LMFDB - Embedded newform 300.5.f.c.199.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(199,300)]

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, 1]))

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

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

chi := DirichletCharacter("300.199");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, not 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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.7
Character	$\chi$	$=$	300.199
Dual form			300.5.f.c.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.85111 - 2.80556i) q^{2} +5.19615 q^{3} +(0.257663 + 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232 q^{7} +(44.1485 - 46.3347i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(-2.85111 - 2.80556i) q^{2} +5.19615 q^{3} +(0.257663 + 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232 q^{7} +(44.1485 - 46.3347i) q^{8} +27.0000 q^{9} +220.737i q^{11} +(1.33886 + 83.1277i) q^{12} +236.856i q^{13} +(-181.397 - 178.499i) q^{14} +(-255.867 + 8.24415i) q^{16} +46.7414i q^{17} +(-76.9800 - 75.7501i) q^{18} -195.899i q^{19} +330.596 q^{21} +(619.291 - 629.345i) q^{22} -741.830 q^{23} +(229.402 - 240.762i) q^{24} +(664.512 - 675.301i) q^{26} +140.296 q^{27} +(16.3934 + 1017.84i) q^{28} -1059.06 q^{29} -1067.12i q^{31} +(752.635 + 694.346i) q^{32} +1146.98i q^{33} +(131.136 - 133.265i) q^{34} +(6.95691 + 431.944i) q^{36} +2287.23i q^{37} +(-549.606 + 558.530i) q^{38} +1230.74i q^{39} -1141.57 q^{41} +(-942.565 - 927.506i) q^{42} -1245.24 q^{43} +(-3531.33 + 56.8758i) q^{44} +(2115.04 + 2081.25i) q^{46} -406.719 q^{47} +(-1329.53 + 42.8379i) q^{48} +1646.91 q^{49} +242.875i q^{51} +(-3789.20 + 61.0290i) q^{52} +1442.39i q^{53} +(-400.000 - 393.609i) q^{54} +(2808.87 - 2947.96i) q^{56} -1017.92i q^{57} +(3019.49 + 2971.25i) q^{58} +2472.02i q^{59} +4819.29 q^{61} +(-2993.86 + 3042.47i) q^{62} +1717.83 q^{63} +(-197.817 - 4091.22i) q^{64} +(3217.93 - 3270.17i) q^{66} +5792.14 q^{67} +(-747.765 + 12.0435i) q^{68} -3854.66 q^{69} +309.369i q^{71} +(1192.01 - 1251.04i) q^{72} +996.733i q^{73} +(6416.96 - 6521.15i) q^{74} +(3133.98 - 50.4759i) q^{76} +14044.0i q^{77} +(3452.91 - 3508.97i) q^{78} -1096.99i q^{79} +729.000 q^{81} +(3254.76 + 3202.76i) q^{82} -3097.31 q^{83} +(85.1824 + 5288.85i) q^{84} +(3550.32 + 3493.60i) q^{86} -5503.02 q^{87} +(10227.8 + 9745.21i) q^{88} -10965.3 q^{89} +15069.5i q^{91} +(-191.142 - 11867.7i) q^{92} -5544.91i q^{93} +(1159.60 + 1141.07i) q^{94} +(3910.81 + 3607.93i) q^{96} +12339.0i q^{97} +(-4695.52 - 4620.50i) q^{98} +5959.90i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 36 q^{6} + 864 q^{9}+O(q^{10}) $ 32 * q - 16 * q^4 + 36 * q^6 + 864 * q^9	$ 32 q - 16 q^{4} + 36 q^{6} + 864 q^{9} - 156 q^{14} - 752 q^{16} - 288 q^{21} - 216 q^{24} + 1356 q^{26} - 3456 q^{29} + 5864 q^{34} - 432 q^{36} + 2496 q^{41} - 16176 q^{44} + 11912 q^{46} + 21440 q^{49} + 972 q^{54} - 20472 q^{56} - 7520 q^{61} - 21088 q^{64} + 16200 q^{66} - 19584 q^{69} + 34008 q^{74} - 56688 q^{76} + 23328 q^{81} - 30240 q^{84} + 48828 q^{86} + 1536 q^{89} + 90312 q^{94} - 22176 q^{96}+O(q^{100}) $ 32 * q - 16 * q^4 + 36 * q^6 + 864 * q^9 - 156 * q^14 - 752 * q^16 - 288 * q^21 - 216 * q^24 + 1356 * q^26 - 3456 * q^29 + 5864 * q^34 - 432 * q^36 + 2496 * q^41 - 16176 * q^44 + 11912 * q^46 + 21440 * q^49 + 972 * q^54 - 20472 * q^56 - 7520 * q^61 - 21088 * q^64 + 16200 * q^66 - 19584 * q^69 + 34008 * q^74 - 56688 * q^76 + 23328 * q^81 - 30240 * q^84 + 48828 * q^86 + 1536 * q^89 + 90312 * q^94 - 22176 * q^96

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 $

$2$	−2.85111	−	2.80556i	−0.712778	−	0.701390i
$2$	−2.85111	−	2.80556i	−0.712778	−	0.701390i
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	0.257663	+	15.9979i	0.0161040	+	0.999870i
$5$		0			0
$5$		0			0
$6$	−14.8148	−	14.5781i	−0.411522	−	0.404948i
$7$	63.6232			1.29843			0.649216	−	0.760604i	$-0.275097\pi$
$7$	63.6232			1.29843			0.649216	+	0.760604i	$0.275097\pi$
$8$	44.1485	−	46.3347i	0.689821	−	0.723980i
$9$	27.0000			0.333333
$10$		0			0
$11$			220.737i			1.82427i	0.409888	+	0.912136i	$0.365568\pi$
$11$			220.737i			1.82427i	−0.409888	+	0.912136i	$0.634432\pi$
$12$	1.33886	+	83.1277i	0.00929762	+	0.577275i
$13$			236.856i			1.40151i	0.713401	+	0.700756i	$0.247154\pi$
$13$			236.856i			1.40151i	−0.713401	+	0.700756i	$0.752846\pi$
$14$	−181.397	−	178.499i	−0.925493	−	0.910707i
$15$		0			0
$16$	−255.867	+	8.24415i	−0.999481	+	0.0322037i
$17$			46.7414i			0.161735i	0.996725	+	0.0808674i	$0.0257690\pi$
$17$			46.7414i			0.161735i	−0.996725	+	0.0808674i	$0.974231\pi$
$18$	−76.9800	−	75.7501i	−0.237593	−	0.233797i
$19$		−	195.899i		−	0.542656i	−0.962487	−	0.271328i	$-0.912537\pi$
$19$		−	195.899i		−	0.542656i	0.962487	−	0.271328i	$-0.0874629\pi$
$20$		0			0
$21$	330.596			0.749650
$22$	619.291	−	629.345i	1.27953	−	1.30030i
$23$	−741.830			−1.40232			−0.701162	−	0.713002i	$-0.747335\pi$
$23$	−741.830			−1.40232			−0.701162	+	0.713002i	$0.747335\pi$
$24$	229.402	−	240.762i	0.398268	−	0.417990i
$25$		0			0
$26$	664.512	−	675.301i	0.983007	−	0.998966i
$27$	140.296			0.192450
$28$	16.3934	+	1017.84i	0.0209099	+	1.29826i
$29$	−1059.06			−1.25928			−0.629641	−	0.776886i	$-0.716798\pi$
$29$	−1059.06			−1.25928			−0.629641	+	0.776886i	$0.716798\pi$
$30$		0			0
$31$		−	1067.12i		−	1.11042i	−0.831709	−	0.555212i	$-0.812637\pi$
$31$		−	1067.12i		−	1.11042i	0.831709	−	0.555212i	$-0.187363\pi$
$32$	752.635	+	694.346i	0.734995	+	0.678072i
$33$			1146.98i			1.05324i
$34$	131.136	−	133.265i	0.113439	−	0.115281i
$35$		0			0
$36$	6.95691	+	431.944i	0.00536798	+	0.333290i
$37$			2287.23i			1.67073i	0.549695	+	0.835366i	$0.314744\pi$
$37$			2287.23i			1.67073i	−0.549695	+	0.835366i	$0.685256\pi$
$38$	−549.606	+	558.530i	−0.380614	+	0.386793i
$39$			1230.74i			0.809163i
$40$		0			0
$41$	−1141.57			−0.679105			−0.339552	−	0.940587i	$-0.610276\pi$
$41$	−1141.57			−0.679105			−0.339552	+	0.940587i	$0.610276\pi$
$42$	−942.565	−	927.506i	−0.534334	−	0.525797i
$43$	−1245.24			−0.673468			−0.336734	−	0.941600i	$-0.609322\pi$
$43$	−1245.24			−0.673468			−0.336734	+	0.941600i	$0.609322\pi$
$44$	−3531.33	+	56.8758i	−1.82404	+	0.0293780i
$45$		0			0
$46$	2115.04	+	2081.25i	0.999546	+	0.983577i
$47$	−406.719			−0.184119			−0.0920595	−	0.995754i	$-0.529345\pi$
$47$	−406.719			−0.184119			−0.0920595	+	0.995754i	$0.529345\pi$
$48$	−1329.53	+	42.8379i	−0.577051	+	0.0185928i
$49$	1646.91			0.685926
$50$		0			0
$51$			242.875i			0.0933777i
$52$	−3789.20	+	61.0290i	−1.40133	+	0.0225699i
$53$			1442.39i			0.513488i	0.966479	+	0.256744i	$0.0826497\pi$
$53$			1442.39i			0.513488i	−0.966479	+	0.256744i	$0.917350\pi$
$54$	−400.000	−	393.609i	−0.137174	−	0.134983i
$55$		0			0
$56$	2808.87	−	2947.96i	0.895685	−	0.940039i
$57$		−	1017.92i		−	0.313303i
$58$	3019.49	+	2971.25i	0.897588	+	0.883248i
$59$			2472.02i			0.710147i	0.934838	+	0.355074i	$0.115544\pi$
$59$			2472.02i			0.710147i	−0.934838	+	0.355074i	$0.884456\pi$
$60$		0			0
$61$	4819.29			1.29516			0.647579	−	0.761998i	$-0.275781\pi$
$61$	4819.29			1.29516			0.647579	+	0.761998i	$0.275781\pi$
$62$	−2993.86	+	3042.47i	−0.778841	+	0.791486i
