LMFDB - Embedded newform 690.3.k.a.553.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.14
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(4.99686 + 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 + 4.63984i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(4.99686 + 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 + 4.63984i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(5.17412 - 4.81959i) q^{10} +2.27620 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.59512 + 6.59512i) q^{13} +9.27967i q^{14} +(5.90277 + 6.33698i) q^{15} -4.00000 q^{16} +(16.0847 - 16.0847i) q^{17} +(3.00000 + 3.00000i) q^{18} +33.4152i q^{19} +(0.354533 - 9.99371i) q^{20} -11.3652 q^{21} +(2.27620 - 2.27620i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(24.9372 + 1.77155i) q^{25} +13.1902 q^{26} +(-3.67423 + 3.67423i) q^{27} +(9.27967 + 9.27967i) q^{28} -8.75349i q^{29} +(12.2397 + 0.434212i) q^{30} +26.0099 q^{31} +(-4.00000 + 4.00000i) q^{32} +(2.78777 + 2.78777i) q^{33} -32.1694i q^{34} +(-24.0071 + 22.3621i) q^{35} +6.00000 q^{36} +(18.6213 - 18.6213i) q^{37} +(33.4152 + 33.4152i) q^{38} +16.1547i q^{39} +(-9.63918 - 10.3482i) q^{40} +4.34271 q^{41} +(-11.3652 + 11.3652i) q^{42} +(33.4812 + 33.4812i) q^{43} -4.55240i q^{44} +(-0.531799 + 14.9906i) q^{45} +6.78233 q^{46} +(-28.7769 + 28.7769i) q^{47} +(-4.89898 - 4.89898i) q^{48} +5.94385i q^{49} +(26.7087 - 23.1656i) q^{50} +39.3992 q^{51} +(13.1902 - 13.1902i) q^{52} +(-34.3298 - 34.3298i) q^{53} +7.34847i q^{54} +(11.3739 + 0.403494i) q^{55} +18.5593 q^{56} +(-40.9250 + 40.9250i) q^{57} +(-8.75349 - 8.75349i) q^{58} -71.9203i q^{59} +(12.6740 - 11.8055i) q^{60} -71.6157 q^{61} +(26.0099 - 26.0099i) q^{62} +(-13.9195 - 13.9195i) q^{63} +8.00000i q^{64} +(31.7858 + 34.1240i) q^{65} +5.57553 q^{66} +(-80.0034 + 80.0034i) q^{67} +(-32.1694 - 32.1694i) q^{68} +8.30662i q^{69} +(-1.64497 + 46.3692i) q^{70} +103.758 q^{71} +(6.00000 - 6.00000i) q^{72} +(1.17476 + 1.17476i) q^{73} -37.2426i q^{74} +(28.3720 + 32.7113i) q^{75} +66.8303 q^{76} +(-10.5612 + 10.5612i) q^{77} +(16.1547 + 16.1547i) q^{78} -134.376i q^{79} +(-19.9874 - 0.709066i) q^{80} -9.00000 q^{81} +(4.34271 - 4.34271i) q^{82} +(-11.8656 - 11.8656i) q^{83} +22.7305i q^{84} +(83.2241 - 77.5215i) q^{85} +66.9623 q^{86} +(10.7208 - 10.7208i) q^{87} +(-4.55240 - 4.55240i) q^{88} -40.9315i q^{89} +(14.4588 + 15.5224i) q^{90} -61.2005 q^{91} +(6.78233 - 6.78233i) q^{92} +(31.8555 + 31.8555i) q^{93} +57.5539i q^{94} +(-5.92339 + 166.971i) q^{95} -9.79796 q^{96} +(31.1861 - 31.1861i) q^{97} +(5.94385 + 5.94385i) q^{98} +6.82860i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	4.99686	+	0.177266i	0.999371	+	0.0354533i
$5$	4.99686	+	0.177266i	0.999371	+	0.0354533i
$6$	2.44949			0.408248
$7$	−4.63984	+	4.63984i	−0.662834	+	0.662834i	−0.956047	−	0.293213i	$-0.905275\pi$
$7$	−4.63984	+	4.63984i	−0.662834	+	0.662834i	0.293213	+	0.956047i	$0.405275\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	5.17412	−	4.81959i	0.517412	−	0.481959i
$11$	2.27620			0.206927			0.103464	−	0.994633i	$-0.467007\pi$
$11$	2.27620			0.206927			0.103464	+	0.994633i	$0.467007\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	6.59512	+	6.59512i	0.507317	+	0.507317i	0.913702	−	0.406385i	$-0.133211\pi$
$13$	6.59512	+	6.59512i	0.507317	+	0.507317i	−0.406385	+	0.913702i	$0.633211\pi$
$14$			9.27967i			0.662834i
$15$	5.90277	+	6.33698i	0.393518	+	0.422465i
$16$	−4.00000			−0.250000
$17$	16.0847	−	16.0847i	0.946157	−	0.946157i	−0.0524654	−	0.998623i	$-0.516708\pi$
$17$	16.0847	−	16.0847i	0.946157	−	0.946157i	0.998623	+	0.0524654i	$0.0167079\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			33.4152i			1.75869i	0.476183	+	0.879346i	$0.342020\pi$
$19$			33.4152i			1.75869i	−0.476183	+	0.879346i	$0.657980\pi$
$20$	0.354533	−	9.99371i	0.0177266	−	0.499686i
$21$	−11.3652			−0.541201
$22$	2.27620	−	2.27620i	0.103464	−	0.103464i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	24.9372	+	1.77155i	0.997486	+	0.0708620i
$26$	13.1902			0.507317
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	9.27967	+	9.27967i	0.331417	+	0.331417i
$29$		−	8.75349i		−	0.301844i	−0.988546	−	0.150922i	$-0.951776\pi$
$29$		−	8.75349i		−	0.301844i	0.988546	−	0.150922i	$-0.0482243\pi$
$30$	12.2397	+	0.434212i	0.407992	+	0.0144737i
$31$	26.0099			0.839028			0.419514	−	0.907749i	$-0.362200\pi$
$31$	26.0099			0.839028			0.419514	+	0.907749i	$0.362200\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	2.78777	+	2.78777i	0.0844778	+	0.0844778i
$34$		−	32.1694i		−	0.946157i
$35$	−24.0071	+	22.3621i	−0.685917	+	0.638917i
$36$	6.00000			0.166667
$37$	18.6213	−	18.6213i	0.503278	−	0.503278i	−0.409177	−	0.912455i	$-0.634184\pi$
$37$	18.6213	−	18.6213i	0.503278	−	0.503278i	0.912455	+	0.409177i	$0.134184\pi$
$38$	33.4152	+	33.4152i	0.879346	+	0.879346i
$39$			16.1547i			0.414222i
$40$	−9.63918	−	10.3482i	−0.240980	−	0.258706i
$41$	4.34271			0.105920			0.0529599	−	0.998597i	$-0.483134\pi$
$41$	4.34271			0.105920			0.0529599	+	0.998597i	$0.483134\pi$
$42$	−11.3652	+	11.3652i	−0.270601	+	0.270601i
$43$	33.4812	+	33.4812i	0.778631	+	0.778631i	0.979598	−	0.200967i	$-0.0644083\pi$
$43$	33.4812	+	33.4812i	0.778631	+	0.778631i	−0.200967	+	0.979598i	$0.564408\pi$
$44$		−	4.55240i		−	0.103464i
$45$	−0.531799	+	14.9906i	−0.0118178	+	0.333124i
$46$	6.78233			0.147442
$47$	−28.7769	+	28.7769i	−0.612275	+	0.612275i	−0.943538	−	0.331263i	$-0.892525\pi$
$47$	−28.7769	+	28.7769i	−0.612275	+	0.612275i	0.331263	+	0.943538i	$0.392525\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$			5.94385i			0.121303i
$50$	26.7087	−	23.1656i	0.534174	−	0.463312i
$51$	39.3992			0.772534
$52$	13.1902	−	13.1902i	0.253658	−	0.253658i
$53$	−34.3298	−	34.3298i	−0.647732	−	0.647732i	0.304712	−	0.952444i	$-0.401440\pi$
$53$	−34.3298	−	34.3298i	−0.647732	−	0.647732i	−0.952444	+	0.304712i	$0.901440\pi$
$54$			7.34847i			0.136083i
$55$	11.3739	+	0.403494i	0.206797	+	0.00733626i
$56$	18.5593			0.331417
$57$	−40.9250	+	40.9250i	−0.717983	+	0.717983i
$58$	−8.75349	−	8.75349i	−0.150922	−	0.150922i
$59$		−	71.9203i		−	1.21899i	−0.792791	−	0.609494i	$-0.791373\pi$
$59$		−	71.9203i		−	1.21899i	0.792791	−	0.609494i	$-0.208627\pi$
$60$	12.6740	−	11.8055i	0.211233	−	0.196759i
$61$	−71.6157			−1.17403			−0.587014	−	0.809577i	$-0.699697\pi$
$61$	−71.6157			−1.17403			−0.587014	+	0.809577i	$0.699697\pi$
$62$	26.0099	−	26.0099i	0.419514	−	0.419514i
$63$	−13.9195	−	13.9195i	−0.220945	−	0.220945i
$64$			8.00000i			0.125000i
$65$	31.7858	+	34.1240i	0.489012	+	0.524984i
$66$	5.57553			0.0844778
$67$	−80.0034	+	80.0034i	−1.19408	+	1.19408i	−0.218169	+	0.975911i	$0.570009\pi$
$67$	−80.0034	+	80.0034i	−1.19408	+	1.19408i	−0.975911	+	0.218169i	$0.929991\pi$
$68$	−32.1694	−	32.1694i	−0.473079	−	0.473079i
$69$			8.30662i			0.120386i
$70$	−1.64497	+	46.3692i	−0.0234996	+	0.662417i
$71$	103.758			1.46139			0.730694	−	0.682706i	$-0.239197\pi$
$71$	103.758			1.46139			0.730694	+	0.682706i	$0.239197\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	1.17476	+	1.17476i	0.0160926	+	0.0160926i	0.715107	−	0.699015i	$-0.246378\pi$
$73$	1.17476	+	1.17476i	0.0160926	+	0.0160926i	−0.699015	+	0.715107i	$0.746378\pi$
$74$		−	37.2426i		−	0.503278i
$75$	28.3720	+	32.7113i	0.378293	+	0.436151i
$76$	66.8303			0.879346
$77$	−10.5612	+	10.5612i	−0.137158	+	0.137158i
$78$	16.1547	+	16.1547i	0.207111	+	0.207111i
$79$		−	134.376i		−	1.70096i	−0.526008	−	0.850479i	$-0.676312\pi$
$79$		−	134.376i		−	1.70096i	0.526008	−	0.850479i	$-0.323688\pi$
$80$	−19.9874	−	0.709066i	−0.249843	−	0.00886332i
$81$	−9.00000			−0.111111
$82$	4.34271	−	4.34271i	0.0529599	−	0.0529599i
$83$	−11.8656	−	11.8656i	−0.142959	−	0.142959i	0.632005	−	0.774964i	$-0.282232\pi$
$83$	−11.8656	−	11.8656i	−0.142959	−	0.142959i	−0.774964	+	0.632005i	$0.782232\pi$
$84$			22.7305i			0.270601i
$85$	83.2241	−	77.5215i	0.979107	−	0.912018i
$86$	66.9623			0.778631
