159.7	+	23148.0i	−0.851755	+	0.205038i
$337$	46849.1			0.412517			0.206258	−	0.978498i	$-0.433871\pi$
$337$	46849.1			0.412517			0.206258	+	0.978498i	$0.433871\pi$
$338$	−82589.9	−	73368.7i	−0.722925	−	0.642210i
$339$		−	97587.3i		−	0.849169i
$340$		0			0
$341$	−44175.4			−0.379902
$342$	25661.6	−	28886.8i	0.219397	−	0.246972i
$343$		−	54017.9i		−	0.459145i
$344$	−172269.	−	119948.i	−1.45576	−	1.01362i
$345$		0			0
$346$	33248.6	+	29536.3i	0.277729	+	0.246720i
$347$			170481.i			1.41585i	0.706290	+	0.707923i	$0.250368\pi$
$347$			170481.i			1.41585i	−0.706290	+	0.707923i	$0.749632\pi$
$348$	−85510.7	+	10147.3i	−0.706093	+	0.0837901i
$349$	93820.0			0.770273			0.385136	−	0.922860i	$-0.374154\pi$
$349$	93820.0			0.770273			0.385136	+	0.922860i	$0.374154\pi$
$350$		0			0
$351$		−	4308.28i		−	0.0349695i
$352$	−51749.7	+	96994.8i	−0.417660	+	0.782822i
$353$	−150254.			−1.20581			−0.602903	−	0.797814i	$-0.705989\pi$
$353$	−150254.			−1.20581			−0.602903	+	0.797814i	$0.705989\pi$
$354$	−13231.5	−	11754.2i	−0.105585	−	0.0937968i
$355$		0			0
$356$	5997.37	+	50539.5i	0.0473218	+	0.398778i
$357$	−113126.			−0.887621
$358$	22174.7	−	24961.7i	0.173018	−	0.194764i
$359$			6723.72i			0.0521700i	0.999660	+	0.0260850i	$0.00830406\pi$
$359$			6723.72i			0.0521700i	−0.999660	+	0.0260850i	$0.991696\pi$
$360$		0			0
$361$	2323.47			0.0178288
$362$	163587.	+	145322.i	1.24834	+	1.10896i
$363$		−	16185.3i		−	0.122831i
$364$	36278.2	−	4305.03i	0.273806	−	0.0324917i
$365$		0			0
$366$	−76460.7	+	86070.6i	−0.570790	+	0.642529i
$367$		−	119927.i		−	0.890401i	−0.895431	−	0.445200i	$-0.853132\pi$
$367$		−	119927.i		−	0.890401i	0.895431	−	0.445200i	$-0.146868\pi$
$368$	29291.0	+	121679.i	0.216291	+	0.898502i
$369$	54086.1			0.397222
$370$		0			0
$371$		−	325786.i		−	2.36693i
$372$	−4031.20	−	33970.7i	−0.0291306	−	0.245481i
$373$	−49886.2			−0.358561			−0.179280	−	0.983798i	$-0.557377\pi$
$373$	−49886.2			−0.358561			−0.179280	+	0.983798i	$0.557377\pi$
$374$	−83510.1	+	94005.9i	−0.597029	+	0.672066i
$375$		0			0
$376$	−84191.4	−	58620.9i	−0.595514	−	0.414645i
$377$	31806.3			0.223785
$378$	−31194.9	−	27712.0i	−0.218324	−	0.193948i
$379$		−	42377.4i		−	0.295023i	−0.989060	−	0.147512i	$-0.952874\pi$
$379$		−	42377.4i		−	0.295023i	0.989060	−	0.147512i	$-0.0471264\pi$
$380$		0			0
$381$	−22710.0			−0.156447
$382$	453.244	−	510.209i	0.00310603	−	0.00349641i
$383$			249132.i			1.69837i	0.528098	+	0.849184i	$0.322905\pi$
$383$			249132.i			1.69837i	−0.528098	+	0.849184i	$0.677095\pi$
$384$	−79310.9	−	30944.1i	−0.537862	−	0.209853i
$385$		0			0
$386$	114920.	+	102089.i	0.771299	+	0.685183i
$387$		−	88557.6i		−	0.591294i
$388$	23189.9	+	195420.i	0.154041	+	1.29809i
$389$	187712.			1.24049			0.620244	−	0.784409i	$-0.287034\pi$
$389$	187712.			1.24049			0.620244	+	0.784409i	$0.287034\pi$
$390$		0			0
$391$			143148.i			0.936337i
$392$	114374.	−	164264.i	0.744311	−	1.06898i
$393$	105378.			0.682284
$394$	−140594.	−	124897.i	−0.905680	−	0.804560i
$395$		0			0
$396$	−46056.3	+	5465.37i	−0.293696	+	0.0348521i
$397$	−239081.			−1.51693			−0.758463	−	0.651716i	$-0.774049\pi$
$397$	−239081.			−1.51693			−0.758463	+	0.651716i	$0.774049\pi$
$398$	−130638.	+	147057.i	−0.824715	+	0.928368i
$399$			138225.i			0.868241i
$400$		0			0
$401$	226859.			1.41080			0.705402	−	0.708807i	$-0.250766\pi$
$401$	226859.			1.41080			0.705402	+	0.708807i	$0.250766\pi$
$402$	65092.7	+	57825.0i	0.402791	+	0.357819i
$403$			12635.6i			0.0778014i
$404$	15940.1	+	134326.i	0.0976624	+	0.822995i
$405$		0			0
$406$	204587.	−	230300.i	1.24115	−	1.39715i
$407$		−	161753.i		−	0.976480i
$408$	−79910.8	−	55640.4i	−0.480048	−	0.334249i
$409$	−165859.			−0.991497			−0.495748	−	0.868466i	$-0.665106\pi$
$409$	−165859.			−0.991497			−0.495748	+	0.868466i	$0.665106\pi$
$410$		0			0
$411$		−	135045.i		−	0.799456i
$412$	−201072.	+	23860.6i	−1.18456	+	0.140568i
$413$	63313.7			0.371191
$414$	−35066.3	+	39473.5i	−0.204592	+	0.230306i
$415$		0			0
$416$	27743.7	+	14802.1i	0.160317	+	0.0855338i
$417$	−109375.			−0.628996
$418$	114862.	+	102038.i	0.657393	+	0.583994i
$419$			154230.i			0.878498i	0.898365	+	0.439249i	$0.144755\pi$
$419$			154230.i			0.878498i	−0.898365	+	0.439249i	$0.855245\pi$
$420$		0			0
$421$	−247852.			−1.39839			−0.699196	−	0.714930i	$-0.746459\pi$
$421$	−247852.			−1.39839			−0.699196	+	0.714930i	$0.746459\pi$
