LMFDB - Embedded newform 300.5.c.b.151.10

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			151.10
Root			$-3.04390 - 2.59512i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.b.151.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725488 + 3.93366i) q^{2} +5.19615i q^{3} +(-14.9473 - 5.70765i) q^{4} +(-20.4399 - 3.76975i) q^{6} +36.7329i q^{7} +(33.2960 - 54.6569i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-0.725488 + 3.93366i) q^{2} +5.19615i q^{3} +(-14.9473 - 5.70765i) q^{4} +(-20.4399 - 3.76975i) q^{6} +36.7329i q^{7} +(33.2960 - 54.6569i) q^{8} -27.0000 q^{9} -156.989i q^{11} +(29.6578 - 77.6686i) q^{12} +62.1869 q^{13} +(-144.495 - 26.6493i) q^{14} +(190.846 + 170.628i) q^{16} +306.493 q^{17} +(19.5882 - 106.209i) q^{18} -242.784i q^{19} -190.870 q^{21} +(617.541 + 113.894i) q^{22} -571.211i q^{23} +(284.005 + 173.011i) q^{24} +(-45.1158 + 244.622i) q^{26} -140.296i q^{27} +(209.658 - 549.059i) q^{28} -266.538 q^{29} +759.271i q^{31} +(-809.649 + 626.932i) q^{32} +815.738 q^{33} +(-222.357 + 1205.64i) q^{34} +(403.578 + 154.106i) q^{36} +1214.97 q^{37} +(955.029 + 176.137i) q^{38} +323.132i q^{39} +2677.60 q^{41} +(138.474 - 750.816i) q^{42} -2635.37i q^{43} +(-896.037 + 2346.57i) q^{44} +(2246.95 + 414.407i) q^{46} +2374.46i q^{47} +(-886.610 + 991.663i) q^{48} +1051.70 q^{49} +1592.58i q^{51} +(-929.528 - 354.941i) q^{52} +1396.48 q^{53} +(551.877 + 101.783i) q^{54} +(2007.70 + 1223.06i) q^{56} +1261.54 q^{57} +(193.370 - 1048.47i) q^{58} +2901.75i q^{59} -4786.97 q^{61} +(-2986.71 - 550.842i) q^{62} -991.788i q^{63} +(-1878.75 - 3639.72i) q^{64} +(-591.809 + 3208.84i) q^{66} +4656.43i q^{67} +(-4581.25 - 1749.35i) q^{68} +2968.10 q^{69} +6767.57i q^{71} +(-898.993 + 1475.74i) q^{72} -6581.94 q^{73} +(-881.450 + 4779.29i) q^{74} +(-1385.72 + 3628.97i) q^{76} +5766.65 q^{77} +(-1271.09 - 234.429i) q^{78} -8545.74i q^{79} +729.000 q^{81} +(-1942.57 + 10532.8i) q^{82} -2173.65i q^{83} +(2852.99 + 1089.42i) q^{84} +(10366.6 + 1911.93i) q^{86} -1384.97i q^{87} +(-8580.52 - 5227.11i) q^{88} +6633.68 q^{89} +2284.30i q^{91} +(-3260.27 + 8538.08i) q^{92} -3945.29 q^{93} +(-9340.31 - 1722.64i) q^{94} +(-3257.64 - 4207.06i) q^{96} +15704.1 q^{97} +(-762.993 + 4137.01i) q^{98} +4238.70i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.725488	+	3.93366i	−0.181372	+	0.983415i
$2$	−0.725488	+	3.93366i	−0.181372	+	0.983415i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−14.9473	−	5.70765i	−0.934208	−	0.356728i
$5$		0			0
$5$		0			0
$6$	−20.4399	−	3.76975i	−0.567775	−	0.104715i
$7$			36.7329i			0.749650i	0.927095	+	0.374825i	$0.122297\pi$
$7$			36.7329i			0.749650i	−0.927095	+	0.374825i	$0.877703\pi$
$8$	33.2960	−	54.6569i	0.520251	−	0.854014i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	156.989i		−	1.29743i	−0.761032	−	0.648715i	$-0.775307\pi$
$11$		−	156.989i		−	1.29743i	0.761032	−	0.648715i	$-0.224693\pi$
$12$	29.6578	−	77.6686i	0.205957	−	0.539365i
$13$	62.1869			0.367970			0.183985	−	0.982929i	$-0.441100\pi$
$13$	62.1869			0.367970			0.183985	+	0.982929i	$0.441100\pi$
$14$	−144.495	−	26.6493i	−0.737217	−	0.135966i
$15$		0			0
$16$	190.846	+	170.628i	0.745490	+	0.666516i
$17$	306.493			1.06053			0.530264	−	0.847832i	$-0.322093\pi$
$17$	306.493			1.06053			0.530264	+	0.847832i	$0.322093\pi$
$18$	19.5882	−	106.209i	0.0604574	−	0.327805i
$19$		−	242.784i		−	0.672532i	−0.941767	−	0.336266i	$-0.890836\pi$
$19$		−	242.784i		−	0.672532i	0.941767	−	0.336266i	$-0.109164\pi$
$20$		0			0
$21$	−190.870			−0.432811
$22$	617.541	+	113.894i	1.27591	+	0.235317i
$23$		−	571.211i		−	1.07979i	−0.841731	−	0.539897i	$-0.818463\pi$
$23$		−	571.211i		−	1.07979i	0.841731	−	0.539897i	$-0.181537\pi$
$24$	284.005	+	173.011i	0.493065	+	0.300367i
$25$		0			0
$26$	−45.1158	+	244.622i	−0.0667394	+	0.361867i
$27$		−	140.296i		−	0.192450i
$28$	209.658	−	549.059i	0.267421	−	0.700330i
$29$	−266.538			−0.316930			−0.158465	−	0.987365i	$-0.550654\pi$
$29$	−266.538			−0.316930			−0.158465	+	0.987365i	$0.550654\pi$
$30$		0			0
$31$			759.271i			0.790084i	0.918663	+	0.395042i	$0.129270\pi$
$31$			759.271i			0.790084i	−0.918663	+	0.395042i	$0.870730\pi$
$32$	−809.649	+	626.932i	−0.790673	+	0.612239i
$33$	815.738			0.749071
$34$	−222.357	+	1205.64i	−0.192350	+	1.04294i
$35$		0			0
$36$	403.578	+	154.106i	0.311403	+	0.118909i
$37$	1214.97			0.887490			0.443745	−	0.896153i	$-0.353650\pi$
$37$	1214.97			0.887490			0.443745	+	0.896153i	$0.353650\pi$
$38$	955.029	+	176.137i	0.661377	+	0.121978i
$39$			323.132i			0.212447i
$40$		0			0
$41$	2677.60			1.59286			0.796431	−	0.604730i	$-0.206719\pi$
$41$	2677.60			1.59286			0.796431	+	0.604730i	$0.206719\pi$
$42$	138.474	−	750.816i	0.0784998	−	0.425633i
$43$		−	2635.37i		−	1.42530i	−0.701522	−	0.712648i	$-0.747496\pi$
$43$		−	2635.37i		−	1.42530i	0.701522	−	0.712648i	$-0.252504\pi$
$44$	−896.037	+	2346.57i	−0.462829	+	1.21207i
$45$		0			0
$46$	2246.95	+	414.407i	1.06188	+	0.195844i
$47$			2374.46i			1.07490i	0.843295	+	0.537451i	$0.180613\pi$
$47$			2374.46i			1.07490i	−0.843295	+	0.537451i	$0.819387\pi$
$48$	−886.610	+	991.663i	−0.384813	+	0.430409i
$49$	1051.70			0.438024
$50$		0			0
$51$			1592.58i			0.612297i
$52$	−929.528	−	354.941i	−0.343760	−	0.131265i
$53$	1396.48			0.497143			0.248572	−	0.968613i	$-0.420039\pi$
$53$	1396.48			0.497143			0.248572	+	0.968613i	$0.420039\pi$
$54$	551.877	+	101.783i	0.189258	+	0.0349051i
$55$		0			0
$56$	2007.70	+	1223.06i	0.640212	+	0.390006i
$57$	1261.54			0.388286
$58$	193.370	−	1048.47i	0.0574822	−	0.311673i
$59$			2901.75i			0.833597i	0.908999	+	0.416798i	$0.136848\pi$
$59$			2901.75i			0.833597i	−0.908999	+	0.416798i	$0.863152\pi$
$60$		0			0
$61$	−4786.97			−1.28647			−0.643237	−	0.765667i	$-0.722409\pi$
$61$	−4786.97			−1.28647			−0.643237	+	0.765667i	$0.722409\pi$
$62$	−2986.71	−	550.842i	−0.776980	−	0.143299i
$63$		−	991.788i		−	0.249883i
$64$	−1878.75	−	3639.72i	−0.458678	−	0.888602i
$65$		0			0
$66$	−591.809	+	3208.84i	−0.135861	+	0.736647i
$67$			4656.43i			1.03730i	0.854987	+	0.518649i	$0.173565\pi$
$67$			4656.43i			1.03730i	−0.854987	+	0.518649i	$0.826435\pi$
$68$	−4581.25	−	1749.35i	−0.990755	−	0.378320i
$69$	2968.10			0.623419
$70$		0			0
$71$			6767.57i			1.34251i	0.741228	+	0.671253i	$0.234244\pi$
$71$			6767.57i			1.34251i	−0.741228	+	0.671253i	$0.765756\pi$
$72$	−898.993	+	1475.74i	−0.173417	+	0.284671i
$73$	−6581.94			−1.23512			−0.617559	−	0.786525i	$-0.711878\pi$
$73$	−6581.94			−1.23512			−0.617559	+	0.786525i	$0.711878\pi$
$74$	−881.450	+	4779.29i	−0.160966	+	0.872771i
$75$		0			0
$76$	−1385.72	+	3628.97i	−0.239911	+	0.628285i
$77$	5766.65			0.972618
$78$	−1271.09	−	234.429i	−0.208924	−	0.0385320i
$79$		−	8545.74i		−	1.36929i	−0.728876	−	0.684645i	$-0.759957\pi$
$79$		−	8545.74i		−	1.36929i	0.728876	−	0.684645i	$-0.240043\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−1942.57	+	10532.8i	−0.288901	+	1.56644i