$87$	10.7208	−	10.7208i	0.123227	−	0.123227i
$88$	−4.55240	−	4.55240i	−0.0517319	−	0.0517319i
$89$		−	40.9315i		−	0.459905i	−0.973202	−	0.229952i	$-0.926143\pi$
$89$		−	40.9315i		−	0.459905i	0.973202	−	0.229952i	$-0.0738570\pi$
$90$	14.4588	+	15.5224i	0.160653	+	0.172471i
$91$	−61.2005			−0.672533
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	31.8555	+	31.8555i	0.342532	+	0.342532i
$94$			57.5539i			0.612275i
$95$	−5.92339	+	166.971i	−0.0623514	+	1.75759i
$96$	−9.79796			−0.102062
$97$	31.1861	−	31.1861i	0.321506	−	0.321506i	−0.527839	−	0.849345i	$-0.676997\pi$
$97$	31.1861	−	31.1861i	0.321506	−	0.321506i	0.849345	+	0.527839i	$0.176997\pi$
$98$	5.94385	+	5.94385i	0.0606515	+	0.0606515i
$99$			6.82860i			0.0689758i
$100$	3.54310	−	49.8743i	0.0354310	−	0.498743i
$101$	44.4799			0.440395			0.220197	−	0.975455i	$-0.429330\pi$
$101$	44.4799			0.440395			0.220197	+	0.975455i	$0.429330\pi$
$102$	39.3992	−	39.3992i	0.386267	−	0.386267i
$103$	87.3328	+	87.3328i	0.847891	+	0.847891i	0.989870	−	0.141979i	$-0.0453465\pi$
$103$	87.3328	+	87.3328i	0.847891	+	0.847891i	−0.141979	+	0.989870i	$0.545346\pi$
$104$		−	26.3805i		−	0.253658i
$105$	−56.7904	−	2.01467i	−0.540861	−	0.0191874i
$106$	−68.6596			−0.647732
$107$	15.9149	−	15.9149i	0.148737	−	0.148737i	−0.628817	−	0.777554i	$-0.716460\pi$
$107$	15.9149	−	15.9149i	0.148737	−	0.148737i	0.777554	+	0.628817i	$0.216460\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	40.4073i		−	0.370709i	−0.982672	−	0.185355i	$-0.940657\pi$
$109$		−	40.4073i		−	0.370709i	0.982672	−	0.185355i	$-0.0593434\pi$
$110$	11.7773	−	10.9704i	0.107067	−	0.0997305i
$111$	45.6127			0.410925
$112$	18.5593	−	18.5593i	0.165708	−	0.165708i
$113$	−44.9394	−	44.9394i	−0.397694	−	0.397694i	0.479725	−	0.877419i	$-0.340736\pi$
$113$	−44.9394	−	44.9394i	−0.397694	−	0.397694i	−0.877419	+	0.479725i	$0.840736\pi$
$114$			81.8501i			0.717983i
$115$	16.3440	+	17.5463i	0.142122	+	0.152577i
$116$	−17.5070			−0.150922
$117$	−19.7854	+	19.7854i	−0.169106	+	0.169106i
$118$	−71.9203	−	71.9203i	−0.609494	−	0.609494i
$119$			149.260i			1.25429i
$120$	0.868424	−	24.4795i	0.00723687	−	0.203996i
$121$	−115.819			−0.957181
$122$	−71.6157	+	71.6157i	−0.587014	+	0.587014i
$123$	5.31871	+	5.31871i	0.0432416	+	0.0432416i
$124$		−	52.0197i		−	0.419514i
$125$	124.293	+	13.2727i	0.994347	+	0.106182i
$126$	−27.8390			−0.220945
$127$	84.8776	−	84.8776i	0.668328	−	0.668328i	−0.289001	−	0.957329i	$-0.593323\pi$
$127$	84.8776	−	84.8776i	0.668328	−	0.668328i	0.957329	+	0.289001i	$0.0933231\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			82.0117i			0.635750i
$130$	65.9097	+	2.33819i	0.506998	+	0.0179860i
$131$	−29.0659			−0.221877			−0.110939	−	0.993827i	$-0.535386\pi$
$131$	−29.0659			−0.221877			−0.110939	+	0.993827i	$0.535386\pi$
$132$	5.57553	−	5.57553i	0.0422389	−	0.0422389i
$133$	−155.041	−	155.041i	−1.16572	−	1.16572i
$134$			160.007i			1.19408i
$135$	−19.0109	+	17.7083i	−0.140822	+	0.131173i
$136$	−64.3387			−0.473079
$137$	50.3452	−	50.3452i	0.367483	−	0.367483i	−0.499076	−	0.866558i	$-0.666327\pi$
$137$	50.3452	−	50.3452i	0.367483	−	0.367483i	0.866558	+	0.499076i	$0.166327\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	83.2681i		−	0.599051i	−0.954088	−	0.299525i	$-0.903172\pi$
$139$		−	83.2681i		−	0.599051i	0.954088	−	0.299525i	$-0.0968283\pi$
$140$	44.7242	+	48.0142i	0.319459	+	0.342958i
$141$	−70.4888			−0.499921
$142$	103.758	−	103.758i	0.730694	−	0.730694i
$143$	15.0118	+	15.0118i	0.104978	+	0.104978i
$144$		−	12.0000i		−	0.0833333i
$145$	1.55170	−	43.7399i	0.0107014	−	0.301655i
$146$	2.34952			0.0160926
$147$	−7.27970	+	7.27970i	−0.0495218	+	0.0495218i
$148$	−37.2426	−	37.2426i	−0.251639	−	0.251639i
$149$			35.8235i			0.240426i	0.992748	+	0.120213i	$0.0383578\pi$
$149$			35.8235i			0.240426i	−0.992748	+	0.120213i	$0.961642\pi$
$150$	61.0833	+	4.33939i	0.407222	+	0.0289293i
$151$	−296.868			−1.96602			−0.983008	−	0.183562i	$-0.941237\pi$
$151$	−296.868			−1.96602			−0.983008	+	0.183562i	$0.941237\pi$
$152$	66.8303	−	66.8303i	0.439673	−	0.439673i
$153$	48.2540	+	48.2540i	0.315386	+	0.315386i
$154$			21.1224i			0.137158i
$155$	129.968	+	4.61068i	0.838501	+	0.0297463i
$156$	32.3094			0.207111
$157$	−171.782	+	171.782i	−1.09415	+	1.09415i	−0.0990741	+	0.995080i	$0.531588\pi$
$157$	−171.782	+	171.782i	−1.09415	+	1.09415i	−0.995080	+	0.0990741i	$0.968412\pi$
$158$	−134.376	−	134.376i	−0.850479	−	0.850479i
$159$		−	84.0905i		−	0.528871i
$160$	−20.6965	+	19.2784i	−0.129353	+	0.120490i
$161$	−31.4689			−0.195459
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−153.218	−	153.218i	−0.939991	−	0.939991i	0.0583080	−	0.998299i	$-0.481429\pi$
$163$	−153.218	−	153.218i	−0.939991	−	0.939991i	−0.998299	+	0.0583080i	$0.981429\pi$
$164$		−	8.68542i		−	0.0529599i
$165$	13.4359	+	14.4242i	0.0814296	+	0.0874197i
$166$	−23.7312			−0.142959
$167$	−125.613	+	125.613i	−0.752174	+	0.752174i	−0.974885	−	0.222711i	$-0.928510\pi$
$167$	−125.613	+	125.613i	−0.752174	+	0.752174i	0.222711	+	0.974885i	$0.428510\pi$
$168$	22.7305	+	22.7305i	0.135300	+	0.135300i
$169$		−	82.0088i		−	0.485259i
$170$	5.70254	−	160.746i	0.0335444	−	0.945563i
$171$	−100.245			−0.586231
$172$	66.9623	−	66.9623i	0.389316	−	0.389316i
$173$	−125.643	−	125.643i	−0.726262	−	0.726262i	0.243611	−	0.969873i	$-0.421668\pi$
$173$	−125.643	−	125.643i	−0.726262	−	0.726262i	−0.969873	+	0.243611i	$0.921668\pi$
$174$		−	21.4416i		−	0.123227i
$175$	−123.924	+	107.485i	−0.708137	+	0.614198i
$176$	−9.10481			−0.0517319
$177$	88.0840	−	88.0840i	0.497650	−	0.497650i
$178$	−40.9315	−	40.9315i	−0.229952	−	0.229952i
$179$		−	92.2918i		−	0.515596i	−0.966199	−	0.257798i	$-0.917003\pi$
$179$		−	92.2918i		−	0.515596i	0.966199	−	0.257798i	$-0.0829970\pi$
$180$	29.9811	+	1.06360i	0.166562	+	0.00590888i
$181$	−111.846			−0.617932			−0.308966	−	0.951073i	$-0.599983\pi$
$181$	−111.846			−0.617932			−0.308966	+	0.951073i	$0.599983\pi$
$182$	−61.2005	+	61.2005i	−0.336267	+	0.336267i
$183$	−87.7110	−	87.7110i	−0.479295	−	0.479295i
$184$		−	13.5647i		−	0.0737210i
$185$	96.3489	−	89.7470i	0.520805	−	0.485119i
$186$	63.7109			0.342532
$187$	36.6120	−	36.6120i	0.195786	−	0.195786i
$188$	57.5539	+	57.5539i	0.306138	+	0.306138i
$189$		−	34.0957i		−	0.180400i
$190$	161.047	+	172.894i	0.847618	+	0.909969i
$191$	−93.7491			−0.490833			−0.245416	−	0.969418i	$-0.578925\pi$
$191$	−93.7491			−0.490833			−0.245416	+	0.969418i	$0.578925\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−100.013	−	100.013i	−0.518201	−	0.518201i	0.398826	−	0.917027i	$-0.369418\pi$
$193$	−100.013	−	100.013i	−0.518201	−	0.518201i	−0.917027	+	0.398826i	$0.869418\pi$
$194$		−	62.3722i		−	0.321506i
$195$	−2.86368	+	80.7226i	−0.0146855	+	0.413962i
$196$	11.8877			0.0606515
$197$	112.363	−	112.363i	0.570371	−	0.570371i	−0.361861	−	0.932232i	$-0.617859\pi$
$197$	112.363	−	112.363i	0.570371	−	0.570371i	0.932232	+	0.361861i	$0.117859\pi$
$198$	6.82860	+	6.82860i	0.0344879	+	0.0344879i
$199$			60.0337i			0.301677i	0.988558	+	0.150838i	$0.0481973\pi$
$199$			60.0337i			0.301677i	−0.988558	+	0.150838i	$0.951803\pi$
$200$	−46.3312	−	53.4174i	−0.231656	−	0.267087i
$201$	−195.967			−0.974963
$202$	44.4799	−	44.4799i	0.220197	−	0.220197i
$203$	40.6147	+	40.6147i	0.200073	+	0.200073i
$204$		−	78.7985i		−	0.386267i
$205$	21.6999	+	0.769817i	0.105853	+	0.00375520i
$206$	174.666			0.847891
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	−26.3805	−	26.3805i	−0.126829	−	0.126829i
$209$			76.0596i			0.363922i
$210$	−58.8051	+	54.7758i	−0.280024	+	0.260837i
$211$	−72.4262			−0.343252			−0.171626	−	0.985162i	$-0.554902\pi$
$211$	−72.4262			−0.343252			−0.171626	+	0.985162i	$0.554902\pi$
$212$	−68.6596	+	68.6596i	−0.323866	+	0.323866i
$213$	127.078	+	127.078i	0.596609	+	0.596609i
$214$		−	31.8298i		−	0.148737i
$215$	161.365	+	173.236i	0.750537	+	0.805747i
$216$	14.6969			0.0680414
$217$	−120.682	+	120.682i	−0.556136	+	0.556136i
$218$	−40.4073	−	40.4073i	−0.185355	−	0.185355i