$422$	−11955.4	+	13458.0i	−0.0671335	+	0.0755711i
$423$		−	43279.9i		−	0.241883i
$424$	160236.	−	230130.i	0.891306	−	1.28009i
$425$		0			0
$426$	97934.1	+	86999.7i	0.539653	+	0.479400i
$427$		−	411852.i		−	2.25884i
$428$	−110614.	+	13126.3i	−0.603843	+	0.0716564i
$429$	17131.0			0.0930824
$430$		0			0
$431$		−	132150.i		−	0.711396i	−0.934601	−	0.355698i	$-0.884243\pi$
$431$		−	132150.i		−	0.711396i	0.934601	−	0.355698i	$-0.115757\pi$
$432$	−8405.68	−	34918.3i	−0.0450407	−	0.187105i
$433$	−341105.			−1.81933			−0.909666	−	0.415341i	$-0.863662\pi$
$433$	−341105.			−1.81933			−0.909666	+	0.415341i	$0.863662\pi$
$434$	91490.8	+	81275.8i	0.485733	+	0.431501i
$435$		0			0
$436$	−20149.4	−	169798.i	−0.105996	−	0.893222i
$437$	174907.			0.915893
$438$	97050.6	−	109248.i	0.505883	−	0.569464i
$439$		−	1536.95i		−	0.00797498i	−0.999992	−	0.00398749i	$-0.998731\pi$
$439$		−	1536.95i		−	0.00797498i	0.999992	−	0.00398749i	$-0.00126926\pi$
$440$		0			0
$441$	84442.4			0.434194
$442$	26888.8	+	23886.7i	0.137634	+	0.122267i
$443$		−	259829.i		−	1.32398i	−0.749513	−	0.661989i	$-0.769712\pi$
$443$		−	259829.i		−	1.32398i	0.749513	−	0.661989i	$-0.230288\pi$
$444$	124387.	−	14760.7i	0.630972	−	0.0748756i
$445$		0			0
$446$	1275.88	−	1436.24i	0.00641418	−	0.00722034i
$447$			101337.i			0.507171i
$448$	285633.	−	105673.i	1.42315	−	0.526510i
$449$	123490.			0.612547			0.306274	−	0.951944i	$-0.400918\pi$
$449$	123490.			0.612547			0.306274	+	0.951944i	$0.400918\pi$
$450$		0			0
$451$			215062.i			1.05733i
$452$	35409.9	+	298397.i	0.173320	+	1.46056i
$453$	172949.			0.842796
$454$	103592.	−	116611.i	0.502589	−	0.565756i
$455$		0			0
$456$	−67984.9	+	97639.9i	−0.326951	+	0.469567i
$457$	24937.6			0.119405			0.0597024	−	0.998216i	$-0.480985\pi$
$457$	24937.6			0.119405			0.0597024	+	0.998216i	$0.480985\pi$
$458$	82444.7	+	73239.7i	0.393036	+	0.349153i
$459$		−	41079.4i		−	0.194984i
$460$		0			0
$461$	−142842.			−0.672130			−0.336065	−	0.941839i	$-0.609096\pi$
$461$	−142842.			−0.672130			−0.336065	+	0.941839i	$0.609096\pi$
$462$	110191.	−	124040.i	0.516252	−	0.581137i
$463$		−	58133.2i		−	0.271183i	−0.990765	−	0.135591i	$-0.956707\pi$
$463$		−	58133.2i		−	0.271183i	0.990765	−	0.135591i	$-0.0432935\pi$
$464$	257788.	−	62055.8i	1.19737	−	0.288235i
$465$		0			0
$466$	125643.	+	111615.i	0.578586	+	0.513986i
$467$			305454.i			1.40059i	0.713852	+	0.700296i	$0.246949\pi$
$467$			305454.i			1.40059i	−0.713852	+	0.700296i	$0.753051\pi$
$468$	1563.28	+	13173.6i	0.00713747	+	0.0601470i
$469$	−311472.			−1.41603
$470$		0			0
$471$			56417.5i			0.254315i
$472$	44723.8	+	31140.4i	0.200750	+	0.139778i
$473$	352131.			1.57392
$474$	−108997.	−	96827.7i	−0.485131	−	0.430966i
$475$		0			0
$476$	345912.	−	41048.4i	1.52669	−	0.181168i
$477$	118302.			0.519943
$478$	247481.	−	278585.i	1.08314	−	1.21928i
$479$			214385.i			0.934378i	0.884157	+	0.467189i	$0.154733\pi$
$479$			214385.i			0.934378i	−0.884157	+	0.467189i	$0.845267\pi$
$480$		0			0
$481$	−46266.7			−0.199976
$482$	−325605.	−	289251.i	−1.40151	−	1.24503i
$483$		−	188883.i		−	0.809652i
$484$	5872.91	+	49490.6i	0.0250705	+	0.211267i
$485$		0			0
$486$	10063.0	−	11327.8i	0.0426045	−	0.0479592i
$487$		−	132928.i		−	0.560480i	−0.959930	−	0.280240i	$-0.909586\pi$
$487$		−	132928.i		−	0.560480i	0.959930	−	0.280240i	$-0.0904140\pi$
$488$	202566.	−	290926.i	0.850605	−	1.22164i
$489$	150292.			0.628517
$490$		0			0
$491$			203534.i			0.844256i	0.906536	+	0.422128i	$0.138717\pi$
$491$			203534.i			0.844256i	−0.906536	+	0.422128i	$0.861283\pi$
$492$	−165382.	+	19625.4i	−0.683215	+	0.0810752i
$493$	303273.			1.24779
$494$	29186.2	−	32854.4i	0.119598	−	0.134629i
$495$		0			0
$496$	24652.8	+	102411.i	0.100208	+	0.416278i
$497$	−468620.			−1.89718
$498$	−141832.	−	125996.i	−0.571892	−	0.508040i
$499$		−	282205.i		−	1.13335i	−0.823942	−	0.566674i	$-0.808230\pi$
$499$		−	282205.i		−	1.13335i	0.823942	−	0.566674i	$-0.191770\pi$
$500$		0			0
$501$	161895.			0.644999
$502$	−83965.5	+	94518.6i	−0.333191	+	0.375068i
$503$			307654.i			1.21598i	0.793944	+	0.607991i	$0.208024\pi$
$503$			307654.i			1.21598i	−0.793944	+	0.607991i	$0.791976\pi$
$504$	105442.	+	73417.1i	0.415098	+	0.289025i
$505$		0			0
$506$	−156958.	−	139434.i	−0.613031	−	0.544586i
$507$			143507.i			0.558288i
$508$	69441.3	−	8240.40i	0.269086	−	0.0319316i
$509$	164324.			0.634256			0.317128	−	0.948383i	$-0.397282\pi$