$63$	1717.83			0.432811
$64$	−197.817	−	4091.22i	−0.0482951	−	0.998833i
$65$		0			0
$66$	3217.93	−	3270.17i	0.738735	−	0.750729i
$67$	5792.14			1.29030			0.645149	−	0.764057i	$-0.276795\pi$
$67$	5792.14			1.29030			0.645149	+	0.764057i	$0.276795\pi$
$68$	−747.765	+	12.0435i	−0.161714	+	0.00260457i
$69$	−3854.66			−0.809633
$70$		0			0
$71$			309.369i			0.0613706i	0.999529	+	0.0306853i	$0.00976897\pi$
$71$			309.369i			0.0613706i	−0.999529	+	0.0306853i	$0.990231\pi$
$72$	1192.01	−	1251.04i	0.229940	−	0.241327i
$73$			996.733i			0.187039i	0.995617	+	0.0935197i	$0.0298118\pi$
$73$			996.733i			0.187039i	−0.995617	+	0.0935197i	$0.970188\pi$
$74$	6416.96	−	6521.15i	1.17183	−	1.19086i
$75$		0			0
$76$	3133.98	−	50.4759i	0.542586	−	0.00873891i
$77$			14044.0i			2.36869i
$78$	3452.91	−	3508.97i	0.567539	−	0.576754i
$79$		−	1096.99i		−	0.175772i	−0.996131	−	0.0878860i	$-0.971989\pi$
$79$		−	1096.99i		−	0.175772i	0.996131	−	0.0878860i	$-0.0280111\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	3254.76	+	3202.76i	0.484051	+	0.476317i
$83$	−3097.31			−0.449603			−0.224801	−	0.974405i	$-0.572173\pi$
$83$	−3097.31			−0.449603			−0.224801	+	0.974405i	$0.572173\pi$
$84$	85.1824	+	5288.85i	0.0120723	+	0.749553i
$85$		0			0
$86$	3550.32	+	3493.60i	0.480033	+	0.472364i
$87$	−5503.02			−0.727047
$88$	10227.8	+	9745.21i	1.32074	+	1.25842i
$89$	−10965.3			−1.38433			−0.692167	−	0.721738i	$-0.743344\pi$
$89$	−10965.3			−1.38433			−0.692167	+	0.721738i	$0.743344\pi$
$90$		0			0
$91$			15069.5i			1.81977i
$92$	−191.142	−	11867.7i	−0.0225830	−	1.40214i
$93$		−	5544.91i		−	0.641104i
$94$	1159.60	+	1141.07i	0.131236	+	0.129139i
$95$		0			0
$96$	3910.81	+	3607.93i	0.424350	+	0.391485i
$97$			12339.0i			1.31140i	0.755020	+	0.655701i	$0.227627\pi$
$97$			12339.0i			1.31140i	−0.755020	+	0.655701i	$0.772373\pi$
$98$	−4695.52	−	4620.50i	−0.488913	−	0.481102i
$99$			5959.90i			0.608091i
$100$		0			0
$101$	14918.3			1.46244			0.731219	−	0.682143i	$-0.238952\pi$
$101$	14918.3			1.46244			0.731219	+	0.682143i	$0.238952\pi$
$102$	681.401	−	692.464i	0.0654942	−	0.0665575i
$103$	10083.1			0.950433			0.475216	−	0.879869i	$-0.342370\pi$
$103$	10083.1			0.950433			0.475216	+	0.879869i	$0.342370\pi$
$104$	10974.6	+	10456.8i	1.01467	+	0.966792i
$105$		0			0
$106$	4046.71	−	4112.41i	0.360155	−	0.366003i
$107$	18475.7			1.61374			0.806869	−	0.590731i	$-0.201161\pi$
$107$	18475.7			1.61374			0.806869	+	0.590731i	$0.201161\pi$
$108$	36.1491	+	2244.45i	0.00309921	+	0.192425i
$109$	676.882			0.0569718			0.0284859	−	0.999594i	$-0.490931\pi$
$109$	676.882			0.0569718			0.0284859	+	0.999594i	$0.490931\pi$
$110$		0			0
$111$			11884.8i			0.964597i
$112$	−16279.1	+	524.519i	−1.29776	+	0.0418144i
$113$		−	5693.92i		−	0.445917i	−0.974828	−	0.222959i	$-0.928429\pi$
$113$		−	5693.92i		−	0.445917i	0.974828	−	0.222959i	$-0.0715715\pi$
$114$	−2855.84	+	2902.20i	−0.219747	+	0.223315i
$115$		0			0
$116$	−272.880	−	16942.7i	−0.0202794	−	1.25912i
$117$			6395.10i			0.467171i
$118$	6935.41	−	7048.01i	0.498090	−	0.506177i
$119$			2973.83i			0.210002i
$120$		0			0
$121$	−34083.8			−2.32797
$122$	−13740.3	−	13520.8i	−0.923160	−	0.908412i
$123$	−5931.80			−0.392081
$124$	17071.7	−	274.957i	1.11028	−	0.0178822i
$125$		0			0
$126$	−4897.71	−	4819.46i	−0.308498	−	0.303569i
$127$	21834.4			1.35374			0.676869	−	0.736103i	$-0.263336\pi$
$127$	21834.4			1.35374			0.676869	+	0.736103i	$0.263336\pi$
$128$	−10914.2	+	12219.5i	−0.666148	+	0.745820i
$129$	−6470.47			−0.388827
$130$		0			0
$131$		−	6919.28i		−	0.403198i	−0.979468	−	0.201599i	$-0.935386\pi$
$131$		−	6919.28i		−	0.403198i	0.979468	−	0.201599i	$-0.0646138\pi$
$132$	−18349.3	+	295.535i	−1.05311	+	0.0169614i
$133$		−	12463.7i		−	0.704602i
$134$	−16514.0	−	16250.2i	−0.919695	−	0.905002i
$135$		0			0
$136$	2165.75	+	2063.56i	0.117093	+	0.111568i
$137$		−	24619.2i		−	1.31169i	−0.754895	−	0.655846i	$-0.772312\pi$
$137$		−	24619.2i		−	1.31169i	0.754895	−	0.655846i	$-0.227688\pi$
$138$	10990.1	+	10814.5i	0.577088	+	0.567868i
$139$			18767.2i			0.971336i	0.874143	+	0.485668i	$0.161424\pi$
$139$			18767.2i			0.971336i	−0.874143	+	0.485668i	$0.838576\pi$
$140$		0			0
$141$	−2113.37			−0.106301
$142$	867.954	−	882.046i	0.0430447	−	0.0437436i
$143$	−52282.8			−2.55674
$144$	−6908.41	+	222.592i	−0.333160	+	0.0107346i
$145$		0			0
$146$	2796.39	−	2841.80i	0.131188	−	0.133318i
$147$	8557.59			0.396020
$148$	−36590.9	+	589.335i	−1.67051	+	0.0269054i
$149$	−6573.00			−0.296068			−0.148034	−	0.988982i	$-0.547294\pi$
$149$	−6573.00			−0.296068			−0.148034	+	0.988982i	$0.547294\pi$
$150$		0			0
$151$		−	7823.28i		−	0.343111i	−0.985174	−	0.171556i	$-0.945121\pi$
$151$		−	7823.28i		−	0.343111i	0.985174	−	0.171556i	$-0.0548793\pi$
$152$	−9076.93	−	8648.65i	−0.392873	−	0.374335i
$153$			1262.02i			0.0539116i
$154$	39401.2	−	40041.0i	1.66138	−	1.68835i
$155$		0			0
$156$	−19689.2	+	317.116i	−0.809058	+	0.0130307i
$157$			9202.59i			0.373346i	0.982422	+	0.186673i	$0.0597704\pi$
$157$			9202.59i			0.373346i	−0.982422	+	0.186673i	$0.940230\pi$
$158$	−3077.68	+	3127.65i	−0.123285	+	0.125286i
$159$			7494.87i			0.296462i
$160$		0			0
$161$	−47197.6			−1.82082
$162$	−2078.46	−	2045.25i	−0.0791975	−	0.0779322i
$163$	43667.2			1.64354			0.821769	−	0.569820i	$-0.192987\pi$
$163$	43667.2			1.64354			0.821769	+	0.569820i	$0.192987\pi$
$164$	−294.142	−	18262.8i	−0.0109363	−	0.679017i
$165$		0			0
$166$	8830.78	+	8689.70i	0.320467	+	0.315347i
$167$	19662.7			0.705034			0.352517	−	0.935805i	$-0.385326\pi$
$167$	19662.7			0.705034			0.352517	+	0.935805i	$0.385326\pi$
$168$	14595.3	−	15318.1i	0.517124	−	0.542732i
$169$	−27539.5			−0.964236
$170$		0			0
$171$		−	5289.27i		−	0.180885i
$172$	−320.853	−	19921.3i	−0.0108455	−	0.673381i
$173$		−	31871.9i		−	1.06492i	−0.846456	−	0.532459i	$-0.821268\pi$
$173$		−	31871.9i		−	1.06492i	0.846456	−	0.532459i	$-0.178732\pi$
$174$	15689.7	+	15439.1i	0.518223	+	0.509944i
$175$		0			0
$176$	−1819.79	−	56479.3i	−0.0587484	−	1.82333i
$177$			12845.0i			0.410004i
$178$	31263.3	+	30763.8i	0.986722	+	0.970958i
$179$		−	52843.2i		−	1.64924i	−0.565689	−	0.824619i	$-0.691390\pi$
$179$		−	52843.2i		−	1.64924i	0.565689	−	0.824619i	$-0.308610\pi$
$180$		0			0
$181$	−63045.0			−1.92439			−0.962197	−	0.272356i	$-0.912197\pi$
$181$	−63045.0			−1.92439			−0.962197	+	0.272356i	$0.912197\pi$
$182$	42278.4	−	42964.8i	1.27637	−	1.29709i
$183$	25041.7			0.747760
$184$	−32750.7	+	34372.5i	−0.967352	+	1.01526i
$185$		0			0
$186$	−15556.6	+	15809.1i	−0.449664	+	0.456964i
$187$	−10317.5			−0.295048
$188$	−104.796	−	6506.66i	−0.00296504	−	0.184095i
$189$	8926.08			0.249883
$190$		0			0
$191$			20730.2i			0.568246i	0.958788	+	0.284123i	$0.0917024\pi$
$191$			20730.2i			0.568246i	−0.958788	+	0.284123i	$0.908298\pi$
$192$	−1027.89	−	21258.6i	−0.0278832	−	0.576677i
$193$			17567.6i			0.471627i	0.971798	+	0.235813i	$0.0757754\pi$
$193$			17567.6i			0.471627i	−0.971798	+	0.235813i	$0.924225\pi$
$194$	34617.8	−	35179.8i	0.919805	−	0.934739i
$195$		0			0
$196$	424.348	+	26347.1i	0.0110461	+	0.685837i
$197$			50800.9i			1.30900i	0.756063	+	0.654499i	$0.227120\pi$
$197$			50800.9i			1.30900i	−0.756063	+	0.654499i	$0.772880\pi$