$219$			2.87757i			0.0131396i
$220$	0.806988	−	22.7477i	0.00366813	−	0.103399i
$221$	212.161			0.960003
$222$	45.6127	−	45.6127i	0.205463	−	0.205463i
$223$	161.871	+	161.871i	0.725879	+	0.725879i	0.969796	−	0.243917i	$-0.0784324\pi$
$223$	161.871	+	161.871i	0.725879	+	0.725879i	−0.243917	+	0.969796i	$0.578432\pi$
$224$		−	37.1187i		−	0.165708i
$225$	−5.31465	+	74.8115i	−0.0236207	+	0.332495i
$226$	−89.8788			−0.397694
$227$	−258.326	+	258.326i	−1.13800	+	1.13800i	−0.149193	+	0.988808i	$0.547668\pi$
$227$	−258.326	+	258.326i	−1.13800	+	1.13800i	−0.988808	+	0.149193i	$0.952332\pi$
$228$	81.8501	+	81.8501i	0.358992	+	0.358992i
$229$		−	210.083i		−	0.917395i	−0.888593	−	0.458697i	$-0.848316\pi$
$229$		−	210.083i		−	0.917395i	0.888593	−	0.458697i	$-0.151684\pi$
$230$	33.8903	+	1.20228i	0.147349	+	0.00522730i
$231$	−25.8696			−0.111989
$232$	−17.5070	+	17.5070i	−0.0754611	+	0.0754611i
$233$	244.089	+	244.089i	1.04759	+	1.04759i	0.998809	+	0.0487828i	$0.0155342\pi$
$233$	244.089	+	244.089i	1.04759	+	1.04759i	0.0487828	+	0.998809i	$0.484466\pi$
$234$			39.5707i			0.169106i
$235$	−148.895	+	138.693i	−0.633598	+	0.590183i
$236$	−143.841			−0.609494
$237$	164.576	−	164.576i	0.694414	−	0.694414i
$238$	149.260	+	149.260i	0.627145	+	0.627145i
$239$		−	314.702i		−	1.31675i	−0.752692	−	0.658373i	$-0.771245\pi$
$239$		−	314.702i		−	1.31675i	0.752692	−	0.658373i	$-0.228755\pi$
$240$	−23.6111	−	25.3479i	−0.0983795	−	0.105616i
$241$	−178.804			−0.741927			−0.370964	−	0.928647i	$-0.620973\pi$
$241$	−178.804			−0.741927			−0.370964	+	0.928647i	$0.620973\pi$
$242$	−115.819	+	115.819i	−0.478591	+	0.478591i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			143.231i			0.587014i
$245$	−1.05364	+	29.7006i	−0.00430059	+	0.121227i
$246$	10.6374			0.0432416
$247$	−220.377	+	220.377i	−0.892215	+	0.892215i
$248$	−52.0197	−	52.0197i	−0.209757	−	0.209757i
$249$		−	29.0646i		−	0.116725i
$250$	137.566	−	111.021i	0.550264	−	0.444083i
$251$	183.648			0.731664			0.365832	−	0.930681i	$-0.380784\pi$
$251$	183.648			0.731664			0.365832	+	0.930681i	$0.380784\pi$
$252$	−27.8390	+	27.8390i	−0.110472	+	0.110472i
$253$	7.71898	+	7.71898i	0.0305098	+	0.0305098i
$254$		−	169.755i		−	0.668328i
$255$	196.872	+	6.98416i	0.772049	+	0.0273889i
$256$	16.0000			0.0625000
$257$	−258.659	+	258.659i	−1.00646	+	1.00646i	−0.00647714	+	0.999979i	$0.502062\pi$
$257$	−258.659	+	258.659i	−1.00646	+	1.00646i	−0.999979	+	0.00647714i	$0.997938\pi$
$258$	82.0117	+	82.0117i	0.317875	+	0.317875i
$259$			172.800i			0.667180i
$260$	68.2479	−	63.5715i	0.262492	−	0.244506i
$261$	26.2605			0.100615
$262$	−29.0659	+	29.0659i	−0.110939	+	0.110939i
$263$	−6.73066	−	6.73066i	−0.0255919	−	0.0255919i	0.694195	−	0.719787i	$-0.255761\pi$
$263$	−6.73066	−	6.73066i	−0.0255919	−	0.0255919i	−0.719787	+	0.694195i	$0.755761\pi$
$264$		−	11.1511i		−	0.0422389i
$265$	−165.456	−	177.627i	−0.624361	−	0.670289i
$266$	−310.082			−1.16572
$267$	50.1307	−	50.1307i	0.187755	−	0.187755i
$268$	160.007	+	160.007i	0.597040	+	0.597040i
$269$			195.237i			0.725787i	0.931831	+	0.362893i	$0.118211\pi$
$269$			195.237i			0.725787i	−0.931831	+	0.362893i	$0.881789\pi$
$270$	−1.30264	+	36.7192i	−0.00482458	+	0.135997i
$271$	−190.383			−0.702522			−0.351261	−	0.936278i	$-0.614247\pi$
$271$	−190.383			−0.702522			−0.351261	+	0.936278i	$0.614247\pi$
$272$	−64.3387	+	64.3387i	−0.236539	+	0.236539i
$273$	−74.9550	−	74.9550i	−0.274561	−	0.274561i
$274$		−	100.690i		−	0.367483i
$275$	56.7620	+	4.03240i	0.206407	+	0.0146633i
$276$	16.6132			0.0601929
$277$	361.616	−	361.616i	1.30547	−	1.30547i	0.380824	−	0.924647i	$-0.375640\pi$
$277$	361.616	−	361.616i	1.30547	−	1.30547i	0.924647	−	0.380824i	$-0.124360\pi$
$278$	−83.2681	−	83.2681i	−0.299525	−	0.299525i
$279$			78.0296i			0.279676i
$280$	92.7384	+	3.28995i	0.331208	+	0.0117498i
$281$	−259.206			−0.922440			−0.461220	−	0.887286i	$-0.652588\pi$
$281$	−259.206			−0.922440			−0.461220	+	0.887286i	$0.652588\pi$
$282$	−70.4888	+	70.4888i	−0.249960	+	0.249960i
$283$	−283.592	−	283.592i	−1.00209	−	1.00209i	−0.999998	−	0.00209570i	$-0.999333\pi$
$283$	−283.592	−	283.592i	−1.00209	−	1.00209i	−0.00209570	−	0.999998i	$-0.500667\pi$
$284$		−	207.517i		−	0.730694i
$285$	−211.751	+	197.242i	−0.742987	+	0.692077i
$286$	30.0236			0.104978
$287$	−20.1495	+	20.1495i	−0.0702072	+	0.0702072i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$		−	228.434i		−	0.790428i
$290$	−42.1882	−	45.2916i	−0.145477	−	0.156178i
$291$	76.3900			0.262509
$292$	2.34952	−	2.34952i	0.00804632	−	0.00804632i
$293$	104.580	+	104.580i	0.356927	+	0.356927i	0.862679	−	0.505752i	$-0.168785\pi$
$293$	104.580	+	104.580i	0.356927	+	0.356927i	−0.505752	+	0.862679i	$0.668785\pi$
$294$			14.5594i			0.0495218i
$295$	12.7490	−	359.375i	0.0432171	−	1.21822i
$296$	−74.4852			−0.251639
$297$	−8.36330	+	8.36330i	−0.0281593	+	0.0281593i
$298$	35.8235	+	35.8235i	0.120213	+	0.120213i
$299$			44.7303i			0.149600i
$300$	65.4227	−	56.7439i	0.218076	−	0.189146i
$301$	−310.694			−1.03221
$302$	−296.868	+	296.868i	−0.983008	+	0.983008i
$303$	54.4765	+	54.4765i	0.179790	+	0.179790i
$304$		−	133.661i		−	0.439673i
$305$	−357.853	−	12.6951i	−1.17329	−	0.0416231i
$306$	96.5081			0.315386
$307$	212.425	−	212.425i	0.691938	−	0.691938i	−0.270720	−	0.962658i	$-0.587262\pi$
$307$	212.425	−	212.425i	0.691938	−	0.691938i	0.962658	+	0.270720i	$0.0872618\pi$
$308$	21.1224	+	21.1224i	0.0685792	+	0.0685792i
$309$			213.921i			0.692300i
$310$	134.578	−	125.357i	0.434124	−	0.404377i
$311$	−206.221			−0.663089			−0.331545	−	0.943440i	$-0.607570\pi$
$311$	−206.221			−0.663089			−0.331545	+	0.943440i	$0.607570\pi$
$312$	32.3094	−	32.3094i	0.103556	−	0.103556i
$313$	203.838	+	203.838i	0.651240	+	0.651240i	0.953292	−	0.302052i	$-0.0976716\pi$
$313$	203.838	+	203.838i	0.651240	+	0.651240i	−0.302052	+	0.953292i	$0.597672\pi$
$314$			343.564i			1.09415i
$315$	−67.0863	−	72.0212i	−0.212972	−	0.228639i
$316$	−268.751			−0.850479
$317$	71.5639	−	71.5639i	0.225754	−	0.225754i	−0.585162	−	0.810916i	$-0.698969\pi$
$317$	71.5639	−	71.5639i	0.225754	−	0.225754i	0.810916	+	0.585162i	$0.198969\pi$
$318$	−84.0905	−	84.0905i	−0.264436	−	0.264436i
$319$		−	19.9247i		−	0.0624599i
$320$	−1.41813	+	39.9749i	−0.00443166	+	0.124921i
$321$	38.9833			0.121443
$322$	−31.4689	+	31.4689i	−0.0977295	+	0.0977295i
$323$	537.472	+	537.472i	1.66400	+	1.66400i
$324$			18.0000i			0.0555556i
$325$	152.780	+	176.147i	0.470092	+	0.541991i
$326$	−306.437			−0.939991
$327$	49.4887	−	49.4887i	0.151341	−	0.151341i
$328$	−8.68542	−	8.68542i	−0.0264799	−	0.0264799i
$329$		−	267.041i		−	0.811673i
$330$	27.8601	+	0.988355i	0.0844247	+	0.00299501i
$331$	480.713			1.45230			0.726152	−	0.687534i	$-0.241307\pi$
$331$	480.713			1.45230			0.726152	+	0.687534i	$0.241307\pi$
$332$	−23.7312	+	23.7312i	−0.0714794	+	0.0714794i
$333$	55.8639	+	55.8639i	0.167759	+	0.167759i
$334$			251.226i			0.752174i
$335$	−413.947	+	385.584i	−1.23566	+	1.15100i
$336$	45.4609			0.135300
$337$	−220.766	+	220.766i	−0.655093	+	0.655093i	−0.954215	−	0.299122i	$-0.903306\pi$
$337$	−220.766	+	220.766i	−0.655093	+	0.655093i	0.299122	+	0.954215i	$0.403306\pi$
$338$	−82.0088	−	82.0088i	−0.242630	−	0.242630i
$339$		−	110.079i		−	0.324716i
$340$	−155.043	−	166.448i	−0.456009	−	0.489553i
$341$	59.2037			0.173618
$342$	−100.245	+	100.245i	−0.293115	+	0.293115i
$343$	−254.930	−	254.930i	−0.743237	−	0.743237i
$344$		−	133.925i		−	0.389316i
$345$	−1.47249	+	41.5070i	−0.00426807	+	0.120310i
$346$	−251.287			−0.726262
$347$	229.061	−	229.061i	0.660118	−	0.660118i	−0.295290	−	0.955408i	$-0.595416\pi$
$347$	229.061	−	229.061i	0.660118	−	0.660118i	0.955408	+	0.295290i	$0.0954163\pi$
$348$	−21.4416	−	21.4416i	−0.0616137	−	0.0616137i
$349$		−	498.993i		−	1.42978i	−0.699237	−	0.714890i	$-0.746477\pi$
$349$		−	498.993i		−	1.42978i	0.699237	−	0.714890i	$-0.253523\pi$
$350$	−16.4394	+	231.409i	−0.0469697	+	0.661167i
$351$	−48.4640			−0.138074
$352$	−9.10481	+	9.10481i	−0.0258659	+	0.0258659i