$83$		−	2173.65i		−	0.315525i	−0.987477	−	0.157763i	$-0.949572\pi$
$83$		−	2173.65i		−	0.315525i	0.987477	−	0.157763i	$-0.0504281\pi$
$84$	2852.99	+	1089.42i	0.404336	+	0.154396i
$85$		0			0
$86$	10366.6	+	1911.93i	1.40166	+	0.258509i
$87$		−	1384.97i		−	0.182980i
$88$	−8580.52	−	5227.11i	−1.10802	−	0.674988i
$89$	6633.68			0.837480			0.418740	−	0.908106i	$-0.362472\pi$
$89$	6633.68			0.837480			0.418740	+	0.908106i	$0.362472\pi$
$90$		0			0
$91$			2284.30i			0.275849i
$92$	−3260.27	+	8538.08i	−0.385192	+	1.00875i
$93$	−3945.29			−0.456155
$94$	−9340.31	−	1722.64i	−1.05707	−	0.194957i
$95$		0			0
$96$	−3257.64	−	4207.06i	−0.353476	−	0.456495i
$97$	15704.1			1.66905			0.834525	−	0.550970i	$-0.185742\pi$
$97$	15704.1			1.66905			0.834525	+	0.550970i	$0.185742\pi$
$98$	−762.993	+	4137.01i	−0.0794454	+	0.430759i
$99$			4238.70i			0.432476i
$100$		0			0
$101$	−13188.7			−1.29288			−0.646440	−	0.762965i	$-0.723743\pi$
$101$	−13188.7			−1.29288			−0.646440	+	0.762965i	$0.723743\pi$
$102$	−6264.68	−	1155.40i	−0.602141	−	0.111054i
$103$			2187.77i			0.206218i	0.994670	+	0.103109i	$0.0328791\pi$
$103$			2187.77i			0.206218i	−0.994670	+	0.103109i	$0.967121\pi$
$104$	2070.58	−	3398.94i	0.191436	−	0.314251i
$105$		0			0
$106$	−1013.13	+	5493.26i	−0.0901680	+	0.488898i
$107$		−	12415.4i		−	1.08441i	−0.840246	−	0.542205i	$-0.817590\pi$
$107$		−	12415.4i		−	1.08441i	0.840246	−	0.542205i	$-0.182410\pi$
$108$	−800.761	+	2097.05i	−0.0686523	+	0.179788i
$109$	13504.8			1.13667			0.568336	−	0.822797i	$-0.307588\pi$
$109$	13504.8			1.13667			0.568336	+	0.822797i	$0.307588\pi$
$110$		0			0
$111$			6313.19i			0.512393i
$112$	−6267.66	+	7010.31i	−0.499654	+	0.558857i
$113$	24496.4			1.91843			0.959213	−	0.282683i	$-0.0912245\pi$
$113$	24496.4			1.91843			0.959213	+	0.282683i	$0.0912245\pi$
$114$	−915.234	+	4962.48i	−0.0704243	+	0.381846i
$115$		0			0
$116$	3984.03	+	1521.30i	0.296079	+	0.113058i
$117$	−1679.05			−0.122657
$118$	−11414.5	−	2105.19i	−0.819771	−	0.151191i
$119$			11258.4i			0.795026i
$120$		0			0
$121$	−10004.5			−0.683322
$122$	3472.89	−	18830.3i	0.233330	−	1.26514i
$123$			13913.2i			0.919639i
$124$	4333.65	−	11349.1i	0.281845	−	0.738103i
$125$		0			0
$126$	3901.35	+	719.530i	0.245739	+	0.0453219i
$127$		−	6927.31i		−	0.429494i	−0.976670	−	0.214747i	$-0.931107\pi$
$127$		−	6927.31i		−	0.429494i	0.976670	−	0.214747i	$-0.0688927\pi$
$128$	15680.4	−	4749.78i	0.957056	−	0.289903i
$129$	13693.8			0.822895
$130$		0			0
$131$			1893.13i			0.110316i	0.998478	+	0.0551579i	$0.0175662\pi$
$131$			1893.13i			0.110316i	−0.998478	+	0.0551579i	$0.982434\pi$
$132$	−12193.1	−	4655.95i	−0.699788	−	0.267215i
$133$	8918.15			0.504164
$134$	−18316.8	−	3378.19i	−1.02009	−	0.188137i
$135$		0			0
$136$	10205.0	−	16751.9i	0.551741	−	0.905706i
$137$	35998.2			1.91796			0.958981	−	0.283470i	$-0.0914857\pi$
$137$	35998.2			1.91796			0.958981	+	0.283470i	$0.0914857\pi$
$138$	−2153.32	+	11675.5i	−0.113071	+	0.613079i
$139$		−	1899.55i		−	0.0983155i	−0.998791	−	0.0491577i	$-0.984346\pi$
$139$		−	1899.55i		−	0.0983155i	0.998791	−	0.0491577i	$-0.0156537\pi$
$140$		0			0
$141$	−12338.0			−0.620595
$142$	−26621.3	−	4909.80i	−1.32024	−	0.243493i
$143$		−	9762.65i		−	0.477414i
$144$	−5152.83	−	4606.96i	−0.248497	−	0.222172i
$145$		0			0
$146$	4775.12	−	25891.1i	0.224016	−	1.21463i
$147$			5464.77i			0.252893i
$148$	−18160.6	−	6934.64i	−0.829101	−	0.316593i
$149$	6118.77			0.275608			0.137804	−	0.990460i	$-0.455996\pi$
$149$	6118.77			0.275608			0.137804	+	0.990460i	$0.455996\pi$
$150$		0			0
$151$		−	30282.1i		−	1.32810i	−0.747687	−	0.664052i	$-0.768835\pi$
$151$		−	30282.1i		−	1.32810i	0.747687	−	0.664052i	$-0.231165\pi$
$152$	−13269.8	−	8083.74i	−0.574351	−	0.349885i
$153$	−8275.31			−0.353510
$154$	−4183.64	+	22684.0i	−0.176406	+	0.956487i
$155$		0			0
$156$	1844.33	−	4829.97i	0.0757859	−	0.198470i
$157$	11389.8			0.462078			0.231039	−	0.972945i	$-0.425788\pi$
$157$	11389.8			0.462078			0.231039	+	0.972945i	$0.425788\pi$
$158$	33616.0	+	6199.84i	1.34658	+	0.248351i
$159$			7256.30i			0.287026i
$160$		0			0
$161$	20982.2			0.809468
$162$	−528.881	+	2867.64i	−0.0201525	+	0.109268i
$163$			10601.7i			0.399027i	0.979895	+	0.199513i	$0.0639361\pi$
$163$			10601.7i			0.399027i	−0.979895	+	0.199513i	$0.936064\pi$
$164$	−40023.0	−	15282.8i	−1.48806	−	0.568218i
$165$		0			0
$166$	8550.41	+	1576.96i	0.310292	+	0.0572275i
$167$		−	15333.5i		−	0.549803i	−0.961472	−	0.274902i	$-0.911355\pi$
$167$		−	15333.5i		−	0.549803i	0.961472	−	0.274902i	$-0.0886453\pi$
$168$	−6355.20	+	10432.3i	−0.225170	+	0.369626i
$169$	−24693.8			−0.864598
$170$		0			0
$171$			6555.17i			0.224177i
$172$	−15041.8	+	39391.8i	−0.508443	+	1.33152i
$173$	37712.5			1.26007			0.630033	−	0.776568i	$-0.283041\pi$
$173$	37712.5			1.26007			0.630033	+	0.776568i	$0.283041\pi$
$174$	5448.01	+	1004.78i	0.179945	+	0.0331874i
$175$		0			0
$176$	26786.7	−	29960.6i	0.864758	−	0.967221i
$177$	−15077.9			−0.481277
$178$	−4812.65	+	26094.6i	−0.151895	+	0.823590i
$179$		−	26116.7i		−	0.815101i	−0.913183	−	0.407551i	$-0.866383\pi$
$179$		−	26116.7i		−	0.815101i	0.913183	−	0.407551i	$-0.133617\pi$
$180$		0			0
$181$	−44004.0			−1.34318			−0.671591	−	0.740922i	$-0.734389\pi$
$181$	−44004.0			−1.34318			−0.671591	+	0.740922i	$0.734389\pi$
$182$	−8985.66	−	1657.23i	−0.271273	−	0.0500312i
$183$		−	24873.8i		−	0.742746i
$184$	−31220.6	−	19019.1i	−0.922158	−	0.561763i
$185$		0			0
$186$	2862.26	−	15519.4i	0.0827338	−	0.448590i
$187$		−	48116.0i		−	1.37596i
$188$	13552.6	−	35491.8i	0.383448	−	1.00418i
$189$	5153.48			0.144270
$190$		0			0
$191$		−	34103.8i		−	0.934839i	−0.884036	−	0.467419i	$-0.845184\pi$
$191$		−	34103.8i		−	0.934839i	0.884036	−	0.467419i	$-0.154816\pi$
$192$	18912.5	−	9762.25i	0.513035	−	0.264818i
$193$	27574.1			0.740263			0.370132	−	0.928979i	$-0.379313\pi$
$193$	27574.1			0.740263			0.370132	+	0.928979i	$0.379313\pi$
$194$	−11393.1	+	61774.5i	−0.302719	+	1.64137i
$195$		0			0
$196$	−15720.1	−	6002.71i	−0.409206	−	0.156255i
$197$	45162.5			1.16371			0.581856	−	0.813292i	$-0.302327\pi$
$197$	45162.5			1.16371			0.581856	+	0.813292i	$0.302327\pi$
$198$	−16673.6	−	3075.13i	−0.425304	−	0.0784391i
$199$		−	56574.1i		−	1.42860i	−0.699838	−	0.714302i	$-0.746745\pi$
$199$		−	56574.1i		−	1.42860i	0.699838	−	0.714302i	$-0.253255\pi$
$200$		0			0
$201$	−24195.5			−0.598885
$202$	9568.23	−	51879.7i	0.234492	−	1.27144i
$203$		−	9790.71i		−	0.237587i
$204$	9089.90	−	23804.9i	0.218423	−	0.572013i
$205$		0			0
$206$	−8605.94	−	1587.20i	−0.202798	−	0.0374023i
$207$			15422.7i			0.359931i
$208$	11868.1	+	10610.8i	0.274318	+	0.245258i
$209$	−38114.4			−0.872562
$210$		0			0
$211$		−	75965.3i		−	1.70628i	−0.521681	−	0.853140i	$-0.674695\pi$
$211$		−	75965.3i		−	1.70628i	0.521681	−	0.853140i	$-0.325305\pi$
$212$	−20873.6	−	7970.59i	−0.464436	−	0.177345i
$213$	−35165.3			−0.775096