$509$	164324.			0.634256			0.317128	+	0.948383i	$0.397282\pi$
$510$		0			0
$511$			522759.i			2.00198i
$512$	253741.	+	65840.9i	0.967945	+	0.251163i
$513$	−50193.4			−0.190727
$514$	−59867.1	−	53182.9i	−0.226601	−	0.201301i
$515$		0			0
$516$	32133.5	+	270787.i	0.120686	+	1.01702i
$517$	172094.			0.643848
$518$	−297600.	+	335003.i	−1.10911	+	1.24850i
$519$		−	57772.3i		−	0.214479i
$520$		0			0
$521$	317062.			1.16807			0.584034	−	0.811729i	$-0.301473\pi$
$521$	317062.			1.16807			0.584034	+	0.811729i	$0.301473\pi$
$522$	83628.4	+	74291.2i	0.306911	+	0.272644i
$523$		−	55332.3i		−	0.202290i	−0.994872	−	0.101145i	$-0.967749\pi$
$523$		−	55332.3i		−	0.202290i	0.994872	−	0.101145i	$-0.0322507\pi$
$524$	−322220.	+	38236.9i	−1.17352	+	0.139258i
$525$		0			0
$526$	166566.	−	187501.i	0.602027	−	0.677692i
$527$			120481.i			0.433807i
$528$	138845.	−	33423.4i	0.498039	−	0.119890i
$529$	40832.1			0.145912
$530$		0			0
$531$			22991.0i			0.0815396i
$532$	−50155.5	−	422657.i	−0.177213	−	1.49336i
$533$	61514.9			0.216534
$534$	43908.4	−	49427.0i	0.153980	−	0.173333i
$535$		0			0
$536$	−220019.	−	153195.i	−0.765827	−	0.533231i
$537$	−43373.2			−0.150409
$538$	101091.	+	89803.7i	0.349258	+	0.310263i
$539$			335768.i			1.15574i
$540$		0			0
$541$	−86217.1			−0.294577			−0.147289	−	0.989094i	$-0.547055\pi$
$541$	−86217.1			−0.294577			−0.147289	+	0.989094i	$0.547055\pi$
$542$	−149250.	+	168008.i	−0.508060	+	0.571915i
$543$		−	284247.i		−	0.964042i
$544$	264536.	+	141138.i	0.893897	+	0.476922i
$545$		0			0
$546$	−35479.6	−	31518.3i	−0.119013	−	0.105725i
$547$			288324.i			0.963620i	0.876276	+	0.481810i	$0.160020\pi$
$547$			288324.i			0.963620i	−0.876276	+	0.481810i	$0.839980\pi$
$548$	49001.6	+	412933.i	0.163173	+	1.37505i
$549$	149555.			0.496200
$550$		0			0
$551$		−	370558.i		−	1.22054i
$552$	92900.6	−	133424.i	0.304888	−	0.437880i
$553$	521558.			1.70550
$554$	363519.	+	322932.i	1.18442	+	1.05218i
$555$		0			0
$556$	334442.	−	39687.3i	1.08186	−	0.128381i
$557$	−465454.			−1.50026			−0.750129	−	0.661291i	$-0.770009\pi$
$557$	−465454.			−1.50026			−0.750129	+	0.661291i	$0.770009\pi$
$558$	−29513.5	+	33222.9i	−0.0947879	+	0.106701i
$559$		−	100721.i		−	0.322327i
$560$		0			0
$561$	163344.			0.519011
$562$	−154877.	−	137585.i	−0.490361	−	0.435611i
$563$			276410.i			0.872040i	0.899937	+	0.436020i	$0.143612\pi$
$563$			276410.i			0.872040i	−0.899937	+	0.436020i	$0.856388\pi$
$564$	15704.3	+	132339.i	0.0493697	+	0.416035i
$565$		0			0
$566$	−336478.	+	378768.i	−1.05033	+	1.18233i
$567$			54204.0i			0.168603i
$568$	−331026.	−	230487.i	−1.02604	−	0.714414i
$569$	−178268.			−0.550615			−0.275307	−	0.961356i	$-0.588780\pi$
$569$	−178268.			−0.550615			−0.275307	+	0.961356i	$0.588780\pi$
$570$		0			0
$571$		−	430413.i		−	1.32012i	−0.751213	−	0.660060i	$-0.770531\pi$
$571$		−	430413.i		−	1.32012i	0.751213	−	0.660060i	$-0.229469\pi$
$572$	−52382.2	+	6216.04i	−0.160100	+	0.0189986i
$573$	−886.534			−0.00270014
$574$	395680.	−	445411.i	1.20094	−	1.35188i
$575$		0			0
$576$	38372.7	+	103721.i	0.115658	+	0.312625i
$577$	349598.			1.05007			0.525034	−	0.851081i	$-0.324053\pi$
$577$	349598.			1.05007			0.525034	+	0.851081i	$0.324053\pi$
$578$	6620.22	+	5881.07i	0.0198160	+	0.0176036i
$579$		−	199684.i		−	0.595645i
$580$		0			0
$581$	678672.			2.01052
$582$	169780.	−	191118.i	0.501234	−	0.564230i
$583$			470404.i			1.38399i
$584$	−257115.	+	369269.i	−0.753879	+	1.08272i
$585$		0			0
$586$	−17817.5	−	15828.2i	−0.0518862	−	0.0460931i
$587$			401716.i			1.16585i	0.812525	+	0.582926i	$0.198092\pi$
$587$			401716.i			1.16585i	−0.812525	+	0.582926i	$0.801908\pi$
$588$	−258204.	+	30640.3i	−0.746806	+	0.0886213i
$589$	147211.			0.424335
$590$		0			0
$591$			244295.i			0.699422i
$592$	−374989.	+	90268.8i	−1.06998	+	0.257569i
$593$	−83500.7			−0.237455			−0.118727	−	0.992927i	$-0.537881\pi$
$593$	−83500.7			−0.237455			−0.118727	+	0.992927i	$0.537881\pi$
$594$	45042.5	+	40013.5i	0.127658	+	0.113405i
$595$		0			0
$596$	−36770.7	−	309864.i	−0.103516	−	0.872326i
$597$	255525.			0.716943
$598$	−39882.6	+	44895.2i	−0.111527	+	0.125545i
$599$		−	655204.i		−	1.82609i	−0.407855	−	0.913047i	$-0.633723\pi$
$599$		−	655204.i		−	1.82609i	0.407855	−	0.913047i	$-0.366277\pi$
$600$		0			0
$601$	350508.			0.970396			0.485198	−	0.874404i	$-0.338747\pi$
$601$	350508.			0.970396			0.485198	+	0.874404i	$0.338747\pi$