$353$	99.5617	+	99.5617i	0.282044	+	0.282044i	0.833924	−	0.551879i	$-0.186089\pi$
$353$	99.5617	+	99.5617i	0.282044	+	0.282044i	−0.551879	+	0.833924i	$0.686089\pi$
$354$		−	176.168i		−	0.497650i
$355$	518.466	+	18.3929i	1.46047	+	0.0518110i
$356$	−81.8630			−0.229952
$357$	−182.806	+	182.806i	−0.512062	+	0.512062i
$358$	−92.2918	−	92.2918i	−0.257798	−	0.257798i
$359$		−	320.098i		−	0.891639i	−0.895123	−	0.445819i	$-0.852912\pi$
$359$		−	320.098i		−	0.891639i	0.895123	−	0.445819i	$-0.147088\pi$
$360$	31.0447	−	28.9175i	0.0862354	−	0.0803265i
$361$	−755.573			−2.09300
$362$	−111.846	+	111.846i	−0.308966	+	0.308966i
$363$	−141.849	−	141.849i	−0.390768	−	0.390768i
$364$			122.401i			0.336267i
$365$	5.66187	+	6.07836i	0.0155120	+	0.0166531i
$366$	−175.422			−0.479295
$367$	114.617	−	114.617i	0.312308	−	0.312308i	−0.533495	−	0.845803i	$-0.679122\pi$
$367$	114.617	−	114.617i	0.312308	−	0.312308i	0.845803	+	0.533495i	$0.179122\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			13.0281i			0.0353066i
$370$	6.60186	−	186.096i	0.0178429	−	0.502962i
$371$	318.569			0.858677
$372$	63.7109	−	63.7109i	0.171266	−	0.171266i
$373$	444.902	+	444.902i	1.19277	+	1.19277i	0.976287	+	0.216480i	$0.0694576\pi$
$373$	444.902	+	444.902i	1.19277	+	1.19277i	0.216480	+	0.976287i	$0.430542\pi$
$374$		−	73.2239i		−	0.195786i
$375$	135.972	+	168.483i	0.362592	+	0.449289i
$376$	115.108			0.306138
$377$	57.7303	−	57.7303i	0.153131	−	0.153131i
$378$	−34.0957	−	34.0957i	−0.0902002	−	0.0902002i
$379$		−	255.776i		−	0.674870i	−0.941349	−	0.337435i	$-0.890441\pi$
$379$		−	255.776i		−	0.674870i	0.941349	−	0.337435i	$-0.109559\pi$
$380$	333.942	+	11.8468i	0.878794	+	0.0311757i
$381$	207.907			0.545687
$382$	−93.7491	+	93.7491i	−0.245416	+	0.245416i
$383$	336.758	+	336.758i	0.879265	+	0.879265i	0.993458	−	0.114194i	$-0.0364285\pi$
$383$	336.758	+	336.758i	0.879265	+	0.879265i	−0.114194	+	0.993458i	$0.536428\pi$
$384$			19.5959i			0.0510310i
$385$	−54.6450	+	50.9007i	−0.141935	+	0.132210i
$386$	−200.026			−0.518201
$387$	−100.443	+	100.443i	−0.259544	+	0.259544i
$388$	−62.3722	−	62.3722i	−0.160753	−	0.160753i
$389$		−	459.806i		−	1.18202i	−0.806664	−	0.591011i	$-0.798729\pi$
$389$		−	459.806i		−	1.18202i	0.806664	−	0.591011i	$-0.201271\pi$
$390$	77.8589	+	83.5863i	0.199638	+	0.214324i
$391$	109.092			0.279007
$392$	11.8877	−	11.8877i	0.0303258	−	0.0303258i
$393$	−35.5984	−	35.5984i	−0.0905811	−	0.0905811i
$394$		−	224.726i		−	0.570371i
$395$	23.8203	−	671.456i	0.0603046	−	1.69989i
$396$	13.6572			0.0344879
$397$	76.9931	−	76.9931i	0.193937	−	0.193937i	−0.603458	−	0.797395i	$-0.706211\pi$
$397$	76.9931	−	76.9931i	0.193937	−	0.193937i	0.797395	+	0.603458i	$0.206211\pi$
$398$	60.0337	+	60.0337i	0.150838	+	0.150838i
$399$		−	379.771i		−	0.951807i
$400$	−99.7486	−	7.08620i	−0.249372	−	0.0177155i
$401$	50.6120			0.126215			0.0631073	−	0.998007i	$-0.479899\pi$
$401$	50.6120			0.126215			0.0631073	+	0.998007i	$0.479899\pi$
$402$	−195.967	+	195.967i	−0.487481	+	0.487481i
$403$	171.538	+	171.538i	0.425653	+	0.425653i
$404$		−	88.9598i		−	0.220197i
$405$	−44.9717	−	1.59540i	−0.111041	−	0.00393925i
$406$	81.2295			0.200073
$407$	42.3858	−	42.3858i	0.104142	−	0.104142i
$408$	−78.7985	−	78.7985i	−0.193134	−	0.193134i
$409$		−	570.317i		−	1.39442i	−0.716867	−	0.697210i	$-0.754425\pi$
$409$		−	570.317i		−	1.39442i	0.716867	−	0.697210i	$-0.245575\pi$
$410$	22.4697	−	20.9301i	0.0548042	−	0.0510490i
$411$	123.320			0.300049
$412$	174.666	−	174.666i	0.423945	−	0.423945i
$413$	333.698	+	333.698i	0.807986	+	0.807986i
$414$			20.3470i			0.0491473i
$415$	−57.1873	−	61.3940i	−0.137801	−	0.147937i
$416$	−52.7610			−0.126829
$417$	101.982	−	101.982i	0.244561	−	0.244561i
$418$	76.0596	+	76.0596i	0.181961	+	0.181961i
$419$		−	230.287i		−	0.549610i	−0.961500	−	0.274805i	$-0.911387\pi$
$419$		−	230.287i		−	0.549610i	0.961500	−	0.274805i	$-0.0886133\pi$
$420$	−4.02935	+	113.581i	−0.00959368	+	0.270431i
$421$	506.694			1.20355			0.601774	−	0.798666i	$-0.294461\pi$
$421$	506.694			1.20355			0.601774	+	0.798666i	$0.294461\pi$
$422$	−72.4262	+	72.4262i	−0.171626	+	0.171626i
$423$	−86.3308	−	86.3308i	−0.204092	−	0.204092i
$424$			137.319i			0.323866i
$425$	429.601	−	372.611i	1.01083	−	0.876732i
$426$	254.155			0.596609
$427$	332.285	−	332.285i	0.778185	−	0.778185i
$428$	−31.8298	−	31.8298i	−0.0743686	−	0.0743686i
$429$			36.7713i			0.0857140i
$430$	334.601	+	11.8702i	0.778142	+	0.0276050i
$431$	693.838			1.60983			0.804916	−	0.593389i	$-0.202210\pi$
$431$	693.838			1.60983			0.804916	+	0.593389i	$0.202210\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	203.719	+	203.719i	0.470482	+	0.470482i	0.902070	−	0.431589i	$-0.142047\pi$
$433$	203.719	+	203.719i	0.470482	+	0.470482i	−0.431589	+	0.902070i	$0.642047\pi$
$434$			241.363i			0.556136i
$435$	55.4707	−	51.6698i	0.127519	−	0.118781i
$436$	−80.8147			−0.185355
$437$	−113.316	+	113.316i	−0.259305	+	0.259305i
$438$	2.87757	+	2.87757i	0.00656979	+	0.00656979i
$439$			719.749i			1.63952i	0.572708	+	0.819759i	$0.305893\pi$
$439$			719.749i			1.63952i	−0.572708	+	0.819759i	$0.694107\pi$
$440$	−21.9407	−	23.5547i	−0.0498653	−	0.0535334i
$441$	−17.8316			−0.0404344
$442$	212.161	−	212.161i	0.480002	−	0.480002i
$443$	257.483	+	257.483i	0.581225	+	0.581225i	0.935240	−	0.354015i	$-0.115184\pi$
$443$	257.483	+	257.483i	0.581225	+	0.581225i	−0.354015	+	0.935240i	$0.615184\pi$
$444$		−	91.2254i		−	0.205463i
$445$	7.25578	−	204.529i	0.0163051	−	0.459615i
$446$	323.742			0.725879
$447$	−43.8746	+	43.8746i	−0.0981535	+	0.0981535i
$448$	−37.1187	−	37.1187i	−0.0828542	−	0.0828542i
$449$		−	520.870i		−	1.16007i	−0.814593	−	0.580033i	$-0.803040\pi$
$449$		−	520.870i		−	1.16007i	0.814593	−	0.580033i	$-0.196960\pi$
$450$	69.4968	+	80.1261i	0.154437	+	0.178058i
$451$	9.88489			0.0219177
$452$	−89.8788	+	89.8788i	−0.198847	+	0.198847i
$453$	−363.588	−	363.588i	−0.802623	−	0.802623i
$454$			516.653i			1.13800i
$455$	−305.810	−	10.8488i	−0.672111	−	0.0238435i
$456$	163.700			0.358992
$457$	−274.247	+	274.247i	−0.600103	+	0.600103i	−0.940340	−	0.340237i	$-0.889493\pi$
$457$	−274.247	+	274.247i	−0.600103	+	0.600103i	0.340237	+	0.940340i	$0.389493\pi$
$458$	−210.083	−	210.083i	−0.458697	−	0.458697i
$459$			118.198i			0.257511i
$460$	35.0926	−	32.6881i	0.0762883	−	0.0710610i
$461$	−72.7050			−0.157712			−0.0788558	−	0.996886i	$-0.525127\pi$
$461$	−72.7050			−0.157712			−0.0788558	+	0.996886i	$0.525127\pi$
$462$	−25.8696	+	25.8696i	−0.0559947	+	0.0559947i
$463$	455.202	+	455.202i	0.983158	+	0.983158i	0.999861	−	0.0167027i	$-0.00531687\pi$
$463$	455.202	+	455.202i	0.983158	+	0.983158i	−0.0167027	+	0.999861i	$0.505317\pi$
$464$			35.0139i			0.0754611i
$465$	153.530	+	164.824i	0.330173	+	0.354460i
$466$	488.178			1.04759
$467$	−569.865	+	569.865i	−1.22027	+	1.22027i	−0.252733	+	0.967536i	$0.581329\pi$
$467$	−569.865	+	569.865i	−1.22027	+	1.22027i	−0.967536	+	0.252733i	$0.918671\pi$
$468$	39.5707	+	39.5707i	0.0845528	+	0.0845528i
$469$		−	742.405i		−	1.58295i
$470$	−10.2024	+	287.588i	−0.0217072	+	0.611890i
$471$	−420.779			−0.893373
$472$	−143.841	+	143.841i	−0.304747	+	0.304747i
$473$	76.2099	+	76.2099i	0.161120	+	0.161120i
$474$		−	329.152i		−	0.694414i
$475$	−59.1966	+	833.279i	−0.124624	+	1.75427i
$476$	298.521			0.627145
$477$	102.989	−	102.989i	0.215911	−	0.215911i
$478$	−314.702	−	314.702i	−0.658373	−	0.658373i
$479$			681.451i			1.42265i	0.702861	+	0.711327i	$0.251905\pi$
$479$			681.451i			1.42265i	−0.702861	+	0.711327i	$0.748095\pi$
$480$	−48.9590	−	1.73685i	−0.101998	−	0.00361844i
$481$	245.619			0.510643
$482$	−178.804	+	178.804i	−0.370964	+	0.370964i
$483$	−38.5414	−	38.5414i	−0.0797958	−	0.0797958i
$484$			231.638i			0.478591i
$485$	161.361	−	150.304i	0.332703	−	0.309906i
$486$	−22.0454			−0.0453609
$487$	457.067	−	457.067i	0.938535	−	0.938535i	−0.0596820	−	0.998217i	$-0.519009\pi$
$487$	457.067	−	457.067i	0.938535	−	0.938535i	0.998217	+	0.0596820i	$0.0190087\pi$