$198$	16720.8	−	16992.3i	0.426509	−	0.433433i
$199$			32141.3i			0.811629i	0.913955	+	0.405814i	$0.133012\pi$
$199$			32141.3i			0.811629i	−0.913955	+	0.405814i	$0.866988\pi$
$200$		0			0
$201$	30096.9			0.744953
$202$	−42533.8	−	41854.3i	−1.04239	−	1.02574i
$203$	−67380.5			−1.63509
$204$	−3885.50	+	62.5800i	−0.0933656	+	0.00150375i
$205$		0			0
$206$	−28748.1	−	28288.9i	−0.677447	−	0.666624i
$207$	−20029.4			−0.467442
$208$	−1952.67	−	60603.6i	−0.0451339	−	1.40079i
$209$	43242.1			0.989953
$210$		0			0
$211$			9541.34i			0.214311i	0.994242	+	0.107156i	$0.0341743\pi$
$211$			9541.34i			0.214311i	−0.994242	+	0.107156i	$0.965826\pi$
$212$	−23075.2	+	371.650i	−0.513421	+	0.00826919i
$213$			1607.53i			0.0354323i
$214$	−52676.2	−	51834.6i	−1.15024	−	1.13186i
$215$		0			0
$216$	6193.87	−	6500.58i	0.132756	−	0.139330i
$217$		−	67893.4i		−	1.44181i
$218$	−1929.86	−	1899.03i	−0.0406082	−	0.0399594i
$219$			5179.18i			0.107987i
$220$		0			0
$221$	−11071.0			−0.226673
$222$	33343.5	−	33884.9i	0.676559	−	0.687543i
$223$	−33469.4			−0.673037			−0.336518	−	0.941677i	$-0.609249\pi$
$223$	−33469.4			−0.673037			−0.336518	+	0.941677i	$0.609249\pi$
$224$	47885.0	+	44176.5i	0.954342	+	0.880431i
$225$		0			0
$226$	−15974.6	+	16234.0i	−0.312762	+	0.317840i
$227$	1149.27			0.0223033			0.0111517	−	0.999938i	$-0.496450\pi$
$227$	1149.27			0.0223033			0.0111517	+	0.999938i	$0.496450\pi$
$228$	16284.6	−	262.281i	0.313262	−	0.00504541i
$229$	49392.2			0.941863			0.470931	−	0.882170i	$-0.343918\pi$
$229$	49392.2			0.941863			0.470931	+	0.882170i	$0.343918\pi$
$230$		0			0
$231$			72974.7i			1.36757i
$232$	−46755.8	+	49071.1i	−0.868679	+	0.911696i
$233$			42084.0i			0.775184i	0.921831	+	0.387592i	$0.126693\pi$
$233$			42084.0i			0.775184i	−0.921831	+	0.387592i	$0.873307\pi$
$234$	17941.8	−	18233.1i	0.327669	−	0.332989i
$235$		0			0
$236$	−39547.2	+	636.949i	−0.710055	+	0.0114362i
$237$		−	5700.14i		−	0.101482i
$238$	8343.27	−	8478.73i	0.147293	−	0.149685i
$239$			34540.4i			0.604689i	0.953199	+	0.302345i	$0.0977693\pi$
$239$			34540.4i			0.604689i	−0.953199	+	0.302345i	$0.902231\pi$
$240$		0			0
$241$	68666.9			1.18226			0.591131	−	0.806576i	$-0.298682\pi$
$241$	68666.9			1.18226			0.591131	+	0.806576i	$0.298682\pi$
$242$	97176.6	+	95624.1i	1.65932	+	1.63281i
$243$	3788.00			0.0641500
$244$	1241.75	+	77098.6i	0.0208572	+	1.29499i
$245$		0			0
$246$	16912.2	+	16642.0i	0.279467	+	0.275002i
$247$	46399.7			0.760539
$248$	−49444.6	−	47111.7i	−0.803925	−	0.765994i
$249$	−16094.1			−0.259578
$250$		0			0
$251$		−	62003.3i		−	0.984163i	−0.870549	−	0.492082i	$-0.836236\pi$
$251$		−	62003.3i		−	0.984163i	0.870549	−	0.492082i	$-0.163764\pi$
$252$	442.621	+	27481.6i	0.00696996	+	0.432755i
$253$		−	163749.i		−	2.55822i
$254$	−62252.4	−	61257.9i	−0.964914	−	0.949499i
$255$		0			0
$256$	65400.1	−	4218.82i	0.997926	−	0.0643740i
$257$			65977.4i			0.998916i	0.866338	+	0.499458i	$0.166468\pi$
$257$			65977.4i			0.998916i	−0.866338	+	0.499458i	$0.833532\pi$
$258$	18448.0	+	18153.3i	0.277147	+	0.272719i
$259$			145521.i			2.16933i
$260$		0			0
$261$	−28594.5			−0.419761
$262$	−19412.5	+	19727.6i	−0.282799	+	0.287391i
$263$	45889.4			0.663439			0.331719	−	0.943378i	$-0.392371\pi$
$263$	45889.4			0.663439			0.331719	+	0.943378i	$0.392371\pi$
$264$	53145.1	+	50637.6i	0.762528	+	0.726549i
$265$		0			0
$266$	−34967.7	+	35535.4i	−0.494201	+	0.502225i
$267$	−56977.4			−0.799245
$268$	1492.42	+	92662.3i	0.0207789	+	1.29013i
$269$	−66600.2			−0.920388			−0.460194	−	0.887818i	$-0.652220\pi$
$269$	−66600.2			−0.920388			−0.460194	+	0.887818i	$0.652220\pi$
$270$		0			0
$271$		−	107846.i		−	1.46848i	−0.678892	−	0.734239i	$-0.737539\pi$
$271$		−	107846.i		−	1.46848i	0.678892	−	0.734239i	$-0.262461\pi$
$272$	−385.343	−	11959.6i	−0.00520847	−	0.161651i
$273$			78303.4i			1.05064i
$274$	−69070.5	+	70191.9i	−0.920008	+	0.934945i
$275$		0			0
$276$	−993.204	−	61666.6i	−0.0130383	−	0.809528i
$277$		−	76120.9i		−	0.992074i	−0.868301	−	0.496037i	$-0.834788\pi$
$277$		−	76120.9i		−	0.992074i	0.868301	−	0.496037i	$-0.165212\pi$
$278$	52652.5	−	53507.3i	0.681286	−	0.692347i
$279$		−	28812.2i		−	0.370141i
$280$		0			0
$281$	127936.			1.62024			0.810120	−	0.586264i	$-0.199402\pi$
$281$	127936.			1.62024			0.810120	+	0.586264i	$0.199402\pi$
$282$	6025.46	+	5929.19i	0.0757691	+	0.0745586i
$283$	117792.			1.47076			0.735380	−	0.677655i	$-0.237004\pi$
$283$	117792.			1.47076			0.735380	+	0.677655i	$0.237004\pi$
$284$	−4949.27	+	79.7131i	−0.0613627	+	0.000988310i
$285$		0			0
$286$	149064.	+	146682.i	1.82239	+	1.79327i
$287$	−72630.6			−0.881771
$288$	20321.2	+	18747.3i	0.244998	+	0.226024i
$289$	81336.2			0.973842
$290$		0			0
$291$			64115.3i			0.757139i
$292$	−15945.7	+	256.821i	−0.187015	+	0.00301207i
$293$			120518.i			1.40384i	0.712258	+	0.701918i	$0.247673\pi$
$293$			120518.i			1.40384i	−0.712258	+	0.701918i	$0.752327\pi$
$294$	−24398.6	−	24008.8i	−0.282274	−	0.277764i
$295$		0			0
$296$	105978.	+	100978.i	1.20958	+	1.15250i
$297$			30968.5i			0.351081i
$298$	18740.4	+	18441.0i	0.211031	+	0.207659i
$299$		−	175706.i		−	1.96537i
$300$		0			0
$301$	−79226.3			−0.874453
$302$	−21948.7	+	22305.0i	−0.240655	+	0.244562i
$303$	77517.9			0.844339
$304$	1615.02	+	50124.1i	0.0174756	+	0.542375i
$305$		0			0
$306$	3540.67	−	3598.15i	0.0378131	−	0.0384270i
$307$	−90003.1			−0.954950			−0.477475	−	0.878645i	$-0.658448\pi$
$307$	−90003.1			−0.954950			−0.477475	+	0.878645i	$0.658448\pi$
$308$	−224675.	+	3618.62i	−2.36839	+	0.0381453i
$309$	52393.5			0.548732
$310$		0			0
$311$			35944.1i			0.371627i	0.982585	+	0.185813i	$0.0594920\pi$
$311$			35944.1i			0.371627i	−0.982585	+	0.185813i	$0.940508\pi$
$312$	57025.9	+	54335.2i	0.585818	+	0.558178i
$313$		−	10420.7i		−	0.106368i	−0.998585	−	0.0531838i	$-0.983063\pi$
$313$		−	10420.7i		−	0.106368i	0.998585	−	0.0531838i	$-0.0169369\pi$
$314$	25818.4	−	26237.6i	0.261861	−	0.266112i
$315$		0			0
$316$	17549.6	−	282.655i	0.175749	−	0.00283062i
$317$		−	44276.9i		−	0.440614i	−0.975431	−	0.220307i	$-0.929294\pi$
$317$		−	44276.9i		−	0.440614i	0.975431	−	0.220307i	$-0.0707060\pi$
$318$	21027.3	−	21368.7i	0.207936	−	0.211312i
$319$		−	233773.i		−	2.29727i
$320$		0			0
$321$	96002.4			0.931692
$322$	134565.	+	132416.i	1.29784	+	1.27711i
$323$	9156.59			0.0877664
$324$	187.836	+	11662.5i	0.00178933	+	0.111097i
$325$		0			0
$326$	−124500.	−	122511.i	−1.17148	−	1.15276i
$327$	3517.18			0.0328927
$328$	−50398.8	+	52894.6i	−0.468460	+	0.491658i
$329$	−25876.7			−0.239066
$330$		0			0
$331$		−	219017.i		−	1.99904i	−0.0309493	−	0.999521i	$-0.509853\pi$
$331$		−	219017.i		−	1.99904i	0.0309493	−	0.999521i	$-0.490147\pi$
$332$	−798.064	−	49550.6i	−0.00724038	−	0.449544i
$333$			61755.2i			0.556910i
$334$	−56060.5	−	55164.9i	−0.502533	−	0.494504i
$335$		0			0
$336$	−84588.6	+	2725.48i	−0.749261	+	0.0241415i
$337$		−	51173.5i		−	0.450594i	−0.974290	−	0.225297i	$-0.927665\pi$
$337$		−	51173.5i		−	0.450594i	0.974290	−	0.225297i	$-0.0723353\pi$
$338$	78518.3	+	77263.9i	0.687286	+	0.676306i
$339$		−	29586.5i		−	0.257450i
$340$		0			0
$341$	235552.			2.02572
$342$	−14839.4	+	15080.3i	−0.126871	+	0.128931i