$602$	−729290.	−	647864.i	−2.01237	−	1.78769i
$603$		−	113104.i		−	0.311060i
$604$	−528836.	+	62755.4i	−1.44960	+	0.172019i
$605$		0			0
$606$	116702.	−	131369.i	0.317784	−	0.357724i
$607$		−	14709.5i		−	0.0399228i	−0.999801	−	0.0199614i	$-0.993646\pi$
$607$		−	14709.5i		−	0.0399228i	0.999801	−	0.0199614i	$-0.00635434\pi$
$608$	172452.	−	323227.i	0.466509	−	0.874380i
$609$	−400166.			−1.07896
$610$		0			0
$611$		−	49224.5i		−	0.131856i
$612$	14905.8	+	125610.i	0.0397973	+	0.335369i
$613$	−440819.			−1.17311			−0.586556	−	0.809909i	$-0.699517\pi$
$613$	−440819.			−1.17311			−0.586556	+	0.809909i	$0.699517\pi$
$614$	207400.	−	233467.i	0.550138	−	0.619281i
$615$		0			0
$616$	−291928.	+	419267.i	−0.769332	+	1.10491i
$617$	670222.			1.76055			0.880275	−	0.474465i	$-0.157358\pi$
$617$	670222.			1.76055			0.880275	+	0.474465i	$0.157358\pi$
$618$	196646.	+	174690.i	0.514881	+	0.457394i
$619$		−	273459.i		−	0.713692i	−0.934163	−	0.356846i	$-0.883852\pi$
$619$		−	273459.i		−	0.713692i	0.934163	−	0.356846i	$-0.116148\pi$
$620$		0			0
$621$	68588.7			0.177856
$622$	97643.1	−	109915.i	0.252383	−	0.284104i
$623$			236511.i			0.609361i
$624$	−9560.21	−	39714.4i	−0.0245526	−	0.101995i
$625$		0			0
$626$	−505443.	−	449010.i	−1.28980	−	1.14580i
$627$		−	199583.i		−	0.507679i
$628$	−20471.3	−	172510.i	−0.0519071	−	0.437417i
$629$	−441153.			−1.11503
$630$		0			0
$631$			322420.i			0.809774i	0.914367	+	0.404887i	$0.132689\pi$
$631$			322420.i			0.809774i	−0.914367	+	0.404887i	$0.867311\pi$
$632$	368421.	+	256525.i	0.922380	+	0.642236i
$633$	23384.5			0.0583606
$634$	−388218.	−	344873.i	−0.965821	−	0.857986i
$635$		0			0
$636$	−361738.	+	42926.4i	−0.894294	+	0.106123i
$637$	96040.7			0.236688
$638$	−295404.	+	332531.i	−0.725729	+	0.816941i
$639$		−	170169.i		−	0.416753i
$640$		0			0
$641$	−534654.			−1.30124			−0.650619	−	0.759404i	$-0.725490\pi$
$641$	−534654.			−1.30124			−0.650619	+	0.759404i	$0.725490\pi$
$642$	108180.	+	96101.2i	0.262467	+	0.233163i
$643$		−	83676.6i		−	0.202387i	−0.994867	−	0.101193i	$-0.967734\pi$
$643$		−	83676.6i		−	0.202387i	0.994867	−	0.101193i	$-0.0322661\pi$
$644$	68536.9	+	577556.i	0.165254	+	1.39259i
$645$		0			0
$646$	278290.	−	313267.i	0.666857	−	0.750670i
$647$		−	226640.i		−	0.541411i	−0.962662	−	0.270706i	$-0.912743\pi$
$647$		−	226640.i		−	0.541411i	0.962662	−	0.270706i	$-0.0872570\pi$
$648$	−26659.8	+	38288.9i	−0.0634903	+	0.0911848i
$649$	−91418.8			−0.217043
$650$		0			0
$651$		−	158973.i		−	0.375113i
$652$	−459554.	+	54533.9i	−1.08104	+	0.128284i
$653$	−499953.			−1.17247			−0.586236	−	0.810140i	$-0.699391\pi$
$653$	−499953.			−1.17247			−0.586236	+	0.810140i	$0.699391\pi$
$654$	−147519.	+	166060.i	−0.344900	+	0.388249i
$655$		0			0
$656$	498574.	−	120019.i	1.15857	−	0.278896i
$657$	−189828.			−0.439775
$658$	−356419.	−	316625.i	−0.823208	−	0.731296i
$659$			15572.3i			0.0358576i	0.999839	+	0.0179288i	$0.00570722\pi$
$659$			15572.3i			0.0358576i	−0.999839	+	0.0179288i	$0.994293\pi$
$660$		0			0
$661$	17974.5			0.0411390			0.0205695	−	0.999788i	$-0.493452\pi$
$661$	17974.5			0.0411390			0.0205695	+	0.999788i	$0.493452\pi$
$662$	156505.	−	176175.i	0.357118	−	0.402002i
$663$		−	46721.7i		−	0.106290i
$664$	479403.	+	333800.i	1.08734	+	0.757094i
$665$		0			0
$666$	−121649.	−	108067.i	−0.274259	−	0.243638i
$667$			506363.i			1.13818i
$668$	−495035.	+	58744.4i	−1.10939	+	0.131648i
$669$	−2495.60			−0.00557599
$670$		0			0
$671$			594675.i			1.32079i
$672$	−349054.	−	186231.i	−0.772954	−	0.412395i
$673$	−53880.1			−0.118959			−0.0594796	−	0.998230i	$-0.518944\pi$
$673$	−53880.1			−0.118959			−0.0594796	+	0.998230i	$0.518944\pi$
$674$	140099.	+	124457.i	0.308401	+	0.273968i
$675$		0			0
$676$	−52072.2	−	438809.i	−0.113950	−	0.960245i
$677$	694984.			1.51634			0.758172	−	0.652055i	$-0.226093\pi$
$677$	694984.			1.51634			0.758172	+	0.652055i	$0.226093\pi$
$678$	259246.	−	291829.i	0.563965	−	0.634847i
$679$			914512.i			1.98358i
$680$		0			0
$681$	−202623.			−0.436912
$682$	−132104.	−	117354.i	−0.284019	−	0.252308i
$683$			54187.4i			0.116160i	0.998312	+	0.0580800i	$0.0184979\pi$
$683$			54187.4i			0.116160i	−0.998312	+	0.0580800i	$0.981502\pi$
$684$	153479.	−	18212.9i	0.328047	−	0.0389284i
$685$		0			0
$686$	143502.	−	161537.i	0.304936	−	0.343261i
$687$		−	143255.i		−	0.303526i
$688$	−196512.	−	816337.i	−0.415157	−	1.72462i
$689$	134551.			0.283432
$690$		0			0