$214$	48838.0	+	9007.23i	1.06642	+	0.196682i
$215$		0			0
$216$	−7668.15	−	4671.31i	−0.164355	−	0.100122i
$217$	−27890.2			−0.592287
$218$	−9797.57	+	53123.2i	−0.206160	+	1.11782i
$219$		−	34200.8i		−	0.713096i
$220$		0			0
$221$	19059.8			0.390242
$222$	−24833.9	−	4580.15i	−0.503895	−	0.0929338i
$223$			92718.2i			1.86447i	0.361854	+	0.932235i	$0.382144\pi$
$223$			92718.2i			1.86447i	−0.361854	+	0.932235i	$0.617856\pi$
$224$	−23029.0	−	29740.7i	−0.458965	−	0.592728i
$225$		0			0
$226$	−17771.8	+	96360.4i	−0.347949	+	1.88661i
$227$			35666.1i			0.692155i	0.938206	+	0.346078i	$0.112487\pi$
$227$			35666.1i			0.692155i	−0.938206	+	0.346078i	$0.887513\pi$
$228$	−18856.7	−	7200.44i	−0.362740	−	0.138513i
$229$	103760.			1.97861			0.989307	−	0.145850i	$-0.0465916\pi$
$229$	103760.			1.97861			0.989307	+	0.145850i	$0.0465916\pi$
$230$		0			0
$231$			29964.4i			0.561541i
$232$	−8874.66	+	14568.1i	−0.164883	+	0.270662i
$233$	17612.7			0.324425			0.162213	−	0.986756i	$-0.448137\pi$
$233$	17612.7			0.324425			0.162213	+	0.986756i	$0.448137\pi$
$234$	1218.13	−	6604.79i	0.0222465	−	0.120622i
$235$		0			0
$236$	16562.2	−	43373.4i	0.297367	−	0.778753i
$237$	44405.0			0.790560
$238$	−44286.6	−	8167.81i	−0.781840	−	0.144196i
$239$			57194.0i			1.00128i	0.865656	+	0.500639i	$0.166902\pi$
$239$			57194.0i			1.00128i	−0.865656	+	0.500639i	$0.833098\pi$
$240$		0			0
$241$	−32787.4			−0.564512			−0.282256	−	0.959339i	$-0.591083\pi$
$241$	−32787.4			−0.564512			−0.282256	+	0.959339i	$0.591083\pi$
$242$	7258.16	−	39354.4i	0.123936	−	0.671989i
$243$			3788.00i			0.0641500i
$244$	71552.4	+	27322.3i	1.20183	+	0.458921i
$245$		0			0
$246$	−54729.8	−	10093.9i	−0.904386	−	0.166797i
$247$		−	15098.0i		−	0.247471i
$248$	41499.4	+	25280.7i	0.674743	+	0.411042i
$249$	11294.6			0.182169
$250$		0			0
$251$			28803.4i			0.457190i	0.973522	+	0.228595i	$0.0734131\pi$
$251$			28803.4i			0.457190i	−0.973522	+	0.228595i	$0.926587\pi$
$252$	−5660.77	+	14824.6i	−0.0891404	+	0.233443i
$253$	−89673.7			−1.40096
$254$	27249.7	+	5025.69i	0.422371	+	0.0778983i
$255$		0			0
$256$	7308.04	+	65127.3i	0.111512	+	0.993763i
$257$	−97466.3			−1.47567			−0.737833	−	0.674983i	$-0.764151\pi$
$257$	−97466.3			−1.47567			−0.737833	+	0.674983i	$0.764151\pi$
$258$	−9934.69	+	53866.7i	−0.149250	+	0.809247i
$259$			44629.5i			0.665308i
$260$		0			0
$261$	7196.53			0.105643
$262$	−7446.93	−	1373.44i	−0.108486	−	0.0200082i
$263$		−	82950.9i		−	1.19925i	−0.800281	−	0.599625i	$-0.795316\pi$
$263$		−	82950.9i		−	1.19925i	0.800281	−	0.599625i	$-0.204684\pi$
$264$	27160.9	−	44585.7i	0.389705	−	0.639717i
$265$		0			0
$266$	−6470.01	+	35081.0i	−0.0914412	+	0.495802i
$267$			34469.6i			0.483519i
$268$	26577.3	−	69601.3i	0.370033	−	0.969053i
$269$	−76939.2			−1.06327			−0.531634	−	0.846974i	$-0.678422\pi$
$269$	−76939.2			−1.06327			−0.531634	+	0.846974i	$0.678422\pi$
$270$		0			0
$271$			73991.7i			1.00750i	0.863850	+	0.503749i	$0.168046\pi$
$271$			73991.7i			1.00750i	−0.863850	+	0.503749i	$0.831954\pi$
$272$	58492.8	+	52296.3i	0.790614	+	0.706860i
$273$	−11869.6			−0.159261
$274$	−26116.3	+	141605.i	−0.347865	+	1.88615i
$275$		0			0
$276$	−44365.1	−	16940.9i	−0.582403	−	0.222391i
$277$	−40327.2			−0.525580			−0.262790	−	0.964853i	$-0.584643\pi$
$277$	−40327.2			−0.525580			−0.262790	+	0.964853i	$0.584643\pi$
$278$	7472.19	+	1378.10i	0.0966849	+	0.0178317i
$279$		−	20500.3i		−	0.263361i
$280$		0			0
$281$	39798.8			0.504031			0.252016	−	0.967723i	$-0.418907\pi$
$281$	39798.8			0.504031			0.252016	+	0.967723i	$0.418907\pi$
$282$	8951.11	−	48533.7i	0.112559	−	0.610302i
$283$			29271.4i			0.365486i	0.983161	+	0.182743i	$0.0584976\pi$
$283$			29271.4i			0.365486i	−0.983161	+	0.182743i	$0.941502\pi$
$284$	38626.9	−	101157.i	0.478909	−	1.25418i
$285$		0			0
$286$	38402.9	+	7082.69i	0.469496	+	0.0865896i
$287$			98356.0i			1.19409i
$288$	21860.5	−	16927.2i	0.263558	−	0.204080i
$289$	10416.9			0.124722
$290$		0			0
$291$			81600.8i			0.963626i
$292$	98382.5	+	37567.4i	1.15386	+	0.440601i
$293$	14569.2			0.169707			0.0848535	−	0.996393i	$-0.472958\pi$
$293$	14569.2			0.169707			0.0848535	+	0.996393i	$0.472958\pi$
$294$	−21496.5	−	3964.63i	−0.248699	−	0.0458678i
$295$		0			0
$296$	40453.8	−	66406.7i	0.461718	−	0.757929i
$297$	−22024.9			−0.249690
$298$	−4439.09	+	24069.1i	−0.0499875	+	0.271037i
$299$		−	35521.8i		−	0.397331i
$300$		0			0
$301$	96804.8			1.06847
$302$	119119.	+	21969.3i	1.30608	+	0.240881i
$303$		−	68530.3i		−	0.746445i
$304$	41425.8	−	46334.2i	0.448253	−	0.501366i
$305$		0			0
$306$	6003.64	−	32552.2i	0.0641168	−	0.347647i
$307$		−	103447.i		−	1.09759i	−0.835956	−	0.548796i	$-0.815086\pi$
$307$		−	103447.i		−	1.09759i	0.835956	−	0.548796i	$-0.184914\pi$
$308$	−86196.1	−	32914.0i	−0.908628	−	0.346960i
$309$	−11368.0			−0.119060
$310$		0			0
$311$			140701.i			1.45471i	0.686262	+	0.727354i	$0.259250\pi$
$311$			140701.i			1.45471i	−0.686262	+	0.727354i	$0.740750\pi$
$312$	17661.4	+	10759.0i	0.181433	+	0.110526i
$313$	−100063.			−1.02138			−0.510688	−	0.859766i	$-0.670609\pi$
$313$	−100063.			−1.02138			−0.510688	+	0.859766i	$0.670609\pi$
$314$	−8263.14	+	44803.4i	−0.0838080	+	0.454414i
$315$		0			0
$316$	−48776.1	+	127736.i	−0.488464	+	1.27920i
$317$	15226.6			0.151525			0.0757623	−	0.997126i	$-0.475861\pi$
$317$	15226.6			0.151525			0.0757623	+	0.997126i	$0.475861\pi$
$318$	−28543.8	−	5264.36i	−0.282265	−	0.0520585i
$319$			41843.5i			0.411194i
$320$		0			0
$321$	64512.3			0.626084
$322$	−15222.3	+	82536.8i	−0.146815	+	0.796042i
$323$		−	74411.5i		−	0.713239i
$324$	−10896.6	−	4160.87i	−0.103801	−	0.0396364i
$325$		0			0
$326$	−41703.6	−	7691.44i	−0.392409	−	0.0723723i
$327$			70172.9i			0.656257i
$328$	89153.5	−	146349.i	0.828687	−	1.36033i
$329$	−87220.7			−0.805801
$330$		0			0
$331$		−	174253.i		−	1.59047i	−0.606304	−	0.795233i	$-0.707348\pi$
$331$		−	174253.i		−	1.59047i	0.606304	−	0.795233i	$-0.292652\pi$
$332$	−12406.4	+	32490.3i	−0.112557	+	0.294766i
$333$	−32804.3			−0.295830
$334$	60316.6	+	11124.2i	0.540684	+	0.0997189i
$335$		0			0
$336$	−36426.6	−	32567.7i	−0.322656	−	0.288476i
$337$	−202345.			−1.78170			−0.890848	−	0.454302i	$-0.849889\pi$
$337$	−202345.			−1.78170			−0.890848	+	0.454302i	$0.849889\pi$
$338$	17915.1	−	97136.9i	0.156814	−	0.850259i
$339$			127287.i			1.10760i
$340$		0			0
$341$	119197.			1.02508
$342$	−25785.8	−	4755.70i	−0.220459	−	0.0406595i
$343$			126827.i			1.07802i
$344$	−144041.	−	87747.4i	−1.21722	−	0.741511i
$345$		0			0
$346$	−27360.0	+	148348.i	−0.228541	+	1.23917i
$347$			106576.i			0.885115i	0.896740	+	0.442558i	$0.145929\pi$
$347$			106576.i			0.885115i	−0.896740	+	0.442558i	$0.854071\pi$
$348$	−7904.93	+	20701.6i	−0.0652739	+	0.170941i
$349$	−192354.			−1.57925			−0.789624	−	0.613590i	$-0.789725\pi$
$349$	−192354.			−1.57925			−0.789624	+	0.613590i	$0.789725\pi$
$350$		0			0
$351$		−	8724.57i		−	0.0708158i