$343$	−47977.7			−0.407804
$344$	−54975.6	+	57698.0i	−0.464572	+	0.487578i
$345$		0			0
$346$	−89418.7	+	90870.4i	−0.746923	+	0.759050i
$347$	78897.6			0.655247			0.327623	−	0.944808i	$-0.393752\pi$
$347$	78897.6			0.655247			0.327623	+	0.944808i	$0.393752\pi$
$348$	−1417.93	−	88036.9i	−0.0117083	−	0.726953i
$349$	−187086.			−1.53599			−0.767997	−	0.640454i	$-0.778746\pi$
$349$	−187086.			−1.53599			−0.767997	+	0.640454i	$0.778746\pi$
$350$		0			0
$351$			33229.9i			0.269721i
$352$	−153268.	+	166134.i	−1.23699	+	1.34083i
$353$			26576.3i			0.213278i	0.994298	+	0.106639i	$0.0340089\pi$
$353$			26576.3i			0.213278i	−0.994298	+	0.106639i	$0.965991\pi$
$354$	36037.4	−	36622.5i	0.287573	−	0.292242i
$355$		0			0
$356$	−2825.36	−	175422.i	−0.0222932	−	1.38415i
$357$			15452.5i			0.121245i
$358$	−148255.	+	150662.i	−1.15676	+	1.17554i
$359$		−	13211.6i		−	0.102510i	−0.998686	−	0.0512552i	$-0.983678\pi$
$359$		−	13211.6i		−	0.102510i	0.998686	−	0.0512552i	$-0.0163222\pi$
$360$		0			0
$361$	91944.6			0.705524
$362$	179748.	+	176877.i	1.37166	+	1.34975i
$363$	−177105.			−1.34405
$364$	−241081.	+	3882.86i	−1.81953	+	0.0293055i
$365$		0			0
$366$	−71396.8	−	70256.1i	−0.532987	−	0.524472i
$367$	−46921.2			−0.348367			−0.174184	−	0.984713i	$-0.555729\pi$
$367$	−46921.2			−0.348367			−0.174184	+	0.984713i	$0.555729\pi$
$368$	189810.	−	6115.76i	1.40160	−	0.0451601i
$369$	−30822.5			−0.226368
$370$		0			0
$371$			91769.3i			0.666729i
$372$	88707.0	−	1428.72i	0.641021	−	0.0103243i
$373$			237489.i			1.70697i	0.521115	+	0.853487i	$0.325516\pi$
$373$			237489.i			1.70697i	−0.521115	+	0.853487i	$0.674484\pi$
$374$	29416.5	+	28946.5i	0.210304	+	0.206944i
$375$		0			0
$376$	−17956.0	+	18845.2i	−0.127009	+	0.133299i
$377$		−	250843.i		−	1.76490i
$378$	−25449.3	−	25042.7i	−0.178111	−	0.175266i
$379$			108145.i			0.752885i	0.926440	+	0.376442i	$0.122853\pi$
$379$			108145.i			0.752885i	−0.926440	+	0.376442i	$0.877147\pi$
$380$		0			0
$381$	113455.			0.781581
$382$	58159.8	−	59104.0i	0.398562	−	0.405033i
$383$	−143109.			−0.975594			−0.487797	−	0.872957i	$-0.662199\pi$
$383$	−143109.			−0.975594			−0.487797	+	0.872957i	$0.662199\pi$
$384$	−56711.7	+	63494.4i	−0.384601	+	0.430599i
$385$		0			0
$386$	49287.0	−	50087.3i	0.330794	−	0.336165i
$387$	−33621.6			−0.224489
$388$	−197398.	+	3179.30i	−1.31123	+	0.0211188i
$389$	132061.			0.872720			0.436360	−	0.899772i	$-0.356267\pi$
$389$	132061.			0.872720			0.436360	+	0.899772i	$0.356267\pi$
$390$		0			0
$391$		−	34674.1i		−	0.226805i
$392$	72708.6	−	76309.1i	0.473166	−	0.496597i
$393$		−	35953.6i		−	0.232787i
$394$	142525.	−	144839.i	0.918118	−	0.933024i
$395$		0			0
$396$	−95346.0	+	1535.65i	−0.608012	+	0.00979266i
$397$		−	46139.3i		−	0.292745i	−0.989230	−	0.146373i	$-0.953240\pi$
$397$		−	46139.3i		−	0.292745i	0.989230	−	0.146373i	$-0.0467598\pi$
$398$	90174.4	−	91638.5i	0.569269	−	0.578511i
$399$		−	64763.3i		−	0.406802i
$400$		0			0
$401$	3244.97			0.0201800			0.0100900	−	0.999949i	$-0.496788\pi$
$401$	3244.97			0.0201800			0.0100900	+	0.999949i	$0.496788\pi$
$402$	−85809.5	−	84438.6i	−0.530986	−	0.522503i
$403$	252753.			1.55627
$404$	3843.90	+	238662.i	0.0235510	+	1.46225i
$405$		0			0
$406$	192109.	+	189040.i	1.16546	+	1.14684i
$407$	−504876.			−3.04787
$408$	11253.6	+	10722.6i	0.0676036	+	0.0644138i
$409$	190227.			1.13717			0.568585	−	0.822625i	$-0.307491\pi$
$409$	190227.			1.13717			0.568585	+	0.822625i	$0.307491\pi$
$410$		0			0
$411$		−	127925.i		−	0.757306i
$412$	2598.05	+	161309.i	0.0153057	+	0.950309i
$413$			157278.i			0.922078i
$414$	57106.0	+	56193.7i	0.333182	+	0.327859i
$415$		0			0
$416$	−164460.	+	178266.i	−0.950326	+	1.03010i
$417$			97517.2i			0.560801i
$418$	−123288.	−	121318.i	−0.705616	−	0.694343i
$419$		−	38663.2i		−	0.220226i	−0.993919	−	0.110113i	$-0.964879\pi$
$419$		−	38663.2i		−	0.220226i	0.993919	−	0.110113i	$-0.0351213\pi$
$420$		0			0
$421$	−215220.			−1.21428			−0.607140	−	0.794595i	$-0.707683\pi$
$421$	−215220.			−1.21428			−0.607140	+	0.794595i	$0.707683\pi$
$422$	26768.8	−	27203.4i	0.150316	−	0.152756i
$423$	−10981.4			−0.0613730
$424$	66832.7	+	63679.3i	0.371755	+	0.354215i
$425$		0			0
$426$	4510.02	−	4583.25i	0.0248519	−	0.0252554i
$427$	306618.			1.68168
$428$	4760.50	+	295572.i	0.0259875	+	1.61353i
$429$	−271669.			−1.47613
$430$		0			0
$431$			12832.4i			0.0690804i	0.999403	+	0.0345402i	$0.0109967\pi$
$431$			12832.4i			0.0690804i	−0.999403	+	0.0345402i	$0.989003\pi$
$432$	−35897.2	+	1156.62i	−0.192350	+	0.00619761i
$433$		−	245264.i		−	1.30815i	−0.756429	−	0.654076i	$-0.773058\pi$
$433$		−	245264.i		−	1.30815i	0.756429	−	0.654076i	$-0.226942\pi$
$434$	−190479.	+	193572.i	−1.01127	+	1.02769i
$435$		0			0
$436$	174.408	+	10828.7i	0.000917471	+	0.0569644i
$437$			145324.i			0.760980i
$438$	14530.5	−	14766.4i	0.0757412	−	0.0769709i
$439$			8320.58i			0.0431742i	0.999767	+	0.0215871i	$0.00687192\pi$
$439$			8320.58i			0.0431742i	−0.999767	+	0.0215871i	$0.993128\pi$
$440$		0			0
$441$	44466.5			0.228642
$442$	31564.5	+	31060.2i	0.161568	+	0.158986i
$443$	141239.			0.719695			0.359847	−	0.933011i	$-0.382829\pi$
$443$	141239.			0.719695			0.359847	+	0.933011i	$0.382829\pi$
$444$	−190132.	+	3062.28i	−0.964472	+	0.0155338i
$445$		0			0
$446$	95425.1	+	93900.6i	0.479726	+	0.472061i
$447$	−34154.3			−0.170935
$448$	−12585.7	−	260296.i	−0.0627080	−	1.29692i
$449$	197626.			0.980282			0.490141	−	0.871643i	$-0.336945\pi$
$449$	197626.			0.980282			0.490141	+	0.871643i	$0.336945\pi$
$450$		0			0
$451$		−	251988.i		−	1.23887i
$452$	91090.9	−	1467.11i	0.445859	−	0.00718103i
$453$		−	40651.0i		−	0.198095i
$454$	−3276.69	−	3224.34i	−0.0158973	−	0.0156433i
$455$		0			0
$456$	−47165.1	−	44939.7i	−0.226825	−	0.216123i
$457$		−	331333.i		−	1.58647i	−0.608915	−	0.793236i	$-0.708395\pi$
$457$		−	331333.i		−	1.58647i	0.608915	−	0.793236i	$-0.291605\pi$
$458$	−140823.	−	138573.i	−0.671339	−	0.660613i
$459$			6557.63i			0.0311259i
$460$		0			0
$461$	−196090.			−0.922687			−0.461343	−	0.887222i	$-0.652632\pi$
$461$	−196090.			−0.922687			−0.461343	+	0.887222i	$0.652632\pi$
$462$	204735.	−	208059.i	0.959197	−	0.974770i
$463$	168744.			0.787164			0.393582	−	0.919289i	$-0.371236\pi$
$463$	168744.			0.787164			0.393582	+	0.919289i	$0.371236\pi$
$464$	270978.	−	8731.03i	1.25863	−	0.0405536i
$465$		0			0
$466$	118069.	−	119986.i	0.543706	−	0.552534i
$467$	58203.8			0.266881			0.133440	−	0.991057i	$-0.457398\pi$
$467$	58203.8			0.266881			0.133440	+	0.991057i	$0.457398\pi$
$468$	−102308.	+	1647.78i	−0.467110	+	0.00752329i
$469$	368515.			1.67536
$470$		0			0
$471$			47818.1i			0.215551i
$472$	114541.	+	109136.i	0.514133	+	0.489874i
$473$		−	274871.i		−	1.22859i
$474$	−15992.1	+	16251.7i	−0.0711785	+	0.0723341i
$475$		0			0
$476$	−47575.2	+	766.248i	−0.209975	+	0.00338186i
$477$			38944.5i			0.171163i
$478$	96905.3	−	98478.6i	0.424123	−	0.431009i
$479$			221700.i			0.966260i	0.875549	+	0.483130i	$0.160500\pi$
$479$			221700.i			0.966260i	−0.875549	+	0.483130i	$0.839500\pi$
$480$		0			0
$481$	−541743.			−2.34155
$482$	−195777.	−	192649.i	−0.842690	−	0.829227i
$483$	−245246.			−1.05125
$484$	−8782.14	−	545270.i	−0.0374895	−	2.32767i
$485$		0			0