$488$	143.231	+	143.231i	0.293507	+	0.293507i
$489$		−	375.307i		−	0.767499i
$490$	28.6469	+	30.7542i	0.0584631	+	0.0627637i
$491$	−2.82990			−0.00576355			−0.00288178	−	0.999996i	$-0.500917\pi$
$491$	−2.82990			−0.00576355			−0.00288178	+	0.999996i	$0.500917\pi$
$492$	10.6374	−	10.6374i	0.0216208	−	0.0216208i
$493$	−140.797	−	140.797i	−0.285592	−	0.285592i
$494$			440.754i			0.892215i
$495$	−1.21048	+	34.1216i	−0.00244542	+	0.0689324i
$496$	−104.039			−0.209757
$497$	−481.422	+	481.422i	−0.968657	+	0.968657i
$498$	−29.0646	−	29.0646i	−0.0583627	−	0.0583627i
$499$		−	562.240i		−	1.12673i	−0.826207	−	0.563367i	$-0.809506\pi$
$499$		−	562.240i		−	1.12673i	0.826207	−	0.563367i	$-0.190494\pi$
$500$	26.5454	−	248.587i	0.0530908	−	0.497173i
$501$	−307.688			−0.614147
$502$	183.648	−	183.648i	0.365832	−	0.365832i
$503$	−516.973	−	516.973i	−1.02778	−	1.02778i	−0.999603	−	0.0281756i	$-0.991030\pi$
$503$	−516.973	−	516.973i	−1.02778	−	1.02778i	−0.0281756	−	0.999603i	$-0.508970\pi$
$504$			55.6780i			0.110472i
$505$	222.260	+	7.88479i	0.440118	+	0.0156134i
$506$	15.4380			0.0305098
$507$	100.440	−	100.440i	0.198106	−	0.198106i
$508$	−169.755	−	169.755i	−0.334164	−	0.334164i
$509$		−	347.014i		−	0.681756i	−0.940108	−	0.340878i	$-0.889276\pi$
$509$		−	347.014i		−	0.681756i	0.940108	−	0.340878i	$-0.110724\pi$
$510$	203.857	−	189.888i	0.399719	−	0.372330i
$511$	−10.9014			−0.0213335
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−122.775	−	122.775i	−0.239328	−	0.239328i
$514$			517.318i			1.00646i
$515$	420.908	+	451.871i	0.817297	+	0.877418i
$516$	164.023			0.317875
$517$	−65.5021	+	65.5021i	−0.126697	+	0.126697i
$518$	172.800	+	172.800i	0.333590	+	0.333590i
$519$		−	307.762i		−	0.592990i
$520$	4.67637	−	131.819i	0.00899302	−	0.253499i
$521$	910.660			1.74791			0.873954	−	0.486010i	$-0.161548\pi$
$521$	910.660			1.74791			0.873954	+	0.486010i	$0.161548\pi$
$522$	26.2605	−	26.2605i	0.0503074	−	0.0503074i
$523$	595.957	+	595.957i	1.13950	+	1.13950i	0.988540	+	0.150957i	$0.0482355\pi$
$523$	595.957	+	595.957i	1.13950	+	1.13950i	0.150957	+	0.988540i	$0.451765\pi$
$524$			58.1319i			0.110939i
$525$	−283.416	−	20.1341i	−0.539841	−	0.0383506i
$526$	−13.4613			−0.0255919
$527$	418.360	−	418.360i	0.793853	−	0.793853i
$528$	−11.1511	−	11.1511i	−0.0211194	−	0.0211194i
$529$			23.0000i			0.0434783i
$530$	−343.082	−	12.1710i	−0.647325	−	0.0229642i
$531$	215.761			0.406329
$532$	−310.082	+	310.082i	−0.582860	+	0.582860i
$533$	28.6407	+	28.6407i	0.0537349	+	0.0537349i
$534$		−	100.261i		−	0.187755i
$535$	82.3456	−	76.7032i	0.153917	−	0.143370i
$536$	320.014			0.597040
$537$	113.034	−	113.034i	0.210491	−	0.210491i
$538$	195.237	+	195.237i	0.362893	+	0.362893i
$539$			13.5294i			0.0251009i
$540$	35.4166	+	38.0219i	0.0655863	+	0.0704109i
$541$	−876.710			−1.62054			−0.810268	−	0.586059i	$-0.800679\pi$
$541$	−876.710			−1.62054			−0.810268	+	0.586059i	$0.800679\pi$
$542$	−190.383	+	190.383i	−0.351261	+	0.351261i
$543$	−136.983	−	136.983i	−0.252270	−	0.252270i
$544$			128.677i			0.236539i
$545$	7.16286	−	201.910i	0.0131429	−	0.370476i
$546$	−149.910			−0.274561
$547$	−628.878	+	628.878i	−1.14969	+	1.14969i	−0.163071	+	0.986614i	$0.552140\pi$
$547$	−628.878	+	628.878i	−1.14969	+	1.14969i	−0.986614	+	0.163071i	$0.947860\pi$
$548$	−100.690	−	100.690i	−0.183741	−	0.183741i
$549$		−	214.847i		−	0.391343i
$550$	60.7944	−	52.7296i	0.110535	−	0.0958720i
$551$	292.499			0.530852
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	623.481	+	623.481i	1.12745	+	1.12745i
$554$		−	723.231i		−	1.30547i
$555$	227.920	+	8.08560i	0.410667	+	0.0145686i
$556$	−166.536			−0.299525
$557$	628.139	−	628.139i	1.12772	−	1.12772i	0.137170	−	0.990547i	$-0.456199\pi$
$557$	628.139	−	628.139i	1.12772	−	1.12772i	0.990547	−	0.137170i	$-0.0438008\pi$
$558$	78.0296	+	78.0296i	0.139838	+	0.139838i
$559$			441.624i			0.790026i
$560$	96.0283	−	89.4484i	0.171479	−	0.159729i
$561$	89.6806			0.159859
$562$	−259.206	+	259.206i	−0.461220	+	0.461220i
$563$	318.946	+	318.946i	0.566511	+	0.566511i	0.931149	−	0.364638i	$-0.118807\pi$
$563$	318.946	+	318.946i	0.566511	+	0.566511i	−0.364638	+	0.931149i	$0.618807\pi$
$564$			140.978i			0.249960i
$565$	−216.590	−	232.522i	−0.383344	−	0.411543i
$566$	−567.185			−1.00209
$567$	41.7585	−	41.7585i	0.0736482	−	0.0736482i
$568$	−207.517	−	207.517i	−0.365347	−	0.365347i
$569$		−	496.154i		−	0.871976i	−0.899952	−	0.435988i	$-0.856399\pi$
$569$		−	496.154i		−	0.871976i	0.899952	−	0.435988i	$-0.143601\pi$
$570$	−14.5093	+	408.993i	−0.0254549	+	0.717532i
$571$	−623.806			−1.09248			−0.546240	−	0.837629i	$-0.683941\pi$
$571$	−623.806			−1.09248			−0.546240	+	0.837629i	$0.683941\pi$
$572$	30.0236	−	30.0236i	0.0524889	−	0.0524889i
$573$	−114.819	−	114.819i	−0.200382	−	0.200382i
$574$			40.2989i			0.0702072i
$575$	78.5584	+	90.5736i	0.136623	+	0.157519i
$576$	−24.0000			−0.0416667
$577$	299.545	−	299.545i	0.519143	−	0.519143i	−0.398169	−	0.917312i	$-0.630354\pi$
$577$	299.545	−	299.545i	0.519143	−	0.519143i	0.917312	+	0.398169i	$0.130354\pi$
$578$	−228.434	−	228.434i	−0.395214	−	0.395214i
$579$		−	244.980i		−	0.423109i
$580$	−87.4798	−	3.10340i	−0.150827	−	0.00535069i
$581$	110.109			0.189516
$582$	76.3900	−	76.3900i	0.131254	−	0.131254i
$583$	−78.1416	−	78.1416i	−0.134034	−	0.134034i
$584$		−	4.69905i		−	0.00804632i
$585$	−102.372	+	95.3573i	−0.174995	+	0.163004i
$586$	209.159			0.356927
$587$	−76.2399	+	76.2399i	−0.129881	+	0.129881i	−0.769059	−	0.639178i	$-0.779275\pi$
$587$	−76.2399	+	76.2399i	−0.129881	+	0.129881i	0.639178	+	0.769059i	$0.279275\pi$
$588$	14.5594	+	14.5594i	0.0247609	+	0.0247609i
$589$			869.124i			1.47559i
$590$	−346.626	−	372.124i	−0.587502	−	0.630719i
$591$	275.232			0.465706
$592$	−74.4852	+	74.4852i	−0.125820	+	0.125820i
$593$	312.744	+	312.744i	0.527393	+	0.527393i	0.919794	−	0.392401i	$-0.128356\pi$
$593$	312.744	+	312.744i	0.527393	+	0.527393i	−0.392401	+	0.919794i	$0.628356\pi$
$594$			16.7266i			0.0281593i
$595$	−26.4589	+	745.833i	−0.0444687	+	1.25350i
$596$	71.6470			0.120213
$597$	−73.5259	+	73.5259i	−0.123159	+	0.123159i
$598$	44.7303	+	44.7303i	0.0747998	+	0.0747998i
$599$			822.073i			1.37241i	0.727408	+	0.686205i	$0.240725\pi$
$599$			822.073i			1.37241i	−0.727408	+	0.686205i	$0.759275\pi$
$600$	8.67879	−	122.167i	0.0144646	−	0.203611i
$601$	−70.4421			−0.117208			−0.0586040	−	0.998281i	$-0.518665\pi$
$601$	−70.4421			−0.117208			−0.0586040	+	0.998281i	$0.518665\pi$
$602$	−310.694	+	310.694i	−0.516103	+	0.516103i
$603$	−240.010	−	240.010i	−0.398027	−	0.398027i
$604$			593.737i			0.983008i
$605$	−578.730	−	20.5308i	−0.956579	−	0.0339352i
$606$	108.953			0.179790
$607$	66.6471	−	66.6471i	0.109797	−	0.109797i	−0.650074	−	0.759871i	$-0.725262\pi$
$607$	66.6471	−	66.6471i	0.109797	−	0.109797i	0.759871	+	0.650074i	$0.225262\pi$
$608$	−133.661	−	133.661i	−0.219837	−	0.219837i
$609$			99.4854i			0.163359i
$610$	−370.549	+	345.158i	−0.607457	+	0.565833i
$611$	−379.575			−0.621235
$612$	96.5081	−	96.5081i	0.157693	−	0.157693i
$613$	182.027	+	182.027i	0.296945	+	0.296945i	0.839816	−	0.542871i	$-0.182663\pi$
$613$	182.027	+	182.027i	0.296945	+	0.296945i	−0.542871	+	0.839816i	$0.682663\pi$
$614$		−	424.850i		−	0.691938i
$615$	25.6340	+	27.5197i	0.0416813	+	0.0447474i
$616$	42.2448			0.0685792
$617$	−312.757	+	312.757i	−0.506900	+	0.506900i	−0.913573	−	0.406674i	$-0.866689\pi$
$617$	−312.757	+	312.757i	−0.506900	+	0.506900i	0.406674	+	0.913573i	$0.366689\pi$
$618$	213.921	+	213.921i	0.346150	+	0.346150i
$619$			779.683i			1.25958i	0.776764	+	0.629792i	$0.216860\pi$
$619$			779.683i			1.25958i	−0.776764	+	0.629792i	$0.783140\pi$
$620$	9.22135	−	259.935i	0.0148732	−	0.419250i
$621$	−24.9199			−0.0401286
$622$	−206.221	+	206.221i	−0.331545	+	0.331545i
$623$	189.915	+	189.915i	0.304840	+	0.304840i
$624$		−	64.6187i		−	0.103556i
$625$	618.723	+	88.3548i	0.989957	+	0.141368i
$626$	407.676			0.651240