$352$	98421.4	+	127106.i	0.794336	+	1.02584i
$353$	−76180.9			−0.611360			−0.305680	−	0.952134i	$-0.598884\pi$
$353$	−76180.9			−0.611360			−0.305680	+	0.952134i	$0.598884\pi$
$354$	10938.9	−	59311.4i	0.0872902	−	0.473295i
$355$		0			0
$356$	−99155.8	−	37862.7i	−0.782380	−	0.298752i
$357$	−58500.2			−0.459008
$358$	102734.	+	18947.3i	0.801582	+	0.147837i
$359$			169799.i			1.31749i	0.752368	+	0.658743i	$0.228912\pi$
$359$			169799.i			1.31749i	−0.752368	+	0.658743i	$0.771088\pi$
$360$		0			0
$361$	71377.0			0.547701
$362$	31924.4	−	173097.i	0.243616	−	1.32091i
$363$		−	51985.0i		−	0.394516i
$364$	13038.0	−	34144.2i	0.0984029	−	0.257700i
$365$		0			0
$366$	97845.1	+	18045.7i	0.730427	+	0.134713i
$367$			7980.18i			0.0592489i	0.999561	+	0.0296245i	$0.00943114\pi$
$367$			7980.18i			0.0592489i	−0.999561	+	0.0296245i	$0.990569\pi$
$368$	97464.6	−	109013.i	0.719700	−	0.804976i
$369$	−72295.2			−0.530954
$370$		0			0
$371$			51296.6i			0.372684i
$372$	58971.5	+	22518.3i	0.426144	+	0.162723i
$373$	259277.			1.86357			0.931786	−	0.363007i	$-0.118250\pi$
$373$	259277.			1.86357			0.931786	+	0.363007i	$0.118250\pi$
$374$	189272.	+	34907.6i	1.35314	+	0.249561i
$375$		0			0
$376$	129780.	+	79060.1i	0.917981	+	0.559219i
$377$	−16575.2			−0.116621
$378$	−3738.79	+	20272.0i	−0.0261666	+	0.141878i
$379$		−	11693.1i		−	0.0814048i	−0.999171	−	0.0407024i	$-0.987040\pi$
$379$		−	11693.1i		−	0.0814048i	0.999171	−	0.0407024i	$-0.0129596\pi$
$380$		0			0
$381$	35995.4			0.247969
$382$	134153.	+	24741.9i	0.919334	+	0.169554i
$383$		−	34931.5i		−	0.238133i	−0.992886	−	0.119067i	$-0.962010\pi$
$383$		−	34931.5i		−	0.238133i	0.992886	−	0.119067i	$-0.0379902\pi$
$384$	24680.6	+	81477.8i	0.167376	+	0.552557i
$385$		0			0
$386$	−20004.7	+	108467.i	−0.134263	+	0.727986i
$387$			71155.0i			0.475098i
$388$	−234734.	−	89633.4i	−1.55924	−	0.595397i
$389$	110218.			0.728375			0.364187	−	0.931326i	$-0.381347\pi$
$389$	110218.			0.728375			0.364187	+	0.931326i	$0.381347\pi$
$390$		0			0
$391$		−	175072.i		−	1.14515i
$392$	35017.3	−	57482.4i	0.227882	−	0.374079i
$393$	−9836.99			−0.0636909
$394$	−32764.9	+	177654.i	−0.211065	+	1.14441i
$395$		0			0
$396$	24193.0	−	63357.3i	0.154276	−	0.404023i
$397$	−44836.0			−0.284476			−0.142238	−	0.989832i	$-0.545430\pi$
$397$	−44836.0			−0.284476			−0.142238	+	0.989832i	$0.545430\pi$
$398$	222543.	+	41043.9i	1.40491	+	0.259109i
$399$			46340.1i			0.291079i
$400$		0			0
$401$	183752.			1.14273			0.571364	−	0.820697i	$-0.306414\pi$
$401$	183752.			1.14273			0.571364	+	0.820697i	$0.306414\pi$
$402$	17553.6	−	95177.0i	0.108621	−	0.588952i
$403$			47216.7i			0.290727i
$404$	197135.	+	75276.3i	1.20782	+	0.461206i
$405$		0			0
$406$	38513.3	+	7103.05i	0.233646	+	0.0430916i
$407$		−	190738.i		−	1.15146i
$408$	87045.6	+	53026.7i	0.522910	+	0.318548i
$409$	−116120.			−0.694160			−0.347080	−	0.937836i	$-0.612827\pi$
$409$	−116120.			−0.694160			−0.347080	+	0.937836i	$0.612827\pi$
$410$		0			0
$411$			187052.i			1.10734i
$412$	12487.0	−	32701.3i	0.0735638	−	0.192651i
$413$	−106590.			−0.624906
$414$	−60667.6	−	11189.0i	−0.353961	−	0.0652815i
$415$		0			0
$416$	−50349.5	+	38987.0i	−0.290944	+	0.225285i
$417$	9870.37			0.0567625
$418$	27651.5	−	149929.i	0.158258	−	0.858090i
$419$		−	26586.3i		−	0.151436i	−0.997129	−	0.0757181i	$-0.975875\pi$
$419$		−	26586.3i		−	0.151436i	0.997129	−	0.0757181i	$-0.0241249\pi$
$420$		0			0
$421$	−41926.6			−0.236551			−0.118276	−	0.992981i	$-0.537737\pi$
$421$	−41926.6			−0.236551			−0.118276	+	0.992981i	$0.537737\pi$
$422$	298822.	+	55112.0i	1.67798	+	0.309472i
$423$		−	64110.4i		−	0.358301i
$424$	46497.1	−	76327.0i	0.258639	−	0.424567i
$425$		0			0
$426$	25512.1	−	138328.i	0.140581	−	0.762241i
$427$		−	175839.i		−	0.964406i
$428$	−70862.7	+	185577.i	−0.386839	+	1.01306i
$429$	50728.2			0.275635
$430$		0			0
$431$			258465.i			1.39138i	0.718340	+	0.695692i	$0.244902\pi$
$431$			258465.i			1.39138i	−0.718340	+	0.695692i	$0.755098\pi$
$432$	23938.5	−	26774.9i	0.128271	−	0.143470i
$433$	−35539.8			−0.189557			−0.0947784	−	0.995498i	$-0.530214\pi$
$433$	−35539.8			−0.189557			−0.0947784	+	0.995498i	$0.530214\pi$
$434$	20234.0	−	109711.i	0.107424	−	0.582464i
$435$		0			0
$436$	−201861.	−	77080.6i	−1.06189	−	0.405482i
$437$	−138681.			−0.726195
$438$	134534.	+	24812.3i	0.701269	+	0.129336i
$439$		−	238795.i		−	1.23907i	−0.784969	−	0.619535i	$-0.787321\pi$
$439$		−	238795.i		−	1.23907i	0.784969	−	0.619535i	$-0.212679\pi$
$440$		0			0
$441$	−28395.8			−0.146008
$442$	−13827.7	+	74974.8i	−0.0707791	+	0.383770i
$443$			133181.i			0.678632i	0.940672	+	0.339316i	$0.110196\pi$
$443$			133181.i			0.678632i	−0.940672	+	0.339316i	$0.889804\pi$
$444$	36033.5	−	94365.4i	0.182785	−	0.478682i
$445$		0			0
$446$	−364722.	−	67266.0i	−1.83355	−	0.338163i
$447$			31794.0i			0.159122i
$448$	133697.	−	69011.8i	0.666141	−	0.343848i
$449$	190392.			0.944398			0.472199	−	0.881492i	$-0.343460\pi$
$449$	190392.			0.944398			0.472199	+	0.881492i	$0.343460\pi$
$450$		0			0
$451$		−	420354.i		−	2.06662i
$452$	−366156.	−	139817.i	−1.79221	−	0.684356i
$453$	157350.			0.766781
$454$	−140298.	−	25875.3i	−0.680675	−	0.125538i
$455$		0			0
$456$	42004.4	−	68951.9i	0.202006	−	0.331602i
$457$	4305.85			0.0206171			0.0103085	−	0.999947i	$-0.496719\pi$
$457$	4305.85			0.0206171			0.0103085	+	0.999947i	$0.496719\pi$
$458$	−75277.0	+	408158.i	−0.358865	+	1.94580i
$459$		−	42999.8i		−	0.204099i
$460$		0			0
$461$	−346295.			−1.62946			−0.814730	−	0.579840i	$-0.803115\pi$
$461$	−346295.			−1.62946			−0.814730	+	0.579840i	$0.803115\pi$
$462$	−117870.	−	21738.8i	−0.552228	−	0.101848i
$463$		−	148212.i		−	0.691388i	−0.938347	−	0.345694i	$-0.887643\pi$
$463$		−	148212.i		−	0.691388i	0.938347	−	0.345694i	$-0.112357\pi$
$464$	−50867.6	−	45478.9i	−0.236268	−	0.211239i
$465$		0			0
$466$	−12777.8	+	69282.4i	−0.0588417	+	0.319044i
$467$			171205.i			0.785023i	0.919747	+	0.392512i	$0.128394\pi$
$467$			171205.i			0.785023i	−0.919747	+	0.392512i	$0.871606\pi$
$468$	25097.2	+	9583.40i	0.114587	+	0.0437550i
$469$	−171044.			−0.777611
$470$		0			0
$471$			59182.9i			0.266781i
$472$	158601.	+	96616.8i	0.711903	+	0.433679i
$473$	−413724.			−1.84922
$474$	−32215.3	+	174674.i	−0.143386	+	0.777448i
$475$		0			0
$476$	64258.8	−	168283.i	0.283608	−	0.742720i
$477$	−37704.9			−0.165714
$478$	−224982.	−	41493.6i	−0.984672	−	0.181604i
$479$		−	55603.3i		−	0.242342i	−0.992632	−	0.121171i	$-0.961335\pi$
$479$		−	55603.3i		−	0.242342i	0.992632	−	0.121171i	$-0.0386650\pi$
$480$		0			0
$481$	75555.4			0.326569
$482$	23786.9	−	128975.i	0.102387	−	0.555150i
$483$			109027.i			0.467346i
$484$	149541.	+	57102.3i	0.638365	+	0.243760i
$485$		0			0
$486$	−14900.7	−	2748.15i	−0.0630861	−	0.0116350i
$487$			191414.i			0.807077i	0.914963	+	0.403538i	$0.132220\pi$
$487$			191414.i			0.807077i	−0.914963	+	0.403538i	$0.867780\pi$
$488$	−159387.	+	261641.i	−0.669289	+	1.09867i