$486$	−10800.0	−	10627.4i	−0.0457247	−	0.0449942i
$487$	145571.			0.613788			0.306894	−	0.951744i	$-0.400710\pi$
$487$	145571.			0.613788			0.306894	+	0.951744i	$0.400710\pi$
$488$	212764.	−	223300.i	0.893427	−	0.937670i
$489$	226901.			0.948897
$490$		0			0
$491$			244597.i			1.01458i	0.861774	+	0.507292i	$0.169354\pi$
$491$			244597.i			1.01458i	−0.861774	+	0.507292i	$0.830646\pi$
$492$	−1528.41	−	94896.4i	−0.00631406	−	0.392030i
$493$		−	49501.8i		−	0.203670i
$494$	−132291.	−	130177.i	−0.542095	−	0.533435i
$495$		0			0
$496$	8797.48	+	273040.i	0.0357598	+	1.10985i
$497$			19683.1i			0.0796856i
$498$	45886.1	+	45153.0i	0.185022	+	0.182066i
$499$			113422.i			0.455507i	0.973719	+	0.227754i	$0.0731381\pi$
$499$			113422.i			0.455507i	−0.973719	+	0.227754i	$0.926862\pi$
$500$		0			0
$501$	102170.			0.407052
$502$	−173954.	+	176778.i	−0.690282	+	0.701490i
$503$	135516.			0.535616			0.267808	−	0.963472i	$-0.413701\pi$
$503$	135516.			0.535616			0.267808	+	0.963472i	$0.413701\pi$
$504$	75839.5	−	79595.0i	0.298562	−	0.313346i
$505$		0			0
$506$	−459408.	+	466867.i	−1.79431	+	1.82344i
$507$	−143100.			−0.556702
$508$	5625.93	+	349306.i	0.0218005	+	1.35356i
$509$	−393520.			−1.51891			−0.759454	−	0.650561i	$-0.774534\pi$
$509$	−393520.			−1.51891			−0.759454	+	0.650561i	$0.774534\pi$
$510$		0			0
$511$			63415.3i			0.242858i
$512$	−198299.	−	171456.i	−0.756451	−	0.654051i
$513$		−	27483.9i		−	0.104434i
$514$	185104.	−	188109.i	0.700630	−	0.712005i
$515$		0			0
$516$	−1667.20	−	103514.i	−0.00626165	−	0.388777i
$517$		−	89777.9i		−	0.335883i
$518$	408268.	−	414896.i	1.52155	−	1.54625i
$519$		−	165611.i		−	0.614831i
$520$		0			0
$521$	309126.			1.13883			0.569416	−	0.822049i	$-0.307169\pi$
$521$	309126.			1.13883			0.569416	+	0.822049i	$0.307169\pi$
$522$	81526.2	+	80223.7i	0.299196	+	0.294416i
$523$	−49369.3			−0.180490			−0.0902452	−	0.995920i	$-0.528765\pi$
$523$	−49369.3			−0.180490			−0.0902452	+	0.995920i	$0.528765\pi$
$524$	110694.	−	1782.84i	0.403146	−	0.00649308i
$525$		0			0
$526$	−130836.	−	128745.i	−0.472884	−	0.465329i
$527$	49878.6			0.179594
$528$	−9455.90	−	293475.i	−0.0339184	−	1.05270i
$529$	270470.			0.966514
$530$		0			0
$531$			66744.6i			0.236716i
$532$	199394.	−	3211.44i	0.704511	−	0.0113469i
$533$		−	270388.i		−	0.951773i
$534$	162449.	+	159854.i	0.569684	+	0.560583i
$535$		0			0
$536$	255715.	−	268377.i	0.890073	−	0.934150i
$537$		−	274581.i		−	0.952188i
$538$	189885.	+	186851.i	0.656032	+	0.645551i
$539$			363533.i			1.25132i
$540$		0			0
$541$	−102454.			−0.350053			−0.175027	−	0.984564i	$-0.556001\pi$
$541$	−102454.			−0.350053			−0.175027	+	0.984564i	$0.556001\pi$
$542$	−302570.	+	307482.i	−1.02998	+	1.04670i
$543$	−327592.			−1.11105
$544$	−32454.7	+	35179.2i	−0.109668	+	0.118874i
$545$		0			0
$546$	219685.	−	223252.i	0.736911	−	0.748875i
$547$	−66168.6			−0.221145			−0.110573	−	0.993868i	$-0.535268\pi$
$547$	−66168.6			−0.221145			−0.110573	+	0.993868i	$0.535268\pi$
$548$	393855.	−	6343.45i	1.31152	−	0.0211234i
$549$	130121.			0.431720
$550$		0			0
$551$			207468.i			0.683358i
$552$	−170178.	+	178605.i	−0.558501	+	0.586158i
$553$		−	69794.2i		−	0.228228i
$554$	−213562.	+	217029.i	−0.695831	+	0.707128i
$555$		0			0
$556$	−300236.	+	4835.61i	−0.971210	+	0.0156424i
$557$			344220.i			1.10950i	0.832018	+	0.554749i	$0.187186\pi$
$557$			344220.i			1.10950i	−0.832018	+	0.554749i	$0.812814\pi$
$558$	−80834.3	+	82146.7i	−0.259614	+	0.263829i
$559$		−	294943.i		−	0.943874i
$560$		0			0
$561$	−53611.6			−0.170346
$562$	−364759.	−	358931.i	−1.15487	−	1.13642i
$563$	581940.			1.83595			0.917976	−	0.396637i	$-0.129823\pi$
$563$	581940.			1.83595			0.917976	+	0.396637i	$0.129823\pi$
$564$	−544.538	−	33809.6i	−0.00171187	−	0.106287i
$565$		0			0
$566$	−335837.	−	330472.i	−1.04833	−	1.03158i
$567$	46381.3			0.144270
$568$	14334.5	+	13658.2i	0.0444311	+	0.0423347i
$569$	−269874.			−0.833559			−0.416779	−	0.909008i	$-0.636841\pi$
$569$	−269874.			−0.833559			−0.416779	+	0.909008i	$0.636841\pi$
$570$		0			0
$571$		−	248959.i		−	0.763581i	−0.924249	−	0.381790i	$-0.875308\pi$
$571$		−	248959.i		−	0.763581i	0.924249	−	0.381790i	$-0.124692\pi$
$572$	−13471.3	−	836416.i	−0.0411736	−	2.55641i
$573$			107717.i			0.328077i
$574$	207078.	+	203770.i	0.628507	+	0.618466i
$575$		0			0
$576$	−5341.06	−	110463.i	−0.0160984	−	0.332944i
$577$			389168.i			1.16892i	0.811422	+	0.584461i	$0.198694\pi$
$577$			389168.i			1.16892i	−0.811422	+	0.584461i	$0.801306\pi$
$578$	−231899.	−	228194.i	−0.694133	−	0.683043i
$579$			91284.1i			0.272294i
$580$		0			0
$581$	−197061.			−0.583779
$582$	179879.	−	182800.i	0.531050	−	0.539672i
$583$	−318388.			−0.936742
$584$	46183.4	+	44004.3i	0.135413	+	0.129024i
$585$		0			0
$586$	338120.	−	343610.i	0.984636	−	1.00062i
$587$	−67273.5			−0.195240			−0.0976198	−	0.995224i	$-0.531123\pi$
$587$	−67273.5			−0.195240			−0.0976198	+	0.995224i	$0.531123\pi$
$588$	2204.98	+	136904.i	0.00637748	+	0.395968i
$589$	−209047.			−0.602579
$590$		0			0
$591$			263969.i			0.755750i
$592$	−18856.3	−	585227.i	−0.0538038	−	1.66986i
$593$			483157.i			1.37398i	0.726669	+	0.686988i	$0.241067\pi$
$593$			483157.i			1.37398i	−0.726669	+	0.686988i	$0.758933\pi$
$594$	86884.1	−	88294.7i	0.246245	−	0.250243i
$595$		0			0
$596$	−1693.62	−	105154.i	−0.00476786	−	0.296029i
$597$			167011.i			0.468594i
$598$	−492955.	+	500959.i	−1.37849	+	1.40088i
$599$			361016.i			1.00617i	0.864236	+	0.503086i	$0.167802\pi$
$599$			361016.i			1.00617i	−0.864236	+	0.503086i	$0.832198\pi$
$600$		0			0
$601$	−329300.			−0.911681			−0.455841	−	0.890061i	$-0.650661\pi$
$601$	−329300.			−0.911681			−0.455841	+	0.890061i	$0.650661\pi$
$602$	225883.	+	222274.i	0.623290	+	0.613333i
$603$	156388.			0.430099
$604$	125156.	−	2015.77i	0.343067	−	0.00552545i
$605$		0			0
$606$	−221012.	−	217481.i	−0.601826	−	0.592211i
$607$	347112.			0.942090			0.471045	−	0.882109i	$-0.343877\pi$
$607$	347112.			0.942090			0.471045	+	0.882109i	$0.343877\pi$
$608$	136022.	−	147440.i	0.367960	−	0.398850i
$609$	−350120.			−0.944021
$610$		0			0
$611$		−	96333.6i		−	0.258045i
$612$	−20189.7	+	325.175i	−0.0539046	+	0.000868190i
$613$		−	315831.i		−	0.840492i	−0.907410	−	0.420246i	$-0.861944\pi$
$613$		−	315831.i		−	0.840492i	0.907410	−	0.420246i	$-0.138056\pi$
$614$	256609.	+	252509.i	0.680667	+	0.669792i
$615$		0			0
$616$	650724.	+	620021.i	1.71489	+	1.63397i
$617$			302237.i			0.793920i	0.917836	+	0.396960i	$0.129935\pi$
$617$			302237.i			0.793920i	−0.917836	+	0.396960i	$0.870065\pi$
$618$	−149380.	−	146993.i	−0.391124	−	0.384876i
$619$		−	367141.i		−	0.958190i	−0.877763	−	0.479095i	$-0.840965\pi$
$619$		−	367141.i		−	0.958190i	0.877763	−	0.479095i	$-0.159035\pi$
$620$		0			0
$621$	−104076.			−0.269878
$622$	100843.	−	102481.i	0.260655	−	0.264887i
$623$	−697647.			−1.79746
$624$	−10146.4	−	314905.i	−0.0260581	−	0.808744i
$625$		0			0
$626$	−29236.0	+	29710.7i	−0.0746052	+	0.0758165i
$627$	224693.			0.571549
$628$	−147222.	+	2371.17i	−0.373297	+	0.00601234i
$629$	−106908.			−0.270215
$630$		0			0
$631$			210709.i			0.529206i	0.964357	+	0.264603i	$0.0852409\pi$
$631$			210709.i			0.529206i	−0.964357	+	0.264603i	$0.914759\pi$