$627$	−93.1537	+	93.1537i	−0.148570	+	0.148570i
$628$	343.564	+	343.564i	0.547077	+	0.547077i
$629$		−	599.035i		−	0.952361i
$630$	−139.108	−	4.93492i	−0.220806	−	0.00783321i
$631$	286.619			0.454230			0.227115	−	0.973868i	$-0.427071\pi$
$631$	286.619			0.454230			0.227115	+	0.973868i	$0.427071\pi$
$632$	−268.751	+	268.751i	−0.425240	+	0.425240i
$633$	−88.7037	−	88.7037i	−0.140132	−	0.140132i
$634$		−	143.128i		−	0.225754i
$635$	439.167	−	409.075i	0.691602	−	0.644213i
$636$	−168.181			−0.264436
$637$	−39.2004	+	39.2004i	−0.0615391	+	0.0615391i
$638$	−19.9247	−	19.9247i	−0.0312299	−	0.0312299i
$639$			311.275i			0.487129i
$640$	38.5567	+	41.3930i	0.0602449	+	0.0646765i
$641$	328.082			0.511829			0.255914	−	0.966699i	$-0.417623\pi$
$641$	328.082			0.511829			0.255914	+	0.966699i	$0.417623\pi$
$642$	38.9833	−	38.9833i	0.0607217	−	0.0607217i
$643$	159.578	+	159.578i	0.248177	+	0.248177i	0.820222	−	0.572045i	$-0.193850\pi$
$643$	159.578	+	159.578i	0.248177	+	0.248177i	−0.572045	+	0.820222i	$0.693850\pi$
$644$			62.9378i			0.0977295i
$645$	−14.5379	+	409.801i	−0.0225394	+	0.635350i
$646$	1074.94			1.66400
$647$	127.452	−	127.452i	0.196989	−	0.196989i	−0.601719	−	0.798708i	$-0.705517\pi$
$647$	127.452	−	127.452i	0.196989	−	0.196989i	0.798708	+	0.601719i	$0.205517\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$		−	163.705i		−	0.252242i
$650$	328.927	+	23.3672i	0.506042	+	0.0359495i
$651$	−295.608			−0.454083
$652$	−306.437	+	306.437i	−0.469995	+	0.469995i
$653$	−902.017	−	902.017i	−1.38134	−	1.38134i	−0.842238	−	0.539105i	$-0.818762\pi$
$653$	−902.017	−	902.017i	−1.38134	−	1.38134i	−0.539105	−	0.842238i	$-0.681238\pi$
$654$		−	98.9773i		−	0.151341i
$655$	−145.238	−	5.15241i	−0.221738	−	0.00786628i
$656$	−17.3708			−0.0264799
$657$	−3.52429	+	3.52429i	−0.00536421	+	0.00536421i
$658$	−267.041	−	267.041i	−0.405837	−	0.405837i
$659$			723.945i			1.09855i	0.835641	+	0.549276i	$0.185096\pi$
$659$			723.945i			1.09855i	−0.835641	+	0.549276i	$0.814904\pi$
$660$	28.8485	−	26.8718i	0.0437098	−	0.0407148i
$661$	38.6236			0.0584321			0.0292160	−	0.999573i	$-0.490699\pi$
$661$	38.6236			0.0584321			0.0292160	+	0.999573i	$0.490699\pi$
$662$	480.713	−	480.713i	0.726152	−	0.726152i
$663$	259.843	+	259.843i	0.391920	+	0.391920i
$664$			47.4623i			0.0714794i
$665$	−747.233	−	802.201i	−1.12366	−	1.20632i
$666$	111.728			0.167759
$667$	29.6845	−	29.6845i	0.0445045	−	0.0445045i
$668$	251.226	+	251.226i	0.376087	+	0.376087i
$669$			396.502i			0.592678i
$670$	−28.3638	+	799.531i	−0.0423341	+	1.19333i
$671$	−163.012			−0.242939
$672$	45.4609	−	45.4609i	0.0676502	−	0.0676502i
$673$	−691.238	−	691.238i	−1.02710	−	1.02710i	−0.999622	−	0.0274776i	$-0.991253\pi$
$673$	−691.238	−	691.238i	−1.02710	−	1.02710i	−0.0274776	−	0.999622i	$-0.508747\pi$
$674$			441.533i			0.655093i
$675$	−98.1340	+	85.1159i	−0.145384	+	0.126098i
$676$	−164.018			−0.242630
$677$	242.001	−	242.001i	0.357460	−	0.357460i	−0.505416	−	0.862876i	$-0.668661\pi$
$677$	242.001	−	242.001i	0.357460	−	0.357460i	0.862876	+	0.505416i	$0.168661\pi$
$678$	−110.079	−	110.079i	−0.162358	−	0.162358i
$679$			289.397i			0.426210i
$680$	−321.491	−	11.4051i	−0.472781	−	0.0167722i
$681$	−632.768			−0.929174
$682$	59.2037	−	59.2037i	0.0868090	−	0.0868090i
$683$	−166.819	−	166.819i	−0.244245	−	0.244245i	0.574359	−	0.818604i	$-0.305251\pi$
$683$	−166.819	−	166.819i	−0.244245	−	0.244245i	−0.818604	+	0.574359i	$0.805251\pi$
$684$			200.491i			0.293115i
$685$	260.492	−	242.643i	0.380280	−	0.354223i
$686$	−509.861			−0.743237
$687$	257.299	−	257.299i	0.374525	−	0.374525i
$688$	−133.925	−	133.925i	−0.194658	−	0.194658i
$689$		−	452.818i		−	0.657211i
$690$	40.0345	+	42.9795i	0.0580210	+	0.0622891i
$691$	230.554			0.333653			0.166827	−	0.985986i	$-0.446648\pi$
$691$	230.554			0.333653			0.166827	+	0.985986i	$0.446648\pi$
$692$	−251.287	+	251.287i	−0.363131	+	0.363131i
$693$	−31.6836	−	31.6836i	−0.0457195	−	0.0457195i
$694$		−	458.122i		−	0.660118i
$695$	14.7606	−	416.079i	0.0212383	−	0.598674i
$696$	−42.8832			−0.0616137
$697$	69.8511	−	69.8511i	0.100217	−	0.100217i
$698$	−498.993	−	498.993i	−0.714890	−	0.714890i
$699$			597.893i			0.855355i
$700$	214.969	+	247.848i	0.307099	+	0.354069i
$701$	−569.921			−0.813012			−0.406506	−	0.913648i	$-0.633253\pi$
$701$	−569.921			−0.813012			−0.406506	+	0.913648i	$0.633253\pi$
$702$	−48.4640	+	48.4640i	−0.0690371	+	0.0690371i
$703$	622.234	+	622.234i	0.885112	+	0.885112i
$704$			18.2096i			0.0258659i
$705$	−352.222	−	12.4953i	−0.499606	−	0.0177238i
$706$	199.123			0.282044
$707$	−206.379	+	206.379i	−0.291909	+	0.291909i
$708$	−176.168	−	176.168i	−0.248825	−	0.248825i
$709$		−	1007.05i		−	1.42039i	−0.704008	−	0.710193i	$-0.748608\pi$
$709$		−	1007.05i		−	1.42039i	0.704008	−	0.710193i	$-0.251392\pi$
$710$	536.859	−	500.073i	0.756140	−	0.704329i
$711$	403.127			0.566986
$712$	−81.8630	+	81.8630i	−0.114976	+	0.114976i
$713$	88.2038	+	88.2038i	0.123708	+	0.123708i
$714$			365.612i			0.512062i
$715$	72.3508	+	77.6730i	0.101190	+	0.108634i
$716$	−184.584			−0.257798
$717$	385.430	−	385.430i	0.537559	−	0.537559i
$718$	−320.098	−	320.098i	−0.445819	−	0.445819i
$719$		−	1131.87i		−	1.57423i	−0.616806	−	0.787115i	$-0.711574\pi$
$719$		−	1131.87i		−	1.57423i	0.616806	−	0.787115i	$-0.288426\pi$
$720$	2.12720	−	59.9623i	0.00295444	−	0.0832809i
$721$	−810.419			−1.12402
$722$	−755.573	+	755.573i	−1.04650	+	1.04650i
$723$	−218.990	−	218.990i	−0.302891	−	0.302891i
$724$			223.692i			0.308966i
$725$	15.5072	−	218.287i	0.0213893	−	0.301086i
$726$	−283.697			−0.390768
$727$	745.476	−	745.476i	1.02541	−	1.02541i	0.0257448	−	0.999669i	$-0.491804\pi$
$727$	745.476	−	745.476i	1.02541	−	1.02541i	0.999669	−	0.0257448i	$-0.00819574\pi$
$728$	122.401	+	122.401i	0.168133	+	0.168133i
$729$		−	27.0000i		−	0.0370370i
$730$	11.7402	+	0.416492i	0.0160825	+	0.000570537i
$731$	1077.07			1.47342
$732$	−175.422	+	175.422i	−0.239647	+	0.239647i
$733$	917.155	+	917.155i	1.25123	+	1.25123i	0.955167	+	0.296067i	$0.0956753\pi$
$733$	917.155	+	917.155i	1.25123	+	1.25123i	0.296067	+	0.955167i	$0.404325\pi$
$734$		−	229.234i		−	0.312308i
$735$	−37.6661	+	35.0852i	−0.0512463	+	0.0477349i
$736$	−27.1293			−0.0368605
$737$	−182.104	+	182.104i	−0.247088	+	0.247088i
$738$	13.0281	+	13.0281i	0.0176533	+	0.0176533i
$739$		−	413.291i		−	0.559257i	−0.960108	−	0.279629i	$-0.909789\pi$
$739$		−	413.291i		−	0.559257i	0.960108	−	0.279629i	$-0.0902114\pi$
$740$	−179.494	−	192.698i	−0.242560	−	0.260402i
$741$	−539.811			−0.728490
$742$	318.569	−	318.569i	0.429339	−	0.429339i
$743$	674.486	+	674.486i	0.907788	+	0.907788i	0.996093	−	0.0883055i	$-0.0281452\pi$
$743$	674.486	+	674.486i	0.907788	+	0.907788i	−0.0883055	+	0.996093i	$0.528145\pi$
$744$		−	127.422i		−	0.171266i
$745$	−6.35030	+	179.005i	−0.00852389	+	0.240275i
$746$	889.804			1.19277
$747$	35.5968	−	35.5968i	0.0476529	−	0.0476529i
$748$	−73.2239	−	73.2239i	−0.0978930	−	0.0978930i
$749$			147.685i			0.197176i
$750$	304.455	+	32.5113i	0.405940	+	0.0433485i
$751$	233.606			0.311060			0.155530	−	0.987831i	$-0.450291\pi$
$751$	233.606			0.311060			0.155530	+	0.987831i	$0.450291\pi$
$752$	115.108	−	115.108i	0.153069	−	0.153069i
$753$	224.922	+	224.922i	0.298701	+	0.298701i
$754$		−	115.461i		−	0.153131i
$755$	−1483.41	−	52.6248i	−1.96478	−	0.0697017i
$756$	−68.1914			−0.0902002
$757$	0.636656	−	0.636656i	0.000841026	−	0.000841026i	−0.706686	−	0.707527i	$-0.749811\pi$
$757$	0.636656	−	0.636656i	0.000841026	−	0.000841026i	0.707527	+	0.706686i	$0.249811\pi$
$758$	−255.776	−	255.776i	−0.337435	−	0.337435i
$759$			18.9076i			0.0249111i
$760$	345.788	−	322.095i	0.454985	−	0.423809i
$761$	−400.232			−0.525929			−0.262964	−	0.964806i	$-0.584700\pi$
$761$	−400.232			−0.525929			−0.262964	+	0.964806i	$0.584700\pi$
$762$	207.907	−	207.907i	0.272844	−	0.272844i
$763$	187.483	+	187.483i	0.245719	+	0.245719i
$764$			187.498i			0.245416i
$765$	232.565	+	249.672i	0.304006	+	0.326369i
$766$	673.517			0.879265