$489$	−55088.3			−0.230378
$490$		0			0
$491$		−	234139.i		−	0.971206i	−0.874179	−	0.485603i	$-0.838600\pi$
$491$		−	234139.i		−	0.971206i	0.874179	−	0.485603i	$-0.161400\pi$
$492$	79411.7	−	207966.i	0.328061	−	0.859134i
$493$	−81692.0			−0.336113
$494$	59390.2	+	10953.4i	0.243367	+	0.0448844i
$495$		0			0
$496$	−129553.	+	144903.i	−0.526604	+	0.589000i
$497$	−248592.			−1.00641
$498$	−8194.13	+	44429.2i	−0.0330403	+	0.179147i
$499$		−	397603.i		−	1.59679i	−0.602133	−	0.798396i	$-0.705682\pi$
$499$		−	397603.i		−	1.59679i	0.602133	−	0.798396i	$-0.294318\pi$
$500$		0			0
$501$	79675.0			0.317429
$502$	−113303.	−	20896.5i	−0.449607	−	0.0829215i
$503$			34902.1i			0.137948i	0.997618	+	0.0689741i	$0.0219726\pi$
$503$			34902.1i			0.137948i	−0.997618	+	0.0689741i	$0.978027\pi$
$504$	−54208.0	−	33022.6i	−0.213404	−	0.130002i
$505$		0			0
$506$	65057.3	−	352746.i	0.254094	−	1.37772i
$507$		−	128313.i		−	0.499176i
$508$	−39538.7	+	103545.i	−0.153213	+	0.401237i
$509$	14871.2			0.0573997			0.0286999	−	0.999588i	$-0.490863\pi$
$509$	14871.2			0.0573997			0.0286999	+	0.999588i	$0.490863\pi$
$510$		0			0
$511$		−	241774.i		−	0.925907i
$512$	−261490.	−	18501.7i	−0.997506	−	0.0705785i
$513$	−34061.6			−0.129429
$514$	70710.7	−	383399.i	0.267645	−	1.45119i
$515$		0			0
$516$	−204686.	−	78159.3i	−0.768755	−	0.293550i
$517$	372764.			1.39461
$518$	−175557.	−	32378.2i	−0.654273	−	0.120668i
$519$			195960.i			0.727500i
$520$		0			0
$521$	−396677.			−1.46137			−0.730687	−	0.682713i	$-0.760800\pi$
$521$	−396677.			−1.46137			−0.730687	+	0.682713i	$0.760800\pi$
$522$	−5221.00	+	28308.7i	−0.0191607	+	0.103891i
$523$			492462.i			1.80040i	0.435474	+	0.900201i	$0.356581\pi$
$523$			492462.i			1.80040i	−0.435474	+	0.900201i	$0.643419\pi$
$524$	10805.3	−	28297.2i	0.0393527	−	0.103058i
$525$		0			0
$526$	326301.	+	60179.9i	1.17936	+	0.217511i
$527$			232711.i			0.837907i
$528$	155680.	+	139188.i	0.558425	+	0.499268i
$529$	−46440.6			−0.165954
$530$		0			0
$531$		−	78347.2i		−	0.277866i
$532$	−133303.	−	50901.7i	−0.470994	−	0.179849i
$533$	166512.			0.586125
$534$	−135592.	−	25007.3i	−0.475500	−	0.0876969i
$535$		0			0
$536$	254506.	+	155041.i	0.885867	+	0.539655i
$537$	135706.			0.470599
$538$	55818.5	−	302653.i	0.192847	−	1.04563i
$539$		−	165105.i		−	0.568305i
$540$		0			0
$541$	−350781.			−1.19851			−0.599255	−	0.800559i	$-0.704536\pi$
$541$	−350781.			−1.19851			−0.599255	+	0.800559i	$0.704536\pi$
$542$	−291058.	−	53680.1i	−0.990788	−	0.182732i
$543$		−	228651.i		−	0.775487i
$544$	−248152.	+	192150.i	−0.838532	+	0.649297i
$545$		0			0
$546$	8611.24	−	46690.9i	0.0288855	−	0.156620i
$547$		−	426263.i		−	1.42463i	−0.701858	−	0.712317i	$-0.747646\pi$
$547$		−	426263.i		−	1.42463i	0.701858	−	0.712317i	$-0.252354\pi$
$548$	−538078.	−	205465.i	−1.79178	−	0.684191i
$549$	129248.			0.428825
$550$		0			0
$551$			64711.1i			0.213145i
$552$	98825.9	−	162227.i	0.324334	−	0.532408i
$553$	313910.			1.02649
$554$	29256.9	−	158634.i	0.0953255	−	0.516863i
$555$		0			0
$556$	−10842.0	+	28393.3i	−0.0350719	+	0.0918471i
$557$	−46325.5			−0.149317			−0.0746585	−	0.997209i	$-0.523787\pi$
$557$	−46325.5			−0.149317			−0.0746585	+	0.997209i	$0.523787\pi$
$558$	80641.2	+	14872.7i	0.258993	+	0.0477664i
$559$		−	163885.i		−	0.524465i
$560$		0			0
$561$	250018.			0.794411
$562$	−28873.6	+	156555.i	−0.0914172	+	0.495672i
$563$			155857.i			0.491711i	0.969306	+	0.245855i	$0.0790689\pi$
$563$			155857.i			0.491711i	−0.969306	+	0.245855i	$0.920931\pi$
$564$	184421.	+	70421.2i	0.579765	+	0.221384i
$565$		0			0
$566$	−115144.	−	21236.0i	−0.359424	−	0.0662889i
$567$			26778.3i			0.0832945i
$568$	369894.	+	225333.i	1.14652	+	0.698440i
$569$	115079.			0.355443			0.177722	−	0.984081i	$-0.443127\pi$
$569$	115079.			0.355443			0.177722	+	0.984081i	$0.443127\pi$
$570$		0			0
$571$		−	297667.i		−	0.912973i	−0.889730	−	0.456487i	$-0.849108\pi$
$571$		−	297667.i		−	0.912973i	0.889730	−	0.456487i	$-0.150892\pi$
$572$	−55721.7	+	145926.i	−0.170307	+	0.446004i
$573$	177209.			0.539729
$574$	−386899.	−	71356.1i	−1.17428	−	0.216575i
$575$		0			0
$576$	50726.2	+	98272.3i	0.152893	+	0.296201i
$577$	56864.8			0.170802			0.0854008	−	0.996347i	$-0.472783\pi$
$577$	56864.8			0.170802			0.0854008	+	0.996347i	$0.472783\pi$
$578$	−7557.32	+	40976.4i	−0.0226210	+	0.122653i
$579$			143279.i			0.427391i
$580$		0			0
$581$	79844.5			0.236534
$582$	−320990.	−	59200.5i	−0.947644	−	0.174775i
$583$		−	219231.i		−	0.645008i
$584$	−219153.	+	359748.i	−0.642571	+	1.05481i
$585$		0			0
$586$	−10569.8	+	57310.2i	−0.0307801	+	0.166892i
$587$		−	265441.i		−	0.770358i	−0.922842	−	0.385179i	$-0.874140\pi$
$587$		−	265441.i		−	0.770358i	0.922842	−	0.385179i	$-0.125860\pi$
$588$	31191.0	−	81683.8i	0.0902141	−	0.236255i
$589$	184339.			0.531357
$590$		0			0
$591$			234671.i			0.671870i
$592$	231872.	+	207309.i	0.661616	+	0.591527i
$593$	−16961.6			−0.0482343			−0.0241172	−	0.999709i	$-0.507677\pi$
$593$	−16961.6			−0.0482343			−0.0241172	+	0.999709i	$0.507677\pi$
$594$	15978.8	−	86638.6i	0.0452869	−	0.245549i
$595$		0			0
$596$	−91459.2	−	34923.8i	−0.257475	−	0.0983170i
$597$	293968.			0.824804
$598$	139731.	+	25770.6i	0.390741	+	0.0720648i
$599$			236573.i			0.659342i	0.944096	+	0.329671i	$0.106938\pi$
$599$			236573.i			0.659342i	−0.944096	+	0.329671i	$0.893062\pi$
$600$		0			0
$601$	60822.4			0.168389			0.0841947	−	0.996449i	$-0.473168\pi$
$601$	60822.4			0.168389			0.0841947	+	0.996449i	$0.473168\pi$
$602$	−70230.7	+	380797.i	−0.193791	+	1.05075i
$603$		−	125724.i		−	0.345766i
$604$	−172839.	+	452636.i	−0.473772	+	1.24073i
$605$		0			0
$606$	269575.	+	49718.0i	0.734065	+	0.135384i
$607$		−	507342.i		−	1.37697i	−0.725252	−	0.688484i	$-0.758277\pi$
$607$		−	507342.i		−	1.37697i	0.725252	−	0.688484i	$-0.241723\pi$
$608$	152209.	+	196570.i	0.411750	+	0.531753i
$609$	50874.0			0.137171
$610$		0			0
$611$			147660.i			0.395531i
$612$	123694.	+	47232.5i	0.330252	+	0.126107i
$613$	73376.7			0.195271			0.0976354	−	0.995222i	$-0.468872\pi$
$613$	73376.7			0.195271			0.0976354	+	0.995222i	$0.468872\pi$
$614$	406925.	+	75049.6i	1.07939	+	0.199073i
$615$		0			0
$616$	192007.	−	315187.i	0.506005	−	0.830629i
$617$	288711.			0.758391			0.379195	−	0.925317i	$-0.376201\pi$
$617$	288711.			0.758391			0.379195	+	0.925317i	$0.376201\pi$
$618$	8247.34	−	44717.8i	0.0215942	−	0.117086i
$619$			241450.i			0.630153i	0.949066	+	0.315077i	$0.102030\pi$
$619$			241450.i			0.630153i	−0.949066	+	0.315077i	$0.897970\pi$
$620$		0			0
$621$	−80138.6			−0.207806
$622$	−553469.	−	102077.i	−1.43058	−	0.263843i
$623$			243674.i			0.627817i
$624$	−55135.5	+	61668.4i	−0.141600	+	0.158377i
$625$		0			0
$626$	72594.6	−	393614.i	0.185249	−	1.00444i
$627$		−	198048.i		−	0.503774i
$628$	−170247.	−	65008.7i	−0.431677	−	0.164836i
$629$	372381.			0.941209
$630$		0			0
$631$			28166.1i			0.0707404i	0.999374	+	0.0353702i	$0.0112610\pi$