$632$	−50828.9	−	48430.6i	−0.127255	−	0.121251i
$633$			49578.3i			0.123733i
$634$	−124221.	+	126238.i	−0.309043	+	0.314060i
$635$		0			0
$636$	−119902.	+	1931.15i	−0.296424	+	0.00477422i
$637$			390079.i			0.961334i
$638$	−655864.	+	666512.i	−1.61129	+	1.63745i
$639$			8352.97i			0.0204569i
$640$		0			0
$641$	−415962.			−1.01237			−0.506183	−	0.862426i	$-0.668944\pi$
$641$	−415962.			−1.01237			−0.506183	+	0.862426i	$0.668944\pi$
$642$	−273714.	−	269341.i	−0.664089	−	0.653479i
$643$	−732294.			−1.77118			−0.885592	−	0.464465i	$-0.846247\pi$
$643$	−732294.			−1.77118			−0.885592	+	0.464465i	$0.846247\pi$
$644$	−12161.1	−	755063.i	−0.0293225	−	1.82059i
$645$		0			0
$646$	−26106.4	−	25689.4i	−0.0625580	−	0.0615585i
$647$	96321.2			0.230098			0.115049	−	0.993360i	$-0.463297\pi$
$647$	96321.2			0.230098			0.115049	+	0.993360i	$0.463297\pi$
$648$	32184.3	−	33778.0i	0.0766467	−	0.0804423i
$649$	−545667.			−1.29550
$650$		0			0
$651$		−	352785.i		−	0.832430i
$652$	11251.4	+	698584.i	0.0264675	+	1.64333i
$653$		−	274691.i		−	0.644196i	−0.946706	−	0.322098i	$-0.895612\pi$
$653$		−	274691.i		−	0.644196i	0.946706	−	0.322098i	$-0.104388\pi$
$654$	−10027.9	−	9867.66i	−0.0234452	−	0.0230706i
$655$		0			0
$656$	292092.	−	9411.32i	0.678752	−	0.0218697i
$657$			26911.8i			0.0623465i
$658$	73777.5	+	72598.8i	0.170401	+	0.167679i
$659$		−	360421.i		−	0.829927i	−0.909838	−	0.414963i	$-0.863794\pi$
$659$		−	360421.i		−	0.829927i	0.909838	−	0.414963i	$-0.136206\pi$
$660$		0			0
$661$	461663.			1.05663			0.528314	−	0.849049i	$-0.322824\pi$
$661$	461663.			1.05663			0.528314	+	0.849049i	$0.322824\pi$
$662$	−614465.	+	624442.i	−1.40211	+	1.42487i
$663$	−57526.4			−0.130870
$664$	−136742.	+	143513.i	−0.310145	+	0.325504i
$665$		0			0
$666$	173258.	−	176071.i	0.390611	−	0.396953i
$667$	785640.			1.76592
$668$	5066.35	+	314562.i	0.0113538	+	0.704943i
$669$	−173912.			−0.388578
$670$		0			0
$671$			1.06379e6i			2.36272i
$672$	248818.	+	229548.i	0.550989	+	0.508317i
$673$		−	295518.i		−	0.652459i	−0.945291	−	0.326230i	$-0.894222\pi$
$673$		−	295518.i		−	0.652459i	0.945291	−	0.326230i	$-0.105778\pi$
$674$	−143570.	+	145901.i	−0.316042	+	0.321173i
$675$		0			0
$676$	−7095.93	−	440576.i	−0.0155280	−	0.964111i
$677$		−	865789.i		−	1.88901i	−0.328494	−	0.944506i	$-0.606541\pi$
$677$		−	865789.i		−	1.88901i	0.328494	−	0.944506i	$-0.393459\pi$
$678$	−83006.6	+	84354.3i	−0.180573	+	0.183505i
$679$			785046.i			1.70277i
$680$		0			0
$681$	5971.77			0.0128768
$682$	−671586.	−	660856.i	−1.44389	−	1.42082i
$683$	631289.			1.35328			0.676638	−	0.736316i	$-0.263436\pi$
$683$	631289.			1.35328			0.676638	+	0.736316i	$0.263436\pi$
$684$	84617.4	−	1362.85i	0.180862	−	0.00291297i
$685$		0			0
$686$	136790.	+	134604.i	0.290673	+	0.286029i
$687$	256650.			0.543785
$688$	318617.	−	10266.0i	0.673119	−	0.0216882i
$689$	−341638.			−0.719660
$690$		0			0
$691$		−	692970.i		−	1.45130i	−0.688062	−	0.725652i	$-0.741538\pi$
$691$		−	692970.i		−	1.45130i	0.688062	−	0.725652i	$-0.258462\pi$
$692$	509885.	−	8212.23i	1.06478	−	0.0171494i
$693$			379188.i			0.789564i
$694$	−224946.	−	221352.i	−0.467045	−	0.459584i
$695$		0			0
$696$	−242950.	+	254981.i	−0.501532	+	0.526368i
$697$		−	53358.8i		−	0.109835i
$698$	533402.	+	524880.i	1.09482	+	1.07733i
$699$			218675.i			0.447553i
$700$		0			0
$701$	−106868.			−0.217477			−0.108739	−	0.994070i	$-0.534681\pi$
$701$	−106868.			−0.217477			−0.108739	+	0.994070i	$0.534681\pi$
$702$	93228.5	−	94742.2i	0.189180	−	0.192251i
$703$	448066.			0.906633
$704$	903083.	−	43665.5i	1.82214	−	0.0881035i
$705$		0			0
$706$	74561.4	−	75772.0i	0.149591	−	0.152020i
$707$	949151.			1.89888
$708$	−205493.	+	3309.69i	−0.409951	+	0.00660268i
$709$	−71602.5			−0.142441			−0.0712207	−	0.997461i	$-0.522689\pi$
$709$	−71602.5			−0.142441			−0.0712207	+	0.997461i	$0.522689\pi$
$710$		0			0
$711$		−	29618.8i		−	0.0585906i
$712$	−484102.	+	508075.i	−0.954942	+	1.00223i
$713$			791620.i			1.55718i
$714$	43352.9	−	44056.8i	0.0850397	−	0.0864204i
$715$		0			0
$716$	845382.	−	13615.8i	1.64902	−	0.0265592i
$717$			179477.i			0.349117i
$718$	−37066.0	+	37667.8i	−0.0718997	+	0.0730671i
$719$		−	84839.0i		−	0.164111i	−0.996628	−	0.0820555i	$-0.973852\pi$
$719$		−	84839.0i		−	0.164111i	0.996628	−	0.0820555i	$-0.0261485\pi$
$720$		0			0
$721$	641521.			1.23407
$722$	−262144.	−	257956.i	−0.502882	−	0.494848i
$723$	356804.			0.682579
$724$	−16244.4	−	1.00859e6i	−0.0309903	−	1.92414i
$725$		0			0
$726$	504945.	+	496877.i	0.958011	+	0.942706i
$727$	−80916.8			−0.153098			−0.0765491	−	0.997066i	$-0.524390\pi$
$727$	−80916.8			−0.153098			−0.0765491	+	0.997066i	$0.524390\pi$
$728$	698241.	+	665296.i	1.31748	+	1.25531i
$729$	19683.0			0.0370370
$730$		0			0
$731$		−	58204.4i		−	0.108923i
$732$	6452.34	+	400616.i	0.0120419	+	0.747663i
$733$		−	62103.9i		−	0.115588i	−0.998329	−	0.0577938i	$-0.981593\pi$
$733$		−	62103.9i		−	0.115588i	0.998329	−	0.0577938i	$-0.0184066\pi$
$734$	133778.	+	131640.i	0.248308	+	0.244341i
$735$		0			0
$736$	−558327.	−	515086.i	−1.03070	−	0.950877i
$737$			1.27854e6i			2.35385i
$738$	87878.4	+	86474.4i	0.161350	+	0.158772i
$739$			268031.i			0.490790i	0.969423	+	0.245395i	$0.0789176\pi$
$739$			268031.i			0.490790i	−0.969423	+	0.245395i	$0.921082\pi$
$740$		0			0
$741$	241100.			0.439098
$742$	257464.	−	261644.i	0.467637	−	0.475230i
$743$	−348633.			−0.631525			−0.315763	−	0.948838i	$-0.602260\pi$
$743$	−348633.			−0.631525			−0.315763	+	0.948838i	$0.602260\pi$
$744$	−256922.	−	244799.i	−0.464147	−	0.442247i
$745$		0			0
$746$	666291.	−	677109.i	1.19725	−	1.21669i
$747$	−83627.5			−0.149868
$748$	−2658.45	−	165059.i	−0.00475145	−	0.295010i
$749$	1.17548e6			2.09533
$750$		0			0
$751$			757069.i			1.34232i	0.741313	+	0.671159i	$0.234203\pi$
$751$			757069.i			1.34232i	−0.741313	+	0.671159i	$0.765797\pi$
$752$	104066.	−	3353.05i	0.184023	−	0.00592932i
$753$		−	322179.i		−	0.568207i
$754$	−703756.	+	715182.i	−1.23788	+	1.25798i
$755$		0			0
$756$	2299.92	+	142799.i	0.00402411	+	0.249851i
$757$			128542.i			0.224312i	0.993691	+	0.112156i	$0.0357756\pi$
$757$			128542.i			0.224312i	−0.993691	+	0.112156i	$0.964224\pi$
$758$	303408.	−	308334.i	0.528066	−	0.536639i
$759$		−	850866.i		−	1.47699i
$760$		0			0
$761$	460176.			0.794611			0.397306	−	0.917686i	$-0.369945\pi$
$761$	460176.			0.794611			0.397306	+	0.917686i	$0.369945\pi$
$762$	−323473.	−	318305.i	−0.557094	−	0.548193i
$763$	43065.4			0.0739740
$764$	−331640.	+	5341.40i	−0.568172	+	0.00915100i
$765$		0			0
$766$	408019.	+	401501.i	0.695382	+	0.684272i
$767$	−585512.			−0.995280
$768$	339829.	−	21921.6i	0.576153	−	0.0371664i
$769$	−1.10194e6			−1.86340			−0.931701	−	0.363226i	$-0.881675\pi$
$769$	−1.10194e6			−1.86340			−0.931701	+	0.363226i	$0.881675\pi$
$770$		0			0
$771$			342829.i			0.576725i
$772$	−281046.	+	4526.53i	−0.471566	+	0.00759506i
$773$		−	809541.i		−	1.35481i	−0.735608	−	0.677407i	$-0.763103\pi$
$773$		−	809541.i		−	1.35481i	0.735608	−	0.677407i	$-0.236897\pi$
$774$	95858.8	+	94327.3i	0.160011	+	0.157455i
$775$		0			0
$776$	571724.	+	544748.i	0.949430	+	0.904633i
$777$			756149.i			1.25246i
$778$	−376520.	−	370505.i	−0.622055	−	0.612117i
$779$			223633.i			0.368520i