$767$	474.323	−	474.323i	0.618413	−	0.618413i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$			818.791i			1.06475i	0.846509	+	0.532374i	$0.178700\pi$
$769$			818.791i			1.06475i	−0.846509	+	0.532374i	$0.821300\pi$
$770$	−3.74429	+	105.546i	−0.00486272	+	0.137072i
$771$	−633.583			−0.821768
$772$	−200.026	+	200.026i	−0.259100	+	0.259100i
$773$	−836.271	−	836.271i	−1.08185	−	1.08185i	−0.996337	−	0.0855136i	$-0.972747\pi$
$773$	−836.271	−	836.271i	−1.08185	−	1.08185i	−0.0855136	−	0.996337i	$-0.527253\pi$
$774$			200.887i			0.259544i
$775$	648.612	+	46.0778i	0.836919	+	0.0594552i
$776$	−124.744			−0.160753
$777$	−211.635	+	211.635i	−0.272375	+	0.272375i
$778$	−459.806	−	459.806i	−0.591011	−	0.591011i
$779$			145.112i			0.186280i
$780$	161.445	+	5.72736i	0.206981	+	0.00734277i
$781$	236.175			0.302401
$782$	109.092	−	109.092i	0.139503	−	0.139503i
$783$	32.1624	+	32.1624i	0.0410758	+	0.0410758i
$784$		−	23.7754i		−	0.0303258i
$785$	−888.822	+	827.920i	−1.13226	+	1.05467i
$786$	−71.1967			−0.0905811
$787$	112.697	−	112.697i	0.143199	−	0.143199i	−0.631873	−	0.775072i	$-0.717714\pi$
$787$	112.697	−	112.697i	0.143199	−	0.143199i	0.775072	+	0.631873i	$0.217714\pi$
$788$	−224.726	−	224.726i	−0.285185	−	0.285185i
$789$		−	16.4867i		−	0.0208957i
$790$	−647.636	−	695.277i	−0.819792	−	0.880097i
$791$	417.023			0.527210
$792$	13.6572	−	13.6572i	0.0172440	−	0.0172440i
$793$	−472.314	−	472.314i	−0.595604	−	0.595604i
$794$		−	153.986i		−	0.193937i
$795$	14.9064	−	420.188i	0.0187502	−	0.528539i
$796$	120.067			0.150838
$797$	−54.8483	+	54.8483i	−0.0688184	+	0.0688184i	−0.740678	−	0.671860i	$-0.765496\pi$
$797$	−54.8483	+	54.8483i	−0.0688184	+	0.0688184i	0.671860	+	0.740678i	$0.265496\pi$
$798$	−379.771	−	379.771i	−0.475904	−	0.475904i
$799$			925.735i			1.15862i
$800$	−106.835	+	92.6624i	−0.133544	+	0.115828i
$801$	122.795			0.153302
$802$	50.6120	−	50.6120i	0.0631073	−	0.0631073i
$803$	2.67400	+	2.67400i	0.00333001	+	0.00333001i
$804$			391.935i			0.487481i
$805$	−157.246	−	5.57838i	−0.195336	−	0.00692966i
$806$	343.076			0.425653
$807$	−239.115	+	239.115i	−0.296301	+	0.296301i
$808$	−88.9598	−	88.9598i	−0.110099	−	0.110099i
$809$		−	769.211i		−	0.950817i	−0.879765	−	0.475408i	$-0.842300\pi$
$809$		−	769.211i		−	0.950817i	0.879765	−	0.475408i	$-0.157700\pi$
$810$	−46.5671	+	43.3763i	−0.0574903	+	0.0535510i
$811$	−452.045			−0.557392			−0.278696	−	0.960379i	$-0.589902\pi$
$811$	−452.045			−0.557392			−0.278696	+	0.960379i	$0.589902\pi$
$812$	81.2295	−	81.2295i	0.100036	−	0.100036i
$813$	−233.171	−	233.171i	−0.286803	−	0.286803i
$814$		−	84.7717i		−	0.104142i
$815$	−738.450	−	792.771i	−0.906074	−	0.972725i
$816$	−157.597			−0.193134
$817$	−1118.78	+	1118.78i	−1.36937	+	1.36937i
$818$	−570.317	−	570.317i	−0.697210	−	0.697210i
$819$		−	183.602i		−	0.224178i
$820$	1.53963	−	43.3998i	0.00187760	−	0.0529266i
$821$	−683.700			−0.832765			−0.416382	−	0.909190i	$-0.636702\pi$
$821$	−683.700			−0.832765			−0.416382	+	0.909190i	$0.636702\pi$
$822$	123.320	−	123.320i	0.150024	−	0.150024i
$823$	−431.885	−	431.885i	−0.524770	−	0.524770i	0.394238	−	0.919008i	$-0.371008\pi$
$823$	−431.885	−	431.885i	−0.524770	−	0.524770i	−0.919008	+	0.394238i	$0.871008\pi$
$824$		−	349.331i		−	0.423945i
$825$	64.5803	+	74.4576i	0.0782791	+	0.0902517i
$826$	667.397			0.807986
$827$	−319.553	+	319.553i	−0.386400	+	0.386400i	−0.873401	−	0.487001i	$-0.838091\pi$
$827$	−319.553	+	319.553i	−0.386400	+	0.386400i	0.487001	+	0.873401i	$0.338091\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$			809.158i			0.976065i	0.872826	+	0.488032i	$0.162285\pi$
$829$			809.158i			0.976065i	−0.872826	+	0.488032i	$0.837715\pi$
$830$	−118.581	−	4.20674i	−0.142869	−	0.00506836i
$831$	885.774			1.06591
$832$	−52.7610	+	52.7610i	−0.0634146	+	0.0634146i
$833$	95.6049	+	95.6049i	0.114772	+	0.114772i
$834$		−	203.964i		−	0.244561i
$835$	−649.937	+	605.403i	−0.778368	+	0.725034i
$836$	152.119			0.181961
$837$	−95.5664	+	95.5664i	−0.114177	+	0.114177i
$838$	−230.287	−	230.287i	−0.274805	−	0.274805i
$839$		−	66.4582i		−	0.0792112i	−0.999215	−	0.0396056i	$-0.987390\pi$
$839$		−	66.4582i		−	0.0792112i	0.999215	−	0.0396056i	$-0.0126102\pi$
$840$	109.552	+	117.610i	0.130418	+	0.140012i
$841$	764.376			0.908890
$842$	506.694	−	506.694i	0.601774	−	0.601774i
$843$	−317.461	−	317.461i	−0.376584	−	0.376584i
$844$			144.852i			0.171626i
$845$	14.5374	−	409.786i	0.0172040	−	0.484954i
$846$	−172.662			−0.204092
$847$	537.381	−	537.381i	0.634452	−	0.634452i
$848$	137.319	+	137.319i	0.161933	+	0.161933i
$849$		−	694.657i		−	0.818206i
$850$	56.9896	−	802.212i	0.0670466	−	0.943779i
$851$	126.296			0.148409
$852$	254.155	−	254.155i	0.298304	−	0.298304i
$853$	−536.615	−	536.615i	−0.629091	−	0.629091i	0.318748	−	0.947839i	$-0.396737\pi$
$853$	−536.615	−	536.615i	−0.629091	−	0.629091i	−0.947839	+	0.318748i	$0.896737\pi$
$854$		−	664.570i		−	0.778185i
$855$	−500.912	−	17.7702i	−0.585862	−	0.0207838i
$856$	−63.6595			−0.0743686
$857$	−416.027	+	416.027i	−0.485446	+	0.485446i	−0.906866	−	0.421420i	$-0.861532\pi$
$857$	−416.027	+	416.027i	−0.485446	+	0.485446i	0.421420	+	0.906866i	$0.361532\pi$
$858$	36.7713	+	36.7713i	0.0428570	+	0.0428570i
$859$		−	1405.34i		−	1.63601i	−0.575208	−	0.818007i	$-0.695079\pi$
$859$		−	1405.34i		−	1.63601i	0.575208	−	0.818007i	$-0.304921\pi$
$860$	346.471	−	322.731i	0.402873	−	0.375268i
$861$	−49.3559			−0.0573239
$862$	693.838	−	693.838i	0.804916	−	0.804916i
$863$	325.229	+	325.229i	0.376859	+	0.376859i	0.869968	−	0.493109i	$-0.164140\pi$
$863$	325.229	+	325.229i	0.376859	+	0.376859i	−0.493109	+	0.869968i	$0.664140\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−605.549	−	650.094i	−0.700057	−	0.751553i
$866$	407.437			0.470482
$867$	279.773	−	279.773i	0.322691	−	0.322691i
$868$	241.363	+	241.363i	0.278068	+	0.278068i
$869$		−	305.866i		−	0.351975i
$870$	3.80087	−	107.140i	0.00436882	−	0.123150i
$871$	−1055.26			−1.21155
$872$	−80.8147	+	80.8147i	−0.0926774	+	0.0926774i
$873$	93.5583	+	93.5583i	0.107169	+	0.107169i
$874$			226.633i			0.259305i
$875$	−638.284	+	515.118i	−0.729467	+	0.588706i
$876$	5.75514			0.00656979
$877$	−457.930	+	457.930i	−0.522155	+	0.522155i	−0.918222	−	0.396066i	$-0.870375\pi$
$877$	−457.930	+	457.930i	−0.522155	+	0.522155i	0.396066	+	0.918222i	$0.370375\pi$
$878$	719.749	+	719.749i	0.819759	+	0.819759i
$879$			256.166i			0.291429i
$880$	−45.4954	−	1.61398i	−0.0516993	−	0.00183406i
$881$	611.733			0.694362			0.347181	−	0.937798i	$-0.387139\pi$
$881$	611.733			0.694362			0.347181	+	0.937798i	$0.387139\pi$
$882$	−17.8316	+	17.8316i	−0.0202172	+	0.0202172i
$883$	−677.524	−	677.524i	−0.767298	−	0.767298i	0.210332	−	0.977630i	$-0.432546\pi$
$883$	−677.524	−	677.524i	−0.767298	−	0.767298i	−0.977630	+	0.210332i	$0.932546\pi$
$884$		−	424.321i		−	0.480002i
$885$	455.757	−	424.529i	0.514980	−	0.479694i
$886$	514.966			0.581225
$887$	−921.542	+	921.542i	−1.03894	+	1.03894i	−0.0397317	+	0.999210i	$0.512650\pi$
$887$	−921.542	+	921.542i	−1.03894	+	1.03894i	−0.999210	+	0.0397317i	$0.987350\pi$
$888$	−91.2254	−	91.2254i	−0.102731	−	0.102731i
$889$			787.636i			0.885980i
$890$	−197.273	−	211.785i	−0.221655	−	0.237960i
$891$	−20.4858			−0.0229919
$892$	323.742	−	323.742i	0.362940	−	0.362940i
$893$	−961.586	−	961.586i	−1.07680	−	1.07680i
$894$			87.7492i			0.0981535i
$895$	16.3602	−	461.169i	0.0182796	−	0.515272i
$896$	−74.2374			−0.0828542
$897$	−54.7832	+	54.7832i	−0.0610738	+	0.0610738i
$898$	−520.870	−	520.870i	−0.580033	−	0.580033i
$899$		−	227.677i		−	0.253256i
$900$	149.623	+	10.6293i	0.166248	+	0.0118103i
$901$	−1104.37			−1.22571
$902$	9.88489	−	9.88489i	0.0109589	−	0.0109589i
$903$	−380.521	−	380.521i	−0.421396	−	0.421396i
$904$			179.758i			0.198847i
$905$	−558.877	−	19.8265i	−0.617544	−	0.0219077i
$906$	−727.176			−0.802623
$907$	−912.974	+	912.974i	−1.00659	+	1.00659i	−0.00660822	+	0.999978i	$0.502103\pi$
$907$	−912.974	+	912.974i	−1.00659	+	1.00659i	−0.999978	+	0.00660822i	$0.997897\pi$