$631$			28166.1i			0.0707404i	−0.999374	+	0.0353702i	$0.988739\pi$
$632$	−467084.	−	284539.i	−1.16939	−	0.712374i
$633$	394727.			0.985122
$634$	−11046.7	+	59896.1i	−0.0274823	+	0.149011i
$635$		0			0
$636$	41416.4	−	108462.i	0.102390	−	0.268142i
$637$	65401.7			0.161180
$638$	−164598.	−	30357.0i	−0.404374	−	0.0745791i
$639$		−	182725.i		−	0.447502i
$640$		0			0
$641$	−265522.			−0.646226			−0.323113	−	0.946360i	$-0.604729\pi$
$641$	−265522.			−0.646226			−0.323113	+	0.946360i	$0.604729\pi$
$642$	−46803.0	+	253769.i	−0.113554	+	0.615700i
$643$		−	38089.8i		−	0.0921271i	−0.998939	−	0.0460635i	$-0.985332\pi$
$643$		−	38089.8i		−	0.0921271i	0.998939	−	0.0460635i	$-0.0146677\pi$
$644$	−313628.	−	119759.i	−0.756211	−	0.288760i
$645$		0			0
$646$	292710.	+	53984.7i	0.701410	+	0.129362i
$647$			290269.i			0.693414i	0.937974	+	0.346707i	$0.112700\pi$
$647$			290269.i			0.693414i	−0.937974	+	0.346707i	$0.887300\pi$
$648$	24272.8	−	39844.9i	0.0578056	−	0.0948904i
$649$	455542.			1.08153
$650$		0			0
$651$		−	144922.i		−	0.341957i
$652$	60511.0	−	158468.i	0.142344	−	0.372774i
$653$	−145213.			−0.340549			−0.170275	−	0.985397i	$-0.554466\pi$
$653$	−145213.			−0.340549			−0.170275	+	0.985397i	$0.554466\pi$
$654$	−276036.	−	50909.7i	−0.645373	−	0.119027i
$655$		0			0
$656$	511008.	+	456874.i	1.18746	+	1.06167i
$657$	177712.			0.411706
$658$	63277.6	−	343096.i	0.146150	−	0.792436i
$659$			27644.5i			0.0636559i	0.999493	+	0.0318279i	$0.0101329\pi$
$659$			27644.5i			0.0636559i	−0.999493	+	0.0318279i	$0.989867\pi$
$660$		0			0
$661$	−368306.			−0.842958			−0.421479	−	0.906838i	$-0.638489\pi$
$661$	−368306.			−0.842958			−0.421479	+	0.906838i	$0.638489\pi$
$662$	685452.	+	126419.i	1.56409	+	0.288466i
$663$			99037.8i			0.225307i
$664$	−118805.	−	72374.1i	−0.269463	−	0.164152i
$665$		0			0
$666$	23799.1	−	129041.i	0.0536553	−	0.290924i
$667$			152249.i			0.342219i
$668$	−87518.0	+	229194.i	−0.196130	+	0.513631i
$669$	−481778.			−1.07645
$670$		0			0
$671$			751501.i			1.66911i
$672$	154537.	−	119662.i	0.342212	−	0.264984i
$673$	560984.			1.23857			0.619285	−	0.785166i	$-0.287423\pi$
$673$	560984.			1.23857			0.619285	+	0.785166i	$0.287423\pi$
$674$	146799.	−	795957.i	0.323150	−	1.75215i
$675$		0			0
$676$	369106.	+	140943.i	0.807715	+	0.308426i
$677$	887674.			1.93676			0.968381	−	0.249475i	$-0.0802580\pi$
$677$	887674.			1.93676			0.968381	+	0.249475i	$0.0802580\pi$
$678$	−500703.	−	92345.2i	−1.08923	−	0.200888i
$679$			576856.i			1.25120i
$680$		0			0
$681$	−185326.			−0.399616
$682$	−86476.1	+	468881.i	−0.185921	+	1.00808i
$683$		−	673933.i		−	1.44469i	−0.691532	−	0.722346i	$-0.743064\pi$
$683$		−	673933.i		−	1.44469i	0.691532	−	0.722346i	$-0.256936\pi$
$684$	37414.6	−	97982.2i	0.0799703	−	0.209428i
$685$		0			0
$686$	−498896.	−	92011.8i	−1.06014	−	0.195522i
$687$			539155.i			1.14235i
$688$	449669.	−	502949.i	0.949983	−	1.06254i
$689$	86842.5			0.182934
$690$		0			0
$691$			608132.i			1.27363i	0.771019	+	0.636813i	$0.219747\pi$
$691$			608132.i			1.27363i	−0.771019	+	0.636813i	$0.780253\pi$
$692$	−563702.	−	215250.i	−1.17717	−	0.449501i
$693$	−155700.			−0.324206
$694$	−419233.	−	77319.5i	−0.870435	−	0.160535i
$695$		0			0
$696$	−75698.2	−	46114.1i	−0.156267	−	0.0951953i
$697$	820665.			1.68928
$698$	139551.	−	756655.i	0.286432	−	1.55306i
$699$			91518.4i			0.187307i
$700$		0			0
$701$	429210.			0.873442			0.436721	−	0.899597i	$-0.356140\pi$
$701$	429210.			0.873442			0.436721	+	0.899597i	$0.356140\pi$
$702$	34319.5	+	6329.58i	0.0696413	+	0.0128440i
$703$		−	294976.i		−	0.596865i
$704$	−571395.	+	294942.i	−1.15290	+	0.595103i
$705$		0			0
$706$	55268.4	−	299670.i	0.110884	−	0.601220i
$707$		−	484458.i		−	0.969208i
$708$	225375.	+	86059.5i	0.449613	+	0.171685i
$709$	196746.			0.391392			0.195696	−	0.980665i	$-0.437303\pi$
$709$	196746.			0.391392			0.195696	+	0.980665i	$0.437303\pi$
$710$		0			0
$711$			230735.i			0.456430i
$712$	220875.	−	362576.i	0.435699	−	0.715219i
$713$	433704.			0.853128
$714$	42441.2	−	230120.i	0.0832513	−	0.451396i
$715$		0			0
$716$	−149065.	+	390374.i	−0.290769	+	0.761474i
$717$	−297189.			−0.578089
$718$	−667931.	−	123187.i	−1.29564	−	0.238955i
$719$			176676.i			0.341758i	0.985292	+	0.170879i	$0.0546607\pi$
$719$			176676.i			0.341758i	−0.985292	+	0.170879i	$0.945339\pi$
$720$		0			0
$721$	−80363.1			−0.154592
$722$	−51783.2	+	280773.i	−0.0993377	+	0.538617i
$723$		−	170369.i		−	0.325921i
$724$	657742.	+	251159.i	1.25481	+	0.479151i
$725$		0			0
$726$	204491.	+	37714.5i	0.387973	+	0.0715542i
$727$			773494.i			1.46348i	0.681582	+	0.731742i	$0.261292\pi$
$727$			773494.i			1.46348i	−0.681582	+	0.731742i	$0.738708\pi$
$728$	124853.	+	76058.2i	0.235578	+	0.143510i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	807722.i		−	1.51157i
$732$	−141971.	+	371797.i	−0.264958	+	0.693880i
$733$	−405112.			−0.753992			−0.376996	−	0.926215i	$-0.623043\pi$
$733$	−405112.			−0.753992			−0.376996	+	0.926215i	$0.623043\pi$
$734$	−31391.3	−	5789.53i	−0.0582663	−	0.0107461i
$735$		0			0
$736$	358110.	+	462480.i	0.661091	+	0.853763i
$737$	731008.			1.34582
$738$	52449.3	−	284385.i	0.0963002	−	0.522148i
$739$			12430.2i			0.0227609i	0.999935	+	0.0113805i	$0.00362259\pi$
$739$			12430.2i			0.0227609i	−0.999935	+	0.0113805i	$0.996377\pi$
$740$		0			0
$741$	78451.3			0.142878
$742$	−201783.	−	37215.1i	−0.366503	−	0.0675945i
$743$		−	642523.i		−	1.16389i	−0.813229	−	0.581944i	$-0.802292\pi$
$743$		−	642523.i		−	1.16389i	0.813229	−	0.581944i	$-0.197708\pi$
$744$	−131362.	+	215637.i	−0.237315	+	0.389563i
$745$		0			0
$746$	−188102.	+	1.01991e6i	−0.338000	+	1.83266i
$747$			58688.6i			0.105175i
$748$	−274629.	+	719206.i	−0.490844	+	1.28543i
$749$	456054.			0.812928
$750$		0			0
$751$			1.01784e6i			1.80468i	0.431022	+	0.902342i	$0.358153\pi$
$751$			1.01784e6i			1.80468i	−0.431022	+	0.902342i	$0.641847\pi$
$752$	−405150.	+	453155.i	−0.716440	+	0.801329i
$753$	−149667.			−0.263959
$754$	12025.1	−	65201.0i	0.0211517	−	0.114686i
$755$		0			0
$756$	−77030.8	−	29414.2i	−0.134779	−	0.0514652i
$757$	−386917.			−0.675191			−0.337595	−	0.941291i	$-0.609614\pi$
$757$	−386917.			−0.675191			−0.337595	+	0.941291i	$0.609614\pi$
$758$	45996.5	+	8483.19i	0.0800547	+	0.0147646i
$759$		−	465958.i		−	0.808842i
$760$		0			0
$761$	−424041.			−0.732215			−0.366108	−	0.930572i	$-0.619310\pi$
$761$	−424041.			−0.732215			−0.366108	+	0.930572i	$0.619310\pi$
$762$	−26114.2	+	141594.i	−0.0449746	+	0.243856i
$763$			496070.i			0.852106i
$764$	−194653.	+	509762.i	−0.333483	+	0.873334i
$765$		0			0
$766$	137409.	+	25342.4i	0.234183	+	0.0431907i
$767$			180451.i			0.306738i
$768$	−338411.	+	37973.7i	−0.573749	+	0.0643814i
$769$	−267929.			−0.453072			−0.226536	−	0.974003i	$-0.572740\pi$
$769$	−267929.			−0.453072			−0.226536	+	0.974003i	$0.572740\pi$
$770$		0			0
$771$		−	506450.i		−	0.851977i
$772$	−412159.	−	157383.i	−0.691560	−	0.264073i