$691$			138548.i			0.290165i	0.989420	+	0.145083i	$0.0463448\pi$
$691$			138548.i			0.290165i	−0.989420	+	0.145083i	$0.953655\pi$
$692$	20962.9	+	176653.i	0.0437764	+	0.368900i
$693$	−215531.			−0.448789
$694$	−452891.	+	509812.i	−0.940317	+	1.05850i
$695$		0			0
$696$	−282671.	−	196819.i	−0.583530	−	0.406301i
$697$	586544.			1.20736
$698$	280563.	+	249238.i	0.575863	+	0.511568i
$699$		−	218317.i		−	0.446820i
$700$		0			0
$701$	140668.			0.286259			0.143130	−	0.989704i	$-0.454283\pi$
$701$	140668.			0.286259			0.143130	+	0.989704i	$0.454283\pi$
$702$	11445.2	−	12883.6i	0.0232246	−	0.0261435i
$703$			539028.i			1.09069i
$704$	−412426.	+	152581.i	−0.832149	+	0.307861i
$705$		0			0
$706$	−449326.	−	399159.i	−0.901472	−	0.800822i
$707$			628608.i			1.25760i
$708$	−8342.37	−	70300.6i	−0.0166427	−	0.140247i
$709$	−381395.			−0.758723			−0.379361	−	0.925249i	$-0.623856\pi$
$709$	−381395.			−0.758723			−0.379361	+	0.925249i	$0.623856\pi$
$710$		0			0
$711$			189393.i			0.374648i
$712$	−116326.	+	167068.i	−0.229465	+	0.329558i
$713$	−201162.			−0.395701
$714$	−338298.	−	300526.i	−0.663594	−	0.589503i
$715$		0			0
$716$	132624.	−	15738.1i	0.258700	−	0.0306992i
$717$	−484066.			−0.941600
$718$	−17861.9	+	20106.9i	−0.0346481	+	0.0390028i
$719$			66799.3i			0.129215i	0.997911	+	0.0646076i	$0.0205796\pi$
$719$			66799.3i			0.129215i	−0.997911	+	0.0646076i	$0.979420\pi$
$720$		0			0
$721$	−940959.			−1.81009
$722$	6948.19	+	6172.42i	0.0133290	+	0.0118408i
$723$			565767.i			1.08233i
$724$	103140.	+	869155.i	0.196766	+	1.65814i
$725$		0			0
$726$	42997.2	−	48401.2i	0.0815768	−	0.0918297i
$727$			53183.1i			0.100625i	0.998734	+	0.0503124i	$0.0160217\pi$
$727$			53183.1i			0.100625i	−0.998734	+	0.0503124i	$0.983978\pi$
$728$	119924.	+	83501.0i	0.226279	+	0.157554i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	960374.i		−	1.79724i
$732$	−457302.	+	54266.7i	−0.853456	+	0.101277i
$733$	−251943.			−0.468915			−0.234457	−	0.972126i	$-0.575331\pi$
$733$	−251943.			−0.468915			−0.234457	+	0.972126i	$0.575331\pi$
$734$	318593.	−	358635.i	0.591349	−	0.665672i
$735$		0			0
$736$	−235653.	+	441686.i	−0.435029	+	0.815376i
$737$	449736.			0.827985
$738$	161741.	+	143683.i	0.296967	+	0.263810i
$739$		−	417899.i		−	0.765213i	−0.923911	−	0.382607i	$-0.875026\pi$
$739$		−	417899.i		−	0.765213i	0.923911	−	0.382607i	$-0.124974\pi$
$740$		0			0
$741$	−57087.5			−0.103969
$742$	865468.	−	974243.i	1.57197	−	1.76954i
$743$			95941.3i			0.173791i	0.996217	+	0.0868956i	$0.0276947\pi$
$743$			95941.3i			0.173791i	−0.996217	+	0.0868956i	$0.972305\pi$
$744$	78189.9	−	112296.i	0.141255	−	0.202871i
$745$		0			0
$746$	−149182.	−	132525.i	−0.268063	−	0.238134i
$747$			246445.i			0.441650i
$748$	−499464.	+	59269.9i	−0.892690	+	0.105933i
$749$	−517645.			−0.922717
$750$		0			0
$751$			313222.i			0.555358i	0.960674	+	0.277679i	$0.0895651\pi$
$751$			313222.i			0.555358i	−0.960674	+	0.277679i	$0.910435\pi$
$752$	−96039.5	−	398961.i	−0.169830	−	0.705496i
$753$	164234.			0.289650
$754$	95114.9	+	84495.2i	0.167304	+	0.148624i
$755$		0			0
$756$	−19668.1	−	165742.i	−0.0344128	−	0.289994i
$757$	386817.			0.675016			0.337508	−	0.941323i	$-0.390416\pi$
$757$	386817.			0.675016			0.337508	+	0.941323i	$0.390416\pi$
$758$	112578.	−	126727.i	0.195936	−	0.220562i
$759$			272729.i			0.473421i
$760$		0			0
$761$	−447721.			−0.773105			−0.386552	−	0.922267i	$-0.626334\pi$
$761$	−447721.			−0.773105			−0.386552	+	0.922267i	$0.626334\pi$
$762$	−67912.7	−	60330.2i	−0.116961	−	0.103902i
$763$		−	794607.i		−	1.36491i
$764$	2710.80	−	321.683i	0.00464419	−	0.000551113i
$765$		0			0
$766$	−661832.	+	745013.i	−1.12795	+	1.26972i
$767$			26148.8i			0.0444489i
$768$	−154970.	−	303230.i	−0.262739	−	0.514103i
$769$	351782.			0.594869			0.297434	−	0.954742i	$-0.403869\pi$
$769$	351782.			0.594869			0.297434	+	0.954742i	$0.403869\pi$
$770$		0			0
$771$			104024.i			0.174995i
$772$	72456.3	+	610585.i	0.121574	+	1.02450i
$773$	550849.			0.921878			0.460939	−	0.887432i	$-0.347513\pi$
$773$	550849.			0.921878			0.460939	+	0.887432i	$0.347513\pi$
$774$	235258.	−	264826.i	0.392701	−	0.442057i
$775$		0			0
$776$	−449796.	+	645997.i	−0.746951	+	1.07277i
$777$	582098.			0.964171
$778$	561341.	+	498667.i	0.927401	+	0.823856i
$779$		−	716676.i		−	1.18100i
$780$		0			0
$781$	676642.			1.10932
$782$	−380281.	+	428076.i	−0.621857	+	0.700014i