$908$	516.653	+	516.653i	0.569001	+	0.569001i
$909$			133.440i			0.146798i
$910$	−316.659	+	294.962i	−0.347977	+	0.324134i
$911$	−1143.62			−1.25534			−0.627671	−	0.778479i	$-0.715992\pi$
$911$	−1143.62			−1.25534			−0.627671	+	0.778479i	$0.715992\pi$
$912$	163.700	−	163.700i	0.179496	−	0.179496i
$913$	−27.0085	−	27.0085i	−0.0295821	−	0.0295821i
$914$			548.494i			0.600103i
$915$	−422.731	−	453.827i	−0.462001	−	0.495986i
$916$	−420.167			−0.458697
$917$	134.861	−	134.861i	0.147068	−	0.147068i
$918$	118.198	+	118.198i	0.128756	+	0.128756i
$919$			1700.96i			1.85088i	0.378888	+	0.925442i	$0.376306\pi$
$919$			1700.96i			1.85088i	−0.378888	+	0.925442i	$0.623694\pi$
$920$	2.40456	−	67.7807i	0.00261365	−	0.0736746i
$921$	520.333			0.564965
$922$	−72.7050	+	72.7050i	−0.0788558	+	0.0788558i
$923$	684.300	+	684.300i	0.741386	+	0.741386i
$924$			51.7391i			0.0559947i
$925$	497.351	−	431.374i	0.537676	−	0.466350i
$926$	910.404			0.983158
$927$	−261.998	+	261.998i	−0.282630	+	0.282630i
$928$	35.0139	+	35.0139i	0.0377305	+	0.0377305i
$929$		−	707.341i		−	0.761400i	−0.924699	−	0.380700i	$-0.875683\pi$
$929$		−	707.341i		−	0.761400i	0.924699	−	0.380700i	$-0.124317\pi$
$930$	318.354	+	11.2938i	0.342316	+	0.0121439i
$931$	−198.615			−0.213335
$932$	488.178	−	488.178i	0.523796	−	0.523796i
$933$	−252.568	−	252.568i	−0.270705	−	0.270705i
$934$			1139.73i			1.22027i
$935$	189.435	−	176.455i	0.202604	−	0.188722i
$936$	79.1414			0.0845528
$937$	−1184.43	+	1184.43i	−1.26407	+	1.26407i	−0.314962	+	0.949104i	$0.601992\pi$
$937$	−1184.43	+	1184.43i	−1.26407	+	1.26407i	−0.949104	+	0.314962i	$0.898008\pi$
$938$	−742.405	−	742.405i	−0.791477	−	0.791477i
$939$			499.299i			0.531735i
$940$	277.386	+	297.791i	0.295092	+	0.316799i
$941$	326.896			0.347392			0.173696	−	0.984799i	$-0.444429\pi$
$941$	326.896			0.347392			0.173696	+	0.984799i	$0.444429\pi$
$942$	−420.779	+	420.779i	−0.446687	+	0.446687i
$943$	14.7269	+	14.7269i	0.0156170	+	0.0156170i
$944$			287.681i			0.304747i
$945$	6.04402	−	170.371i	0.00639579	−	0.180287i
$946$	152.420			0.161120
$947$	−313.680	+	313.680i	−0.331236	+	0.331236i	−0.853056	−	0.521820i	$-0.825253\pi$
$947$	−313.680	+	313.680i	−0.331236	+	0.331236i	0.521820	+	0.853056i	$0.325253\pi$
$948$	−329.152	−	329.152i	−0.347207	−	0.347207i
$949$			15.4954i			0.0163281i
$950$	774.082	+	892.476i	0.814824	+	0.939448i
$951$	175.295			0.184327
$952$	298.521	−	298.521i	0.313572	−	0.313572i
$953$	1227.85	+	1227.85i	1.28840	+	1.28840i	0.935757	+	0.352645i	$0.114718\pi$
$953$	1227.85	+	1227.85i	1.28840	+	1.28840i	0.352645	+	0.935757i	$0.385282\pi$
$954$		−	205.979i		−	0.215911i
$955$	−468.451	−	16.6186i	−0.490524	−	0.0174016i
$956$	−629.405			−0.658373
$957$	24.4027	−	24.4027i	0.0254991	−	0.0254991i
$958$	681.451	+	681.451i	0.711327	+	0.711327i
$959$			467.187i			0.487160i
$960$	−50.6958	+	47.2221i	−0.0528082	+	0.0491897i
$961$	−284.486			−0.296032
$962$	245.619	−	245.619i	0.255322	−	0.255322i
$963$	47.7446	+	47.7446i	0.0495791	+	0.0495791i
$964$			357.609i			0.370964i
$965$	−482.020	−	517.478i	−0.499503	−	0.536247i
$966$	−77.0827			−0.0797958
$967$	1059.90	−	1059.90i	1.09607	−	1.09607i	0.101206	−	0.994866i	$-0.467730\pi$
$967$	1059.90	−	1059.90i	1.09607	−	1.09607i	0.994866	−	0.101206i	$-0.0322700\pi$
$968$	231.638	+	231.638i	0.239295	+	0.239295i
$969$			1316.53i			1.35865i
$970$	11.0565	−	311.665i	0.0113985	−	0.321304i
$971$	−982.140			−1.01147			−0.505737	−	0.862688i	$-0.668779\pi$
$971$	−982.140			−1.01147			−0.505737	+	0.862688i	$0.668779\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	386.350	+	386.350i	0.397071	+	0.397071i
$974$		−	914.134i		−	0.938535i
$975$	−28.6188	+	402.852i	−0.0293526	+	0.413181i
$976$	286.463			0.293507
$977$	−996.201	+	996.201i	−1.01965	+	1.01965i	−0.0198498	+	0.999803i	$0.506319\pi$
$977$	−996.201	+	996.201i	−1.01965	+	1.01965i	−0.999803	+	0.0198498i	$0.993681\pi$
$978$	−375.307	−	375.307i	−0.383750	−	0.383750i
$979$		−	93.1684i		−	0.0951669i
$980$	59.4011	+	2.10729i	0.0606134	+	0.00215030i
$981$	121.222			0.123570
$982$	−2.82990	+	2.82990i	−0.00288178	+	0.00288178i
$983$	104.476	+	104.476i	0.106283	+	0.106283i	0.758248	−	0.651966i	$-0.226055\pi$
$983$	104.476	+	104.476i	0.106283	+	0.106283i	−0.651966	+	0.758248i	$0.726055\pi$
$984$		−	21.2749i		−	0.0216208i
$985$	581.380	−	541.544i	0.590234	−	0.549791i
$986$	−281.594			−0.285592
$987$	327.057	−	327.057i	0.331364	−	0.331364i
$988$	440.754	+	440.754i	0.446107	+	0.446107i
$989$			227.080i			0.229606i
$990$	32.9111	+	35.3320i	0.0332435	+	0.0356889i
$991$	−901.531			−0.909719			−0.454859	−	0.890563i	$-0.650310\pi$
$991$	−901.531			−0.909719			−0.454859	+	0.890563i	$0.650310\pi$
$992$	−104.039	+	104.039i	−0.104879	+	0.104879i
$993$	588.750	+	588.750i	0.592901	+	0.592901i
$994$			962.845i			0.968657i
$995$	−10.6420	+	299.980i	−0.0106954	+	0.301487i
$996$	−58.1293			−0.0583627
$997$	−175.760	+	175.760i	−0.176289	+	0.176289i	−0.789736	−	0.613447i	$-0.789782\pi$
$997$	−175.760	+	175.760i	−0.176289	+	0.176289i	0.613447	+	0.789736i	$0.289782\pi$
$998$	−562.240	−	562.240i	−0.563367	−	0.563367i
$999$			136.838i			0.136975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.14	yes	40
5.2	odd	4	inner	690.3.k.a.277.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.14	✓	40	5.2	odd	4	inner
690.3.k.a.553.14	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(4.99686 + 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 + 4.63984i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(4.99686 + 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 + 4.63984i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(5.17412 - 4.81959i) q^{10} +2.27620 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.59512 + 6.59512i) q^{13} +9.27967i q^{14} +(5.90277 + 6.33698i) q^{15} -4.00000 q^{16} +(16.0847 - 16.0847i) q^{17} +(3.00000 + 3.00000i) q^{18} +33.4152i q^{19} +(0.354533 - 9.99371i) q^{20} -11.3652 q^{21} +(2.27620 - 2.27620i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(24.9372 + 1.77155i) q^{25} +13.1902 q^{26} +(-3.67423 + 3.67423i) q^{27} +(9.27967 + 9.27967i) q^{28} -8.75349i q^{29} +(12.2397 + 0.434212i) q^{30} +26.0099 q^{31} +(-4.00000 + 4.00000i) q^{32} +(2.78777 + 2.78777i) q^{33} -32.1694i q^{34} +(-24.0071 + 22.3621i) q^{35} +6.00000 q^{36} +(18.6213 - 18.6213i) q^{37} +(33.4152 + 33.4152i) q^{38} +16.1547i q^{39} +(-9.63918 - 10.3482i) q^{40} +4.34271 q^{41} +(-11.3652 + 11.3652i) q^{42} +(33.4812 + 33.4812i) q^{43} -4.55240i q^{44} +(-0.531799 + 14.9906i) q^{45} +6.78233 q^{46} +(-28.7769 + 28.7769i) q^{47} +(-4.89898 - 4.89898i) q^{48} +5.94385i q^{49} +(26.7087 - 23.1656i) q^{50} +39.3992 q^{51} +(13.1902 - 13.1902i) q^{52} +(-34.3298 - 34.3298i) q^{53} +7.34847i q^{54} +(11.3739 + 0.403494i) q^{55} +18.5593 q^{56} +(-40.9250 + 40.9250i) q^{57} +(-8.75349 - 8.75349i) q^{58} -71.9203i q^{59} +(12.6740 - 11.8055i) q^{60} -71.6157 q^{61} +(26.0099 - 26.0099i) q^{62} +(-13.9195 - 13.9195i) q^{63} +8.00000i q^{64} +(31.7858 + 34.1240i) q^{65} +5.57553 q^{66} +(-80.0034 + 80.0034i) q^{67} +(-32.1694 - 32.1694i) q^{68} +8.30662i q^{69} +(-1.64497 + 46.3692i) q^{70} +103.758 q^{71} +(6.00000 - 6.00000i) q^{72} +(1.17476 + 1.17476i) q^{73} -37.2426i q^{74} +(28.3720 + 32.7113i) q^{75} +66.8303 q^{76} +(-10.5612 + 10.5612i) q^{77} +(16.1547 + 16.1547i) q^{78} -134.376i q^{79} +(-19.9874 - 0.709066i) q^{80} -9.00000 q^{81} +(4.34271 - 4.34271i) q^{82} +(-11.8656 - 11.8656i) q^{83} +22.7305i q^{84} +(83.2241 - 77.5215i) q^{85} +66.9623 q^{86} +(10.7208 - 10.7208i) q^{87} +(-4.55240 - 4.55240i) q^{88} -40.9315i q^{89} +(14.4588 + 15.5224i) q^{90} -61.2005 q^{91} +(6.78233 - 6.78233i) q^{92} +(31.8555 + 31.8555i) q^{93} +57.5539i q^{94} +(-5.92339 + 166.971i) q^{95} -9.79796 q^{96} +(31.1861 - 31.1861i) q^{97} +(5.94385 + 5.94385i) q^{98} +6.82860i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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