$773$	−576873.			−0.965431			−0.482715	−	0.875777i	$-0.660349\pi$
$773$	−576873.			−0.965431			−0.482715	+	0.875777i	$0.660349\pi$
$774$	−279900.	−	51622.1i	−0.467219	−	0.0861696i
$775$		0			0
$776$	522884.	−	858336.i	0.868324	−	1.42539i
$777$	−231902.			−0.384116
$778$	−79962.2	+	433561.i	−0.132107	+	0.716294i
$779$		−	650078.i		−	1.07125i
$780$		0			0
$781$	1.06243e6			1.74181
$782$	688673.	+	127013.i	1.12616	+	0.207699i
$783$			37394.3i			0.0609932i
$784$	200711.	+	179449.i	0.326543	+	0.291950i
$785$		0			0
$786$	7136.62	−	38695.4i	0.0115517	−	0.0626345i
$787$			27874.2i			0.0450043i	0.999747	+	0.0225021i	$0.00716326\pi$
$787$			27874.2i			0.0450043i	−0.999747	+	0.0225021i	$0.992837\pi$
$788$	−675059.	−	257772.i	−1.08715	−	0.415129i
$789$	431026.			0.692388
$790$		0			0
$791$			899823.i			1.43815i
$792$	231674.	+	141132.i	0.369341	+	0.224996i
$793$	−297687.			−0.473383
$794$	32528.0	−	176370.i	0.0515961	−	0.279758i
$795$		0			0
$796$	−322905.	+	845632.i	−0.509623	+	1.33461i
$797$	−538595.			−0.847902			−0.423951	−	0.905685i	$-0.639357\pi$
$797$	−538595.			−0.847902			−0.423951	+	0.905685i	$0.639357\pi$
$798$	−182286.	−	33619.2i	−0.286251	−	0.0527936i
$799$			727755.i			1.13996i
$800$		0			0
$801$	−179109.			−0.279160
$802$	−133310.	+	722817.i	−0.207259	+	1.12378i
$803$			1.03329e6i			1.60248i
$804$	361659.	+	138100.i	0.559483	+	0.213639i
$805$		0			0
$806$	−185734.	−	34255.1i	−0.285905	−	0.0527297i
$807$		−	399788.i		−	0.613879i
$808$	−439131.	+	720851.i	−0.672622	+	1.10414i
$809$	−65846.2			−0.100608			−0.0503041	−	0.998734i	$-0.516019\pi$
$809$	−65846.2			−0.100608			−0.0503041	+	0.998734i	$0.516019\pi$
$810$		0			0
$811$		−	42705.4i		−	0.0649294i	−0.999473	−	0.0324647i	$-0.989664\pi$
$811$		−	42705.4i		−	0.0649294i	0.999473	−	0.0324647i	$-0.0103356\pi$
$812$	−55881.9	+	146345.i	−0.0847538	+	0.221955i
$813$	−384472.			−0.581679
$814$	750296.	+	138378.i	1.13236	+	0.208842i
$815$		0			0
$816$	−271740.	+	303937.i	−0.408106	+	0.456461i
$817$	−639826.			−0.958556
$818$	84243.5	−	456775.i	0.125901	−	0.682647i
$819$		−	61676.2i		−	0.0919495i
$820$		0			0
$821$	−534742.			−0.793338			−0.396669	−	0.917962i	$-0.629834\pi$
$821$	−534742.			−0.793338			−0.396669	+	0.917962i	$0.629834\pi$
$822$	−735800.	−	135704.i	−1.08897	−	0.200840i
$823$		−	281733.i		−	0.415947i	−0.978134	−	0.207974i	$-0.933313\pi$
$823$		−	281733.i		−	0.415947i	0.978134	−	0.207974i	$-0.0666869\pi$
$824$	119577.	+	72844.1i	0.176113	+	0.107285i
$825$		0			0
$826$	77329.5	−	419287.i	0.113341	−	0.614542i
$827$		−	44114.6i		−	0.0645017i	−0.999480	−	0.0322509i	$-0.989732\pi$
$827$		−	44114.6i		−	0.0645017i	0.999480	−	0.0322509i	$-0.0102675\pi$
$828$	88027.3	−	230528.i	0.128397	−	0.336251i
$829$	597535.			0.869470			0.434735	−	0.900558i	$-0.356842\pi$
$829$	597535.			0.869470			0.434735	+	0.900558i	$0.356842\pi$
$830$		0			0
$831$		−	209546.i		−	0.303444i
$832$	−116833.	−	226342.i	−0.168780	−	0.326979i
$833$	322337.			0.464537
$834$	−7160.84	+	38826.7i	−0.0102951	+	0.0558210i
$835$		0			0
$836$	569708.	+	217543.i	0.815155	+	0.311267i
$837$	106523.			0.152052
$838$	104581.	+	19288.0i	0.148925	+	0.0274663i
$839$		−	607985.i		−	0.863712i	−0.901943	−	0.431856i	$-0.857859\pi$
$839$		−	607985.i		−	0.863712i	0.901943	−	0.431856i	$-0.142141\pi$
$840$		0			0
$841$	−636238.			−0.899555
$842$	30417.2	−	164925.i	0.0429038	−	0.232628i
$843$			206801.i			0.291003i
$844$	−433583.	+	1.13548e6i	−0.608678	+	1.59402i
$845$		0			0
$846$	252188.	+	46511.3i	0.352358	+	0.0649857i
$847$		−	367495.i		−	0.512253i
$848$	266511.	+	238278.i	0.370616	+	0.331354i
$849$	−152099.			−0.211013
$850$		0			0
$851$		−	694006.i		−	0.958306i
$852$	525628.	+	200711.i	0.724102	+	0.276499i
$853$	86914.1			0.119452			0.0597258	−	0.998215i	$-0.480977\pi$
$853$	86914.1			0.119452			0.0597258	+	0.998215i	$0.480977\pi$
$854$	691691.	+	127569.i	0.948411	+	0.174916i
$855$		0			0
$856$	−678587.	−	413384.i	−0.926101	−	0.564165i
$857$	−864128.			−1.17657			−0.588283	−	0.808655i	$-0.700196\pi$
$857$	−864128.			−1.17657			−0.588283	+	0.808655i	$0.700196\pi$
$858$	−36802.7	+	199547.i	−0.0499926	+	0.271064i
$859$		−	276868.i		−	0.375220i	−0.982244	−	0.187610i	$-0.939926\pi$
$859$		−	276868.i		−	0.375220i	0.982244	−	0.187610i	$-0.0600741\pi$
$860$		0			0
$861$	−511073.			−0.689408
$862$	−1.01671e6	−	187513.i	−1.36831	−	0.252358i
$863$		−	537991.i		−	0.722359i	−0.932496	−	0.361180i	$-0.882374\pi$
$863$		−	537991.i		−	0.722359i	0.932496	−	0.361180i	$-0.117626\pi$
$864$	87956.2	+	113591.i	0.117825	+	0.152165i
$865$		0			0
$866$	25783.7	−	139801.i	0.0343803	−	0.186413i
$867$			54127.7i			0.0720080i
$868$	416884.	+	159187.i	0.553319	+	0.211285i
$869$	−1.34159e6			−1.77656
$870$		0			0
$871$			289569.i			0.381694i
$872$	449656.	−	738130.i	0.591354	−	0.970733i
$873$	−424010.			−0.556350
$874$	100611.	−	545523.i	0.131712	−	0.714151i
$875$		0			0
$876$	−195206.	+	511210.i	−0.254381	+	0.666180i
$877$	96844.0			0.125914			0.0629569	−	0.998016i	$-0.479947\pi$
$877$	96844.0			0.125914			0.0629569	+	0.998016i	$0.479947\pi$
$878$	939337.	+	173243.i	1.21852	+	0.224733i
$879$			75703.7i			0.0979804i
$880$		0			0
$881$	792263.			1.02075			0.510373	−	0.859953i	$-0.329507\pi$
$881$	792263.			1.02075			0.510373	+	0.859953i	$0.329507\pi$
$882$	20600.8	−	111699.i	0.0264818	−	0.143586i
$883$			25402.5i			0.0325803i	0.999867	+	0.0162901i	$0.00518554\pi$
$883$			25402.5i			0.0325803i	−0.999867	+	0.0162901i	$0.994814\pi$
$884$	−284894.	−	108787.i	−0.364568	−	0.139210i
$885$		0			0
$886$	−523888.	−	96621.2i	−0.667377	−	0.123085i
$887$			828735.i			1.05334i	0.850070	+	0.526670i	$0.176560\pi$
$887$			828735.i			1.05334i	−0.850070	+	0.526670i	$0.823440\pi$
$888$	345059.	+	210204.i	0.437590	+	0.266573i
$889$	254460.			0.321971
$890$		0			0
$891$		−	114445.i		−	0.144159i
$892$	529203.	−	1.38589e6i	0.665108	−	1.74180i
$893$	576480.			0.722906
$894$	−125067.	−	23066.2i	−0.156483	−	0.0288603i
$895$		0			0
$896$	174473.	+	575986.i	0.217326	+	0.717457i
$897$	184577.			0.229399
$898$	−138127.	+	748935.i	−0.171287	+	0.928735i
$899$		−	202375.i		−	0.250401i
$900$		0			0
$901$	428010.			0.527235
$902$	1.65353e6	+	304962.i	2.03235	+	0.374828i
$903$			503012.i			0.616883i
$904$	815633.	−	1.33890e6i	0.998063	−	1.63836i
$905$		0			0
$906$	−114156.	+	618962.i	−0.139073	+	0.754063i
$907$			541780.i			0.658580i	0.944229	+	0.329290i	$0.106809\pi$
$907$			541780.i			0.658580i	−0.944229	+	0.329290i	$0.893191\pi$
$908$	203569.	−	533112.i	0.246911	−	0.646617i
$909$	356094.			0.430960
$910$		0			0
$911$		−	1.33634e6i		−	1.61020i	−0.593141	−	0.805099i	$-0.702112\pi$
$911$		−	1.33634e6i		−	1.61020i	0.593141	−	0.805099i	$-0.297888\pi$
$912$	240760.	+	215255.i	0.289464	+	0.258799i
$913$	−341239.			−0.409372
$914$	−3123.85	+	16937.8i	−0.00373936	+	0.0202751i
$915$		0			0
$916$	−1.55094e6	−	592228.i	−1.84844	−	0.705827i
$917$	−69540.1			−0.0826983