$783$		−	145312.i		−	0.237016i
$784$	778404.	−	187380.i	1.26641	−	0.304854i
$785$		0			0
$786$	315127.	+	279943.i	0.510082	+	0.453131i
$787$			414987.i			0.670015i	0.942215	+	0.335008i	$0.108739\pi$
$787$			414987.i			0.670015i	−0.942215	+	0.335008i	$0.891261\pi$
$788$	−88643.4	−	746992.i	−0.142756	−	1.20299i
$789$	−325800.			−0.523355
$790$		0			0
$791$			1.39642e6i			2.23183i
$792$	−152248.	−	106007.i	−0.242717	−	0.168999i
$793$	170097.			0.270489
$794$	−714957.	−	635132.i	−1.13407	−	1.00745i
$795$		0			0
$796$	−781331.	+	92718.3i	−1.23313	+	0.146332i
$797$	47477.2			0.0747426			0.0373713	−	0.999301i	$-0.488102\pi$
$797$	47477.2			0.0747426			0.0373713	+	0.999301i	$0.488102\pi$
$798$	−367202.	+	413353.i	−0.576632	+	0.649106i
$799$		−	469355.i		−	0.735204i
$800$		0			0
$801$	−85883.7			−0.133858
$802$	678407.	+	602662.i	1.05473	+	0.936969i
$803$		−	754813.i		−	1.17060i
$804$	41040.4	+	345844.i	0.0634891	+	0.535018i
$805$		0			0
$806$	−33567.3	+	37786.1i	−0.0516709	+	0.0581651i
$807$		−	175654.i		−	0.269718i
$808$	−309176.	+	444039.i	−0.473569	+	0.680140i
$809$	191528.			0.292640			0.146320	−	0.989237i	$-0.453257\pi$
$809$	191528.			0.292640			0.146320	+	0.989237i	$0.453257\pi$
$810$		0			0
$811$		−	502064.i		−	0.763339i	−0.924299	−	0.381670i	$-0.875349\pi$
$811$		−	502064.i		−	0.763339i	0.924299	−	0.381670i	$-0.124651\pi$
$812$	1.22361e6	−	145202.i	1.85580	−	0.220222i
$813$	291929.			0.441668
$814$	429705.	−	483712.i	0.648518	−	0.730026i
$815$		0			0
$816$	−91156.5	−	378676.i	−0.136901	−	0.568706i
$817$	−1.17345e6			−1.75800
$818$	−495990.	−	440612.i	−0.741253	−	0.658491i
$819$			61648.9i			0.0919089i
$820$		0			0
$821$	−184973.			−0.274424			−0.137212	−	0.990542i	$-0.543814\pi$
$821$	−184973.			−0.274424			−0.137212	+	0.990542i	$0.543814\pi$
$822$	358754.	−	403843.i	0.530949	−	0.597681i
$823$		−	728359.i		−	1.07534i	−0.843155	−	0.537670i	$-0.819305\pi$
$823$		−	728359.i		−	1.07534i	0.843155	−	0.537670i	$-0.180695\pi$
$824$	−664679.	−	462804.i	−0.978944	−	0.681620i
$825$		0			0
$826$	189336.	+	168196.i	0.277506	+	0.246522i
$827$		−	692660.i		−	1.01277i	−0.862309	−	0.506383i	$-0.830982\pi$
$827$		−	692660.i		−	1.01277i	0.862309	−	0.506383i	$-0.169018\pi$
$828$	−209727.	+	24887.7i	−0.305910	+	0.0363015i
$829$	501976.			0.730422			0.365211	−	0.930925i	$-0.380997\pi$
$829$	501976.			0.730422			0.365211	+	0.930925i	$0.380997\pi$
$830$		0			0
$831$		−	631646.i		−	0.914686i
$832$	43643.2	+	117968.i	0.0630479	+	0.170418i
$833$	915747.			1.31973
$834$	−327080.	−	290562.i	−0.470243	−	0.417740i
$835$		0			0
$836$	72419.7	+	610276.i	0.103620	+	0.873200i
$837$	57727.8			0.0824012
$838$	−409720.	+	461215.i	−0.583444	+	0.656774i
$839$		−	275008.i		−	0.390680i	−0.980736	−	0.195340i	$-0.937419\pi$
$839$		−	275008.i		−	0.390680i	0.980736	−	0.195340i	$-0.0625810\pi$
$840$		0			0
$841$	365499.			0.516766
$842$	−741187.	−	658433.i	−1.04545	−	0.928726i
$843$			269113.i			0.378687i
$844$	−71503.8	+	8485.15i	−0.100379	+	0.0119117i
$845$		0			0
$846$	114975.	−	129426.i	0.160644	−	0.180834i
$847$			231602.i			0.322832i
$848$	1.09053e6	−	262516.i	1.51651	−	0.365060i
$849$	658142.			0.913071
$850$		0			0
$851$		−	736576.i		−	1.01709i
$852$	61746.6	+	520334.i	0.0850616	+	0.716809i
$853$	203129.			0.279174			0.139587	−	0.990210i	$-0.455423\pi$
$853$	203129.			0.279174			0.139587	+	0.990210i	$0.455423\pi$
$854$	1.09411e6	−	1.23162e6i	1.50018	−	1.68873i
$855$		0			0
$856$	−365656.	−	254600.i	−0.499029	−	0.347465i
$857$	−219558.			−0.298943			−0.149471	−	0.988766i	$-0.547757\pi$
$857$	−219558.			−0.298943			−0.149471	+	0.988766i	$0.547757\pi$
$858$	51229.1	+	45509.3i	0.0695893	+	0.0618196i
$859$			306354.i			0.415180i	0.978216	+	0.207590i	$0.0665621\pi$
$859$			306354.i			0.415180i	−0.978216	+	0.207590i	$0.933438\pi$
$860$		0			0
$861$	−773941.			−1.04400
$862$	351063.	−	395185.i	0.472466	−	0.531847i
$863$			590022.i			0.792221i	0.918203	+	0.396111i	$0.129640\pi$
$863$			590022.i			0.792221i	−0.918203	+	0.396111i	$0.870360\pi$
$864$	67625.7	−	126751.i	0.0905909	−	0.169795i
$865$		0			0
$866$	−1.02005e6	−	906163.i	−1.36015	−	1.20829i
$867$		−	11503.2i		−	0.0153032i
$868$	57684.2	+	486101.i	0.0765627	+	0.645189i
$869$	−753080.			−0.997244
$870$		0			0
$871$		−	128639.i		−	0.169565i
$872$	390822.	−	561298.i	0.513979	−	0.738177i
$873$	−332085.			−0.435733
$874$	523049.	+	464651.i	0.684731	+	0.608280i
$875$		0			0