$780$		0			0
$781$	−68289.2			−0.111957
$782$	−97280.4	+	98859.8i	−0.159079	+	0.161661i
$783$	−148582.			−0.242349
$784$	−421390.	+	13577.4i	−0.685570	+	0.0220894i
$785$		0			0
$786$	−100870.	+	102508.i	−0.163274	+	0.165925i
$787$	−363079.			−0.586207			−0.293104	−	0.956081i	$-0.594688\pi$
$787$	−363079.			−0.586207			−0.293104	+	0.956081i	$0.594688\pi$
$788$	−812709.	+	13089.5i	−1.30883	+	0.0210800i
$789$	238448.			0.383036
$790$		0			0
$791$		−	362265.i		−	0.578993i
$792$	276150.	+	263121.i	0.440246	+	0.419473i
$793$			1.14147e6i			1.81518i
$794$	−129446.	+	131548.i	−0.205328	+	0.208662i
$795$		0			0
$796$	−514194.	+	8281.64i	−0.811524	+	0.0130704i
$797$			483796.i			0.761633i	0.924651	+	0.380816i	$0.124357\pi$
$797$			483796.i			0.761633i	−0.924651	+	0.380816i	$0.875643\pi$
$798$	−181697.	+	184647.i	−0.285327	+	0.289960i
$799$		−	19010.6i		−	0.0297785i
$800$		0			0
$801$	−296063.			−0.461444
$802$	−9251.77	−	9103.96i	−0.0143839	−	0.0141541i
$803$	−220016.			−0.341211
$804$	7754.85	+	481487.i	0.0119967	+	0.744857i
$805$		0			0
$806$	−720626.	−	709113.i	−1.10928	−	1.09155i
$807$	−346065.			−0.531386
$808$	658622.	−	691237.i	1.00882	−	1.05878i
$809$	−483640.			−0.738966			−0.369483	−	0.929237i	$-0.620465\pi$
$809$	−483640.			−0.738966			−0.369483	+	0.929237i	$0.620465\pi$
$810$		0			0
$811$			406318.i			0.617767i	0.951100	+	0.308883i	$0.0999553\pi$
$811$			406318.i			0.617767i	−0.951100	+	0.308883i	$0.900045\pi$
$812$	−17361.5	−	1.07795e6i	−0.0263315	−	1.63488i
$813$		−	560386.i		−	0.847826i
$814$	1.43946e6	+	1.41646e6i	2.17245	+	2.13774i
$815$		0			0
$816$	−2002.30	−	62143.8i	−0.00300711	−	0.0933292i
$817$			243942.i			0.365462i
$818$	−542358.	−	533693.i	−0.810549	−	0.797599i
$819$			406877.i			0.606589i
$820$		0			0
$821$	489931.			0.726857			0.363428	−	0.931622i	$-0.381606\pi$
$821$	489931.			0.726857			0.363428	+	0.931622i	$0.381606\pi$
$822$	−358901.	+	364728.i	−0.531167	+	0.539791i
$823$	−372808.			−0.550408			−0.275204	−	0.961386i	$-0.588745\pi$
$823$	−372808.			−0.550408			−0.275204	+	0.961386i	$0.588745\pi$
$824$	445156.	−	467200.i	0.655628	−	0.688095i
$825$		0			0
$826$	441253.	−	448417.i	0.646736	−	0.657237i
$827$	−222364.			−0.325127			−0.162563	−	0.986698i	$-0.551976\pi$
$827$	−222364.			−0.325127			−0.162563	+	0.986698i	$0.551976\pi$
$828$	−5160.84	−	320429.i	−0.00752766	−	0.467381i
$829$	−127764.			−0.185908			−0.0929542	−	0.995670i	$-0.529631\pi$
$829$	−127764.			−0.185908			−0.0929542	+	0.995670i	$0.529631\pi$
$830$		0			0
$831$		−	395536.i		−	0.572774i
$832$	969028.	−	46854.0i	1.39988	−	0.0676862i
$833$			76978.8i			0.110938i
$834$	273590.	−	278032.i	0.393341	−	0.399727i
$835$		0			0
$836$	11141.9	+	691784.i	0.0159422	+	0.989824i
$837$		−	149712.i		−	0.213701i
$838$	−108472.	+	110233.i	−0.154465	+	0.156972i
$839$		−	981082.i		−	1.39374i	−0.717198	−	0.696870i	$-0.754576\pi$
$839$		−	981082.i		−	1.39374i	0.717198	−	0.696870i	$-0.245424\pi$
$840$		0			0
$841$	414320.			0.585793
$842$	613617.	+	603814.i	0.865512	+	0.851684i
$843$	664774.			0.935446
$844$	−152642.	+	2458.45i	−0.214283	+	0.00345125i
$845$		0			0
$846$	31309.2	+	30809.0i	0.0437453	+	0.0430464i
$847$	−2.16852e6			−3.02271
$848$	−11891.3	−	369060.i	−0.0165362	−	0.513222i
$849$	612064.			0.849144
$850$		0			0
$851$		−	1.69674e6i		−	2.34291i
$852$	−25717.1	+	414.201i	−0.0354278	+	0.000570601i
$853$			192525.i			0.264599i	0.991210	+	0.132299i	$0.0422360\pi$
$853$			192525.i			0.264599i	−0.991210	+	0.132299i	$0.957764\pi$
$854$	−874203.	−	860236.i	−1.19866	−	1.17951i
$855$		0			0
$856$	815674.	−	856066.i	1.11319	−	1.16831i
$857$		−	1.20031e6i		−	1.63430i	−0.576424	−	0.817151i	$-0.695552\pi$
$857$		−	1.20031e6i		−	1.63430i	0.576424	−	0.817151i	$-0.304448\pi$
$858$	774559.	+	762184.i	1.05216	+	1.03535i
$859$			1.29982e6i			1.76156i	0.473529	+	0.880778i	$0.342980\pi$
$859$			1.29982e6i			1.76156i	−0.473529	+	0.880778i	$0.657020\pi$
$860$		0			0
$861$	−377400.			−0.509091
$862$	36002.2	−	36586.7i	0.0484523	−	0.0492390i
$863$	−148386.			−0.199238			−0.0996188	−	0.995026i	$-0.531762\pi$
$863$	−148386.			−0.199238			−0.0996188	+	0.995026i	$0.531762\pi$
$864$	105592.	+	97414.0i	0.141450	+	0.130495i
$865$		0			0
$866$	−688103.	+	699275.i	−0.917525	+	0.932421i
$867$	422636.			0.562248
$868$	1.08615e6	−	17493.6i	1.44162	−	0.0232188i
$869$	242147.			0.320656
$870$		0			0
$871$			1.37190e6i			1.80837i
$872$	29883.3	−	31363.1i	0.0393003	−	0.0412465i
$873$			333153.i			0.437134i
$874$	407714.	−	414334.i	0.533744	−	0.542410i
$875$		0			0
$876$	−82856.1	+	1334.48i	−0.107973	+	0.00173902i
$877$		−	144747.i		−	0.188196i	−0.995563	−	0.0940981i	$-0.970003\pi$
$877$		−	144747.i		−	0.188196i	0.995563	−	0.0940981i	$-0.0299967\pi$
$878$	23343.9	−	23722.9i	0.0302820	−	0.0307736i
$879$			626229.i			0.810505i
$880$		0			0
$881$	281633.			0.362853			0.181427	−	0.983404i	$-0.441928\pi$
$881$	281633.			0.362853			0.181427	+	0.983404i	$0.441928\pi$
$882$	−126779.	−	124754.i	−0.162971	−	0.160367i
$883$	334210.			0.428645			0.214323	−	0.976763i	$-0.431246\pi$
$883$	334210.			0.428645			0.214323	+	0.976763i	$0.431246\pi$
$884$	−2852.58	−	177112.i	−0.00365034	−	0.226644i
$885$		0			0
$886$	−402689.	−	396255.i	−0.512982	−	0.504787i
$887$	504313.			0.640992			0.320496	−	0.947250i	$-0.396150\pi$
$887$	504313.			0.640992			0.320496	+	0.947250i	$0.396150\pi$
$888$	550679.	+	524696.i	0.698349	+	0.665399i
$889$	1.38918e6			1.75774
$890$		0			0
$891$			160917.i			0.202697i
$892$	−8623.85	−	535442.i	−0.0108386	−	0.672950i
$893$			79675.8i			0.0999133i
$894$	97377.7	+	95822.0i	0.121839	+	0.119892i
$895$		0			0
$896$	−694394.	+	777444.i	−0.864948	+	0.968396i
$897$		−	912998.i		−	1.13471i
$898$	−563453.	−	554451.i	−0.698723	−	0.687560i
$899$			1.13014e6i			1.39834i
$900$		0			0
$901$	−67419.2			−0.0830489
$902$	−706967.	+	718445.i	−0.868932	+	0.883040i
$903$	−411672.			−0.504866
$904$	−263826.	−	251378.i	−0.322835	−	0.307603i
$905$		0			0
$906$	−114049.	+	115900.i	−0.138942	+	0.141198i
$907$	83306.2			0.101266			0.0506329	−	0.998717i	$-0.483876\pi$
$907$	83306.2			0.101266			0.0506329	+	0.998717i	$0.483876\pi$
$908$	296.124	+	18385.9i	0.000359172	+	0.0223004i
$909$	402795.			0.487479
$910$		0			0
$911$			115795.i			0.139525i	0.997564	+	0.0697626i	$0.0222242\pi$
$911$			115795.i			0.139525i	−0.997564	+	0.0697626i	$0.977776\pi$
$912$	8391.89	+	260453.i	0.0100895	+	0.313140i
$913$		−	683691.i		−	0.820198i
$914$	−929574.	+	944667.i	−1.11274	+	1.13080i
$915$		0			0
$916$	12726.6	+	790173.i	0.0151677	+	0.941741i
$917$		−	440227.i		−	0.523525i
$918$	18397.8	−	18696.5i	0.0218314	−	0.0221858i
$919$		−	788234.i		−	0.933306i	−0.884441	−	0.466653i	$-0.845460\pi$
$919$		−	788234.i		−	0.933306i	0.884441	−	0.466653i	$-0.154540\pi$
$920$		0			0
$921$	−467670.			−0.551341
$922$	559075.	+	550143.i	0.657671	+	0.647163i
$923$	−73275.8			−0.0860117
$924$	−1.16744e6	+	18802.9i	−1.36739	+	0.0220232i
$925$		0			0
$926$	−481107.	−	473420.i	−0.561073	−	0.552109i
$927$	272245.			0.316811
$928$	−797083.	−	735352.i	−0.925567	−	0.853884i
$929$	15865.8			0.0183837			0.00919183	−	0.999958i	$-0.497074\pi$
$929$	15865.8			0.0183837			0.00919183	+	0.999958i	$0.497074\pi$
$930$		0			0