$918$	169146.	+	31195.8i	0.200714	+	0.0370178i
$919$			314921.i			0.372881i	0.982466	+	0.186440i	$0.0596951\pi$
$919$			314921.i			0.372881i	−0.982466	+	0.186440i	$0.940305\pi$
$920$		0			0
$921$	537526.			0.633695
$922$	251233.	−	1.36220e6i	0.295539	−	1.60244i
$923$			420854.i			0.494001i
$924$	171026.	−	447888.i	0.200318	−	0.524597i
$925$		0			0
$926$	583016.	+	107526.i	0.679921	+	0.125399i
$927$		−	59069.8i		−	0.0687394i
$928$	215802.	−	167101.i	0.250588	−	0.194037i
$929$	−891827.			−1.03335			−0.516677	−	0.856180i	$-0.672831\pi$
$929$	−891827.			−1.03335			−0.516677	+	0.856180i	$0.672831\pi$
$930$		0			0
$931$		−	255335.i		−	0.294585i
$932$	−263263.	−	100527.i	−0.303081	−	0.115732i
$933$	−731103.			−0.839876
$934$	−673462.	−	124207.i	−0.772003	−	0.142381i
$935$		0			0
$936$	−55905.6	+	91771.3i	−0.0638121	+	0.104750i
$937$	266527.			0.303573			0.151786	−	0.988413i	$-0.451497\pi$
$937$	266527.			0.303573			0.151786	+	0.988413i	$0.451497\pi$
$938$	124091.	−	672829.i	0.141037	−	0.764714i
$939$		−	519943.i		−	0.589691i
$940$		0			0
$941$	710974.			0.802924			0.401462	−	0.915876i	$-0.368502\pi$
$941$	710974.			0.802924			0.401462	+	0.915876i	$0.368502\pi$
$942$	−232805.	−	42936.5i	−0.262356	−	0.0483866i
$943$		−	1.52947e6i		−	1.71996i
$944$	−495120.	+	553786.i	−0.555606	+	0.621438i
$945$		0			0
$946$	300152.	−	1.62745e6i	0.335397	−	1.81855i
$947$		−	895332.i		−	0.998353i	−0.866500	−	0.499177i	$-0.833636\pi$
$947$		−	895332.i		−	0.998353i	0.866500	−	0.499177i	$-0.166364\pi$
$948$	−663736.	−	253448.i	−0.738548	−	0.282015i
$949$	−409310.			−0.454486
$950$		0			0
$951$			79119.5i			0.0874828i
$952$	615347.	+	374859.i	0.678963	+	0.413613i
$953$	308910.			0.340131			0.170066	−	0.985433i	$-0.445602\pi$
$953$	308910.			0.340131			0.170066	+	0.985433i	$0.445602\pi$
$954$	27354.4	−	148318.i	0.0300560	−	0.162966i
$955$		0			0
$956$	326443.	−	854899.i	0.357184	−	0.935403i
$957$	−217425.			−0.237403
$958$	218724.	+	40339.5i	0.238323	+	0.0439541i
$959$			1.32232e6i			1.43780i
$960$		0			0
$961$	347029.			0.375767
$962$	−54814.6	+	297209.i	−0.0592306	+	0.321153i
$963$			335216.i			0.361470i
$964$	490085.	+	187139.i	0.527372	+	0.201377i
$965$		0			0
$966$	−428874.	−	79097.6i	−0.459595	−	0.0847636i
$967$			845374.i			0.904057i	0.892003	+	0.452029i	$0.149300\pi$
$967$			845374.i			0.904057i	−0.892003	+	0.452029i	$0.850700\pi$
$968$	−333111.	+	546816.i	−0.355499	+	0.583566i
$969$	386654.			0.411789
$970$		0			0
$971$		−	1.29869e6i		−	1.37742i	−0.725036	−	0.688711i	$-0.758177\pi$
$971$		−	1.29869e6i		−	1.37742i	0.725036	−	0.688711i	$-0.241823\pi$
$972$	21620.5	−	56620.4i	0.0228841	−	0.0599295i
$973$	69776.0			0.0737022
$974$	−752956.	−	138868.i	−0.793691	−	0.146381i
$975$		0			0
$976$	−913572.	−	816792.i	−0.959054	−	0.857456i
$977$	−191660.			−0.200790			−0.100395	−	0.994948i	$-0.532011\pi$
$977$	−191660.			−0.200790			−0.100395	+	0.994948i	$0.532011\pi$
$978$	39965.9	−	216698.i	0.0417842	−	0.226557i
$979$		−	1.04141e6i		−	1.08657i
$980$		0			0
$981$	−364629.			−0.378890
$982$	921024.	+	169865.i	0.955098	+	0.176150i
$983$		−	69081.0i		−	0.0714910i	−0.999361	−	0.0357455i	$-0.988619\pi$
$983$		−	69081.0i		−	0.0714910i	0.999361	−	0.0357455i	$-0.0113806\pi$
$984$	760453.	+	463255.i	0.785384	+	0.478443i
$985$		0			0
$986$	59266.6	−	321348.i	0.0609616	−	0.330539i
$987$		−	453212.i		−	0.465229i
$988$	−86173.9	+	225674.i	−0.0882799	+	0.231190i
$989$	−1.50535e6			−1.53902
$990$		0			0
$991$			1.79910e6i			1.83192i	0.401266	+	0.915962i	$0.368570\pi$
$991$			1.79910e6i			1.83192i	−0.401266	+	0.915962i	$0.631430\pi$
$992$	−476011.	−	614743.i	−0.483720	−	0.624698i
$993$	905446.			0.918256
$994$	180351.	−	977878.i	0.182535	−	0.989719i
$995$		0			0
$996$	−168825.	−	64465.8i	−0.170183	−	0.0649846i
$997$	−1.95066e6			−1.96241			−0.981206	−	0.192963i	$-0.938190\pi$
$997$	−1.95066e6			−1.96241			−0.981206	+	0.192963i	$0.938190\pi$
$998$	1.56403e6	+	288456.i	1.57031	+	0.289613i
$999$		−	170456.i		−	0.170798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.b.151.10	yes	16
4.3	odd	2	inner	300.5.c.b.151.9	✓	16
5.2	odd	4		300.5.f.c.199.1		32
5.3	odd	4		300.5.f.c.199.32		32
5.4	even	2		300.5.c.c.151.7	yes	16
20.3	even	4		300.5.f.c.199.2		32
20.7	even	4		300.5.f.c.199.31		32
20.19	odd	2		300.5.c.c.151.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.9	✓	16	4.3	odd	2	inner
300.5.c.b.151.10	yes	16	1.1	even	1	trivial
300.5.c.c.151.7	yes	16	5.4	even	2
300.5.c.c.151.8	yes	16	20.19	odd	2
300.5.f.c.199.1		32	5.2	odd	4
300.5.f.c.199.2		32	20.3	even	4
300.5.f.c.199.31		32	20.7	even	4
300.5.f.c.199.32		32	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.725488 + 3.93366i) q^{2} +5.19615i q^{3} +(-14.9473 - 5.70765i) q^{4} +(-20.4399 - 3.76975i) q^{6} +36.7329i q^{7} +(33.2960 - 54.6569i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-0.725488 + 3.93366i) q^{2} +5.19615i q^{3} +(-14.9473 - 5.70765i) q^{4} +(-20.4399 - 3.76975i) q^{6} +36.7329i q^{7} +(33.2960 - 54.6569i) q^{8} -27.0000 q^{9} -156.989i q^{11} +(29.6578 - 77.6686i) q^{12} +62.1869 q^{13} +(-144.495 - 26.6493i) q^{14} +(190.846 + 170.628i) q^{16} +306.493 q^{17} +(19.5882 - 106.209i) q^{18} -242.784i q^{19} -190.870 q^{21} +(617.541 + 113.894i) q^{22} -571.211i q^{23} +(284.005 + 173.011i) q^{24} +(-45.1158 + 244.622i) q^{26} -140.296i q^{27} +(209.658 - 549.059i) q^{28} -266.538 q^{29} +759.271i q^{31} +(-809.649 + 626.932i) q^{32} +815.738 q^{33} +(-222.357 + 1205.64i) q^{34} +(403.578 + 154.106i) q^{36} +1214.97 q^{37} +(955.029 + 176.137i) q^{38} +323.132i q^{39} +2677.60 q^{41} +(138.474 - 750.816i) q^{42} -2635.37i q^{43} +(-896.037 + 2346.57i) q^{44} +(2246.95 + 414.407i) q^{46} +2374.46i q^{47} +(-886.610 + 991.663i) q^{48} +1051.70 q^{49} +1592.58i q^{51} +(-929.528 - 354.941i) q^{52} +1396.48 q^{53} +(551.877 + 101.783i) q^{54} +(2007.70 + 1223.06i) q^{56} +1261.54 q^{57} +(193.370 - 1048.47i) q^{58} +2901.75i q^{59} -4786.97 q^{61} +(-2986.71 - 550.842i) q^{62} -991.788i q^{63} +(-1878.75 - 3639.72i) q^{64} +(-591.809 + 3208.84i) q^{66} +4656.43i q^{67} +(-4581.25 - 1749.35i) q^{68} +2968.10 q^{69} +6767.57i q^{71} +(-898.993 + 1475.74i) q^{72} -6581.94 q^{73} +(-881.450 + 4779.29i) q^{74} +(-1385.72 + 3628.97i) q^{76} +5766.65 q^{77} +(-1271.09 - 234.429i) q^{78} -8545.74i q^{79} +729.000 q^{81} +(-1942.57 + 10532.8i) q^{82} -2173.65i q^{83} +(2852.99 + 1089.42i) q^{84} +(10366.6 + 1911.93i) q^{86} -1384.97i q^{87} +(-8580.52 - 5227.11i) q^{88} +6633.68 q^{89} +2284.30i q^{91} +(-3260.27 + 8538.08i) q^{92} -3945.29 q^{93} +(-9340.31 - 1722.64i) q^{94} +(-3257.64 - 4207.06i) q^{96} +15704.1 q^{97} +(-762.993 + 4137.01i) q^{98} +4238.70i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 8 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 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

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