$876$	580447.	−	68880.0i	0.756406	−	0.0897605i
$877$	−54310.2			−0.0706127			−0.0353063	−	0.999377i	$-0.511241\pi$
$877$	−54310.2			−0.0706127			−0.0353063	+	0.999377i	$0.511241\pi$
$878$	4082.98	−	4596.15i	0.00529649	−	0.00596218i
$879$			30959.5i			0.0400698i
$880$		0			0
$881$	−395072.			−0.509008			−0.254504	−	0.967072i	$-0.581912\pi$
$881$	−395072.			−0.509008			−0.254504	+	0.967072i	$0.581912\pi$
$882$	252520.	+	224326.i	0.324607	+	0.288365i
$883$		−	1.22117e6i		−	1.56623i	−0.621878	−	0.783114i	$-0.713630\pi$
$883$		−	1.22117e6i		−	1.56623i	0.621878	−	0.783114i	$-0.286370\pi$
$884$	16953.2	+	142863.i	0.0216943	+	0.182817i
$885$		0			0
$886$	690251.	−	777004.i	0.879305	−	0.989819i
$887$		−	668218.i		−	0.849319i	−0.905353	−	0.424660i	$-0.860394\pi$
$887$		−	668218.i		−	0.849319i	0.905353	−	0.424660i	$-0.139606\pi$
$888$	411185.	+	286300.i	0.521448	+	0.363075i
$889$	324966.			0.411182
$890$		0			0
$891$		−	78265.3i		−	0.0985857i
$892$	7630.90	−	905.537i	0.00959061	−	0.00113809i
$893$	−573487.			−0.719152
$894$	−269208.	+	303043.i	−0.336832	+	0.379166i
$895$		0			0
$896$	1.13489e6	+	442792.i	1.41364	+	0.551548i
$897$	78009.4			0.0969532
$898$	369290.	+	328058.i	0.457946	+	0.406816i
$899$			426181.i			0.527321i
$900$		0			0
$901$	1.28294e6			1.58037
$902$	−571324.	+	643130.i	−0.702214	+	0.790471i
$903$			1.26721e6i			1.55407i
$904$	−686817.	+	986407.i	−0.840435	+	1.20703i
$905$		0			0
$906$	517195.	+	459449.i	0.630083	+	0.559734i
$907$			426441.i			0.518375i	0.965827	+	0.259188i	$0.0834548\pi$
$907$			426441.i			0.518375i	−0.965827	+	0.259188i	$0.916545\pi$
$908$	619569.	−	73522.5i	0.751481	−	0.0891761i
$909$	−228265.			−0.276256
$910$		0			0
$911$			1.05132e6i			1.26677i	0.773839	+	0.633383i	$0.218334\pi$
$911$			1.05132e6i			1.26677i	−0.773839	+	0.633383i	$0.781666\pi$
$912$	−462690.	+	111381.i	−0.556289	+	0.133912i
$913$	−979936.			−1.17559
$914$	74574.3	+	66248.0i	0.0892682	+	0.0793013i
$915$		0			0
$916$	51980.7	+	438038.i	0.0619514	+	0.522060i
$917$	−1.50790e6			−1.79322
$918$	109130.	−	122845.i	0.129496	−	0.145772i
$919$			1.00986e6i			1.19572i	0.801600	+	0.597861i	$0.203982\pi$
$919$			1.00986e6i			1.19572i	−0.801600	+	0.597861i	$0.796018\pi$
$920$		0			0
$921$	−405669.			−0.478247
$922$	−427160.	−	379467.i	−0.502491	−	0.446388i
$923$		−	193542.i		−	0.227181i
$924$	659038.	−	78206.2i	0.771910	−	0.0916004i
$925$		0			0
$926$	154434.	−	173844.i	0.180103	−	0.202739i
$927$		−	341689.i		−	0.397623i
$928$	935754.	+	499254.i	1.08659	+	0.579730i
$929$	516568.			0.598544			0.299272	−	0.954168i	$-0.403256\pi$
$929$	516568.			0.598544			0.299272	+	0.954168i	$0.403256\pi$
$930$		0			0
$931$		−	1.11892e6i		−	1.29092i
$932$	79217.1	+	667557.i	0.0911984	+	0.768522i
$933$	−190987.			−0.219402
$934$	−811455.	+	913441.i	−0.930187	+	1.04710i
$935$		0			0
$936$	−30321.6	+	43547.9i	−0.0346099	+	0.0497067i
$937$	−1.03317e6			−1.17678			−0.588388	−	0.808579i	$-0.700237\pi$
$937$	−1.03317e6			−1.17678			−0.588388	+	0.808579i	$0.700237\pi$
$938$	−931438.	−	827442.i	−1.05864	−	0.940442i
$939$			878253.i			0.996067i
$940$		0			0
$941$	−755128.			−0.852789			−0.426394	−	0.904537i	$-0.640216\pi$
$941$	−755128.			−0.852789			−0.426394	+	0.904537i	$0.640216\pi$
$942$	−149876.	+	168713.i	−0.168900	+	0.190128i
$943$			979331.i			1.10130i
$944$	51017.7	+	211935.i	0.0572502	+	0.237825i
$945$		0			0
$946$	1.05302e6	+	935454.i	1.17667	+	1.04530i
$947$		−	521546.i		−	0.581558i	−0.956790	−	0.290779i	$-0.906086\pi$
$947$		−	521546.i		−	0.581558i	0.956790	−	0.290779i	$-0.0939144\pi$
$948$	−68721.9	−	579115.i	−0.0764678	−	0.644389i
$949$	−215902.			−0.239731
$950$		0			0
$951$			674562.i			0.745867i
$952$	1.14348e6	+	796181.i	1.26169	+	0.878492i
$953$	278502.			0.306650			0.153325	−	0.988176i	$-0.451002\pi$
$953$	278502.			0.306650			0.153325	+	0.988176i	$0.451002\pi$
$954$	353775.	+	314276.i	0.388715	+	0.345314i
$955$		0			0
$956$	1.48015e6	−	175645.i	1.61954	−	0.192186i
$957$	577802.			0.630892
$958$	−569524.	+	641104.i	−0.620557	+	0.698550i
$959$			1.93241e6i			2.10118i
$960$		0			0
$961$	754213.			0.816671
$962$	−138358.	−	122910.i	−0.149504	−	0.132812i
$963$		−	187972.i		−	0.202693i
$964$	−205291.	−	1.72997e6i	−0.220910	−	1.86160i
$965$		0			0
$966$	501777.	−	564843.i	0.537721	−	0.605303i
$967$		−	1.53687e6i		−	1.64356i	−0.569806	−	0.821779i	$-0.692982\pi$