$931$		−	322628.i		−	0.372222i
$932$	−673256.	+	10843.5i	−0.775084	+	0.0124835i
$933$			186771.i			0.214559i
$934$	−165945.	−	163294.i	−0.190227	−	0.187188i
$935$		0			0
$936$	296315.	+	282334.i	0.338222	+	0.322264i
$937$		−	15433.2i		−	0.0175783i	−0.999961	−	0.00878913i	$-0.997202\pi$
$937$		−	15433.2i		−	0.0175783i	0.999961	−	0.00878913i	$-0.00279770\pi$
$938$	−1.05068e6	−	1.03389e6i	−1.19416	−	1.17508i
$939$		−	54147.7i		−	0.0614114i
$940$		0			0
$941$	−550507.			−0.621704			−0.310852	−	0.950458i	$-0.600614\pi$
$941$	−550507.			−0.621704			−0.310852	+	0.950458i	$0.600614\pi$
$942$	134157.	−	136335.i	0.151185	−	0.153640i
$943$	846854.			0.952325
$944$	−20379.7	−	632510.i	−0.0228694	−	0.709779i
$945$		0			0
$946$	−771167.	+	783688.i	−0.861720	+	0.875711i
$947$	1.27984e6			1.42710			0.713552	−	0.700602i	$-0.247085\pi$
$947$	1.27984e6			1.42710			0.713552	+	0.700602i	$0.247085\pi$
$948$	91190.4	−	1468.72i	0.101469	−	0.00163426i
$949$	−236082.			−0.262138
$950$		0			0
$951$		−	230069.i		−	0.254389i
$952$	137792.	+	131290.i	0.152037	+	0.144864i
$953$		−	491859.i		−	0.541571i	−0.962640	−	0.270785i	$-0.912717\pi$
$953$		−	491859.i		−	0.541571i	0.962640	−	0.270785i	$-0.0872834\pi$
$954$	109261.	−	111035.i	0.120052	−	0.122001i
$955$		0			0
$956$	−552575.	+	8899.80i	−0.604611	+	0.00973788i
$957$		−	1.21472e6i		−	1.32633i
$958$	621992.	−	632090.i	0.677725	−	0.688729i
$959$		−	1.56635e6i		−	1.70314i
$960$		0			0
$961$	−215219.			−0.233042
$962$	1.54457e6	+	1.51989e6i	1.66900	+	1.64234i
$963$	498843.			0.537912
$964$	17692.9	+	1.09853e6i	0.0190391	+	1.18211i
$965$		0			0
$966$	699223.	+	688052.i	0.749310	+	0.737338i
$967$	−628976.			−0.672638			−0.336319	−	0.941748i	$-0.609182\pi$
$967$	−628976.			−0.672638			−0.336319	+	0.941748i	$0.609182\pi$
$968$	−1.50475e6	+	1.57926e6i	−1.60588	+	1.68540i
$969$	47579.0			0.0506720
$970$		0			0
$971$		−	1.78700e6i		−	1.89533i	−0.319264	−	0.947666i	$-0.603436\pi$
$971$		−	1.78700e6i		−	1.89533i	0.319264	−	0.947666i	$-0.396564\pi$
$972$	976.027	+	60600.1i	0.00103307	+	0.0641417i
$973$			1.19403e6i			1.26121i
$974$	−415040.	−	408409.i	−0.437494	−	0.430505i
$975$		0			0
$976$	−1.23310e6	+	39730.9i	−1.29449	+	0.0417089i
$977$		−	842171.i		−	0.882289i	−0.897436	−	0.441145i	$-0.854573\pi$
$977$		−	842171.i		−	0.882289i	0.897436	−	0.441145i	$-0.145427\pi$
$978$	−646921.	−	636585.i	−0.676353	−	0.665547i
$979$		−	2.42045e6i		−	2.52540i
$980$		0			0
$981$	18275.8			0.0189906
$982$	686232.	−	697373.i	0.711620	−	0.723173i
$983$	−877633.			−0.908251			−0.454125	−	0.890938i	$-0.650048\pi$
$983$	−877633.			−0.908251			−0.454125	+	0.890938i	$0.650048\pi$
$984$	−261880.	+	274848.i	−0.270466	+	0.283859i
$985$		0			0
$986$	−138880.	+	141135.i	−0.142852	+	0.145171i
$987$	−134459.			−0.138025
$988$	11955.5	+	742300.i	0.0122477	+	0.760441i
$989$	923758.			0.944421
$990$		0			0
$991$			326910.i			0.332875i	0.986052	+	0.166437i	$0.0532264\pi$
$991$			326910.i			0.332875i	−0.986052	+	0.166437i	$0.946774\pi$
$992$	740949.	−	803150.i	0.752948	−	0.816157i
$993$		−	1.13805e6i		−	1.15415i
$994$	55222.0	−	56118.6i	0.0558907	−	0.0567981i
$995$		0			0
$996$	−4146.86	−	257472.i	−0.00418024	−	0.259545i
$997$		−	935659.i		−	0.941298i	−0.882320	−	0.470649i	$-0.844020\pi$
$997$		−	935659.i		−	0.941298i	0.882320	−	0.470649i	$-0.155980\pi$
$998$	318212.	−	323378.i	0.319488	−	0.324676i
$999$			320890.i			0.321532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.f.c.199.7		32
4.3	odd	2	inner	300.5.f.c.199.25		32
5.2	odd	4		300.5.c.c.151.11	yes	16
5.3	odd	4		300.5.c.b.151.6	yes	16
5.4	even	2	inner	300.5.f.c.199.26		32
20.3	even	4		300.5.c.b.151.5	✓	16
20.7	even	4		300.5.c.c.151.12	yes	16
20.19	odd	2	inner	300.5.f.c.199.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.5	✓	16	20.3	even	4
300.5.c.b.151.6	yes	16	5.3	odd	4
300.5.c.c.151.11	yes	16	5.2	odd	4
300.5.c.c.151.12	yes	16	20.7	even	4
300.5.f.c.199.7		32	1.1	even	1	trivial
300.5.f.c.199.8		32	20.19	odd	2	inner
300.5.f.c.199.25		32	4.3	odd	2	inner
300.5.f.c.199.26		32	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.85111 - 2.80556i) q^{2} +5.19615 q^{3} +(0.257663 + 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232 q^{7} +(44.1485 - 46.3347i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(-2.85111 - 2.80556i) q^{2} +5.19615 q^{3} +(0.257663 + 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232 q^{7} +(44.1485 - 46.3347i) q^{8} +27.0000 q^{9} +220.737i q^{11} +(1.33886 + 83.1277i) q^{12} +236.856i q^{13} +(-181.397 - 178.499i) q^{14} +(-255.867 + 8.24415i) q^{16} +46.7414i q^{17} +(-76.9800 - 75.7501i) q^{18} -195.899i q^{19} +330.596 q^{21} +(619.291 - 629.345i) q^{22} -741.830 q^{23} +(229.402 - 240.762i) q^{24} +(664.512 - 675.301i) q^{26} +140.296 q^{27} +(16.3934 + 1017.84i) q^{28} -1059.06 q^{29} -1067.12i q^{31} +(752.635 + 694.346i) q^{32} +1146.98i q^{33} +(131.136 - 133.265i) q^{34} +(6.95691 + 431.944i) q^{36} +2287.23i q^{37} +(-549.606 + 558.530i) q^{38} +1230.74i q^{39} -1141.57 q^{41} +(-942.565 - 927.506i) q^{42} -1245.24 q^{43} +(-3531.33 + 56.8758i) q^{44} +(2115.04 + 2081.25i) q^{46} -406.719 q^{47} +(-1329.53 + 42.8379i) q^{48} +1646.91 q^{49} +242.875i q^{51} +(-3789.20 + 61.0290i) q^{52} +1442.39i q^{53} +(-400.000 - 393.609i) q^{54} +(2808.87 - 2947.96i) q^{56} -1017.92i q^{57} +(3019.49 + 2971.25i) q^{58} +2472.02i q^{59} +4819.29 q^{61} +(-2993.86 + 3042.47i) q^{62} +1717.83 q^{63} +(-197.817 - 4091.22i) q^{64} +(3217.93 - 3270.17i) q^{66} +5792.14 q^{67} +(-747.765 + 12.0435i) q^{68} -3854.66 q^{69} +309.369i q^{71} +(1192.01 - 1251.04i) q^{72} +996.733i q^{73} +(6416.96 - 6521.15i) q^{74} +(3133.98 - 50.4759i) q^{76} +14044.0i q^{77} +(3452.91 - 3508.97i) q^{78} -1096.99i q^{79} +729.000 q^{81} +(3254.76 + 3202.76i) q^{82} -3097.31 q^{83} +(85.1824 + 5288.85i) q^{84} +(3550.32 + 3493.60i) q^{86} -5503.02 q^{87} +(10227.8 + 9745.21i) q^{88} -10965.3 q^{89} +15069.5i q^{91} +(-191.142 - 11867.7i) q^{92} -5544.91i q^{93} +(1159.60 + 1141.07i) q^{94} +(3910.81 + 3607.93i) q^{96} +12339.0i q^{97} +(-4695.52 - 4620.50i) q^{98} +5959.90i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 36 q^{6} + 864 q^{9}+O(q^{10}) \) 32 * q - 16 * q^4 + 36 * q^6 + 864 * q^9	\( 32 q - 16 q^{4} + 36 q^{6} + 864 q^{9} - 156 q^{14} - 752 q^{16} - 288 q^{21} - 216 q^{24} + 1356 q^{26} - 3456 q^{29} + 5864 q^{34} - 432 q^{36} + 2496 q^{41} - 16176 q^{44} + 11912 q^{46} + 21440 q^{49} + 972 q^{54} - 20472 q^{56} - 7520 q^{61} - 21088 q^{64} + 16200 q^{66} - 19584 q^{69} + 34008 q^{74} - 56688 q^{76} + 23328 q^{81} - 30240 q^{84} + 48828 q^{86} + 1536 q^{89} + 90312 q^{94} - 22176 q^{96}+O(q^{100}) \) 32 * q - 16 * q^4 + 36 * q^6 + 864 * q^9 - 156 * q^14 - 752 * q^16 - 288 * q^21 - 216 * q^24 + 1356 * q^26 - 3456 * q^29 + 5864 * q^34 - 432 * q^36 + 2496 * q^41 - 16176 * q^44 + 11912 * q^46 + 21440 * q^49 + 972 * q^54 - 20472 * q^56 - 7520 * q^61 - 21088 * q^64 + 16200 * q^66 - 19584 * q^69 + 34008 * q^74 - 56688 * q^76 + 23328 * q^81 - 30240 * q^84 + 48828 * q^86 + 1536 * q^89 + 90312 * q^94 - 22176 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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