$967$		−	1.53687e6i		−	1.64356i	0.569806	−	0.821779i	$-0.307018\pi$
$968$	−113912.	+	163600.i	−0.121568	+	0.174596i
$969$	−544329.			−0.579714
$970$		0			0
$971$			889418.i			0.943338i	0.881776	+	0.471669i	$0.156348\pi$
$971$			889418.i			0.943338i	−0.881776	+	0.471669i	$0.843652\pi$
$972$	60185.6	−	7142.06i	0.0637031	−	0.00755946i
$973$	1.56510e6			1.65316
$974$	353132.	−	397514.i	0.372236	−	0.419020i
$975$		0			0
$976$	1.37862e6	−	331868.i	1.44726	−	0.348390i
$977$	−998756.			−1.04633			−0.523167	−	0.852230i	$-0.675250\pi$
$977$	−998756.			−1.04633			−0.523167	+	0.852230i	$0.675250\pi$
$978$	449438.	+	399258.i	0.469885	+	0.417422i
$979$		−	341499.i		−	0.356306i
$980$		0			0
$981$	288544.			0.299830
$982$	−540699.	+	608656.i	−0.560703	+	0.631174i
$983$		−	1.34511e6i		−	1.39204i	−0.718024	−	0.696019i	$-0.754953\pi$
$983$		−	1.34511e6i		−	1.39204i	0.718024	−	0.696019i	$-0.245047\pi$
$984$	−546700.	−	380657.i	−0.564623	−	0.393137i
$985$		0			0
$986$	906919.	+	805661.i	0.932857	+	0.828702i
$987$			619310.i			0.635732i
$988$	174559.	−	20714.4i	0.178825	−	0.0212207i
$989$	1.60350e6			1.63937
$990$		0			0
$991$		−	1.25414e6i		−	1.27702i	−0.769613	−	0.638510i	$-0.779551\pi$
$991$		−	1.25414e6i		−	1.27702i	0.769613	−	0.638510i	$-0.220449\pi$
$992$	−198338.	+	371745.i	−0.201550	+	0.377766i
$993$	−306120.			−0.310451
$994$	−1.40138e6	−	1.24491e6i	−1.41835	−	1.25999i
$995$		0			0
$996$	−89423.5	−	753566.i	−0.0901432	−	0.759631i
$997$	−552753.			−0.556085			−0.278042	−	0.960569i	$-0.589686\pi$
$997$	−552753.			−0.556085			−0.278042	+	0.960569i	$0.589686\pi$
$998$	749692.	−	843915.i	0.752699	−	0.847301i
$999$			211376.i			0.211800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.c.151.14	yes	16
4.3	odd	2	inner	300.5.c.c.151.13	yes	16
5.2	odd	4		300.5.f.c.199.10		32
5.3	odd	4		300.5.f.c.199.23		32
5.4	even	2		300.5.c.b.151.3	✓	16
20.3	even	4		300.5.f.c.199.9		32
20.7	even	4		300.5.f.c.199.24		32
20.19	odd	2		300.5.c.b.151.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.3	✓	16	5.4	even	2
300.5.c.b.151.4	yes	16	20.19	odd	2
300.5.c.c.151.13	yes	16	4.3	odd	2	inner
300.5.c.c.151.14	yes	16	1.1	even	1	trivial
300.5.f.c.199.9		32	20.3	even	4
300.5.f.c.199.10		32	5.2	odd	4
300.5.f.c.199.23		32	5.3	odd	4
300.5.f.c.199.24		32	20.7	even	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 + 15.8885i) q^{4} +(13.8039 - 15.5388i) q^{6} +74.3539i q^{7} +(-36.5704 + 52.5224i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(2.99044 + 2.65655i) q^{2} -5.19615i q^{3} +(1.88545 + 15.8885i) q^{4} +(13.8039 - 15.5388i) q^{6} +74.3539i q^{7} +(-36.5704 + 52.5224i) q^{8} -27.0000 q^{9} -107.360i q^{11} +(82.5592 - 9.79706i) q^{12} -30.7085 q^{13} +(-197.525 + 222.351i) q^{14} +(-248.890 + 59.9139i) q^{16} -292.805 q^{17} +(-80.7418 - 71.7269i) q^{18} +357.767i q^{19} +386.354 q^{21} +(285.207 - 321.053i) q^{22} -488.885i q^{23} +(272.915 + 190.025i) q^{24} +(-91.8318 - 81.5787i) q^{26} +140.296i q^{27} +(-1181.37 + 140.190i) q^{28} -1035.75 q^{29} -411.471i q^{31} +(-903.455 - 482.021i) q^{32} -557.858 q^{33} +(-875.616 - 777.852i) q^{34} +(-50.9070 - 428.990i) q^{36} +1506.64 q^{37} +(-950.428 + 1069.88i) q^{38} +159.566i q^{39} -2003.19 q^{41} +(1155.37 + 1026.37i) q^{42} +3279.91i q^{43} +(1705.79 - 202.421i) q^{44} +(1298.75 - 1461.98i) q^{46} +1602.96i q^{47} +(311.322 + 1293.27i) q^{48} -3127.50 q^{49} +1521.46i q^{51} +(-57.8991 - 487.912i) q^{52} -4381.56 q^{53} +(-372.704 + 419.547i) q^{54} +(-3905.25 - 2719.15i) q^{56} +1859.01 q^{57} +(-3097.35 - 2751.53i) q^{58} -851.518i q^{59} -5539.08 q^{61} +(1093.09 - 1230.48i) q^{62} -2007.55i q^{63} +(-1421.21 - 3841.53i) q^{64} +(-1668.24 - 1481.98i) q^{66} +4189.05i q^{67} +(-552.068 - 4652.24i) q^{68} -2540.32 q^{69} +6302.56i q^{71} +(987.401 - 1418.11i) q^{72} +7030.68 q^{73} +(4505.52 + 4002.48i) q^{74} +(-5684.40 + 674.551i) q^{76} +7982.62 q^{77} +(-423.895 + 477.172i) q^{78} -7014.54i q^{79} +729.000 q^{81} +(-5990.42 - 5321.58i) q^{82} -9127.59i q^{83} +(728.449 + 6138.59i) q^{84} +(-8713.26 + 9808.37i) q^{86} +5381.92i q^{87} +(5638.80 + 3926.19i) q^{88} +3180.88 q^{89} -2283.29i q^{91} +(7767.67 - 921.767i) q^{92} -2138.07 q^{93} +(-4258.35 + 4793.55i) q^{94} +(-2504.66 + 4694.49i) q^{96} +12299.4 q^{97} +(-9352.59 - 8308.37i) q^{98} +2898.72i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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