LMFDB - Embedded newform 930.2.j.h.497.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
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			497.14
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.750564 + 1.56098i) q^{3} -1.00000i q^{4} +(-0.256652 - 2.22129i) q^{5} +(0.573050 + 1.63451i) q^{6} +(0.463267 + 0.463267i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.87331 - 2.34323i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.750564 + 1.56098i) q^{3} -1.00000i q^{4} +(-0.256652 - 2.22129i) q^{5} +(0.573050 + 1.63451i) q^{6} +(0.463267 + 0.463267i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.87331 - 2.34323i) q^{9} +(-1.75217 - 1.38921i) q^{10} -0.686339i q^{11} +(1.56098 + 0.750564i) q^{12} +(-0.948581 + 0.948581i) q^{13} +0.655158 q^{14} +(3.66002 + 1.26659i) q^{15} -1.00000 q^{16} +(3.31382 - 3.31382i) q^{17} +(-2.98154 - 0.332283i) q^{18} +0.717422i q^{19} +(-2.22129 + 0.256652i) q^{20} +(-1.07086 + 0.375438i) q^{21} +(-0.485315 - 0.485315i) q^{22} +(-6.73337 - 6.73337i) q^{23} +(1.63451 - 0.573050i) q^{24} +(-4.86826 + 1.14020i) q^{25} +1.34150i q^{26} +(5.06377 - 1.16545i) q^{27} +(0.463267 - 0.463267i) q^{28} -5.30779 q^{29} +(3.48364 - 1.69241i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.07136 + 0.515141i) q^{33} -4.68646i q^{34} +(0.910151 - 1.14795i) q^{35} +(-2.34323 + 1.87331i) q^{36} +(-5.56932 - 5.56932i) q^{37} +(0.507294 + 0.507294i) q^{38} +(-0.768745 - 2.19269i) q^{39} +(-1.38921 + 1.75217i) q^{40} -2.24156i q^{41} +(-0.491738 + 1.02269i) q^{42} +(4.06381 - 4.06381i) q^{43} -0.686339 q^{44} +(-4.72420 + 4.76256i) q^{45} -9.52242 q^{46} +(8.61031 - 8.61031i) q^{47} +(0.750564 - 1.56098i) q^{48} -6.57077i q^{49} +(-2.63614 + 4.24862i) q^{50} +(2.68557 + 7.66005i) q^{51} +(0.948581 + 0.948581i) q^{52} +(5.32320 + 5.32320i) q^{53} +(2.75652 - 4.40472i) q^{54} +(-1.52456 + 0.176150i) q^{55} -0.655158i q^{56} +(-1.11988 - 0.538471i) q^{57} +(-3.75317 + 3.75317i) q^{58} +13.6137 q^{59} +(1.26659 - 3.66002i) q^{60} -13.2492 q^{61} +(-0.707107 + 0.707107i) q^{62} +(0.217698 - 1.95338i) q^{63} +1.00000i q^{64} +(2.35053 + 1.86362i) q^{65} +(1.12183 - 0.393306i) q^{66} +(3.26537 + 3.26537i) q^{67} +(-3.31382 - 3.31382i) q^{68} +(15.5645 - 5.45682i) q^{69} +(-0.168148 - 1.45530i) q^{70} +6.49437i q^{71} +(-0.332283 + 2.98154i) q^{72} +(1.62118 - 1.62118i) q^{73} -7.87621 q^{74} +(1.87412 - 8.45504i) q^{75} +0.717422 q^{76} +(0.317958 - 0.317958i) q^{77} +(-2.09405 - 1.00688i) q^{78} +5.04224i q^{79} +(0.256652 + 2.22129i) q^{80} +(-1.98143 + 8.77918i) q^{81} +(-1.58502 - 1.58502i) q^{82} +(-6.41694 - 6.41694i) q^{83} +(0.375438 + 1.07086i) q^{84} +(-8.21147 - 6.51047i) q^{85} -5.74710i q^{86} +(3.98383 - 8.28534i) q^{87} +(-0.485315 + 0.485315i) q^{88} -4.84625 q^{89} +(0.0271212 + 6.70815i) q^{90} -0.878892 q^{91} +(-6.73337 + 6.73337i) q^{92} +(0.750564 - 1.56098i) q^{93} -12.1768i q^{94} +(1.59360 - 0.184128i) q^{95} +(-0.573050 - 1.63451i) q^{96} +(-11.0744 - 11.0744i) q^{97} +(-4.64623 - 4.64623i) q^{98} +(-1.60825 + 1.28572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.750564	+	1.56098i	−0.433338	+	0.901231i
$3$	−0.750564	+	1.56098i	−0.433338	+	0.901231i
$4$		−	1.00000i		−	0.500000i
$5$	−0.256652	−	2.22129i	−0.114778	−	0.993391i
$5$	−0.256652	−	2.22129i	−0.114778	−	0.993391i
$6$	0.573050	+	1.63451i	0.233947	+	0.667285i
$7$	0.463267	+	0.463267i	0.175098	+	0.175098i	0.789215	−	0.614117i	$-0.210488\pi$
$7$	0.463267	+	0.463267i	0.175098	+	0.175098i	−0.614117	+	0.789215i	$0.710488\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.87331	−	2.34323i	−0.624436	−	0.781076i
$10$	−1.75217	−	1.38921i	−0.554085	−	0.439306i
$11$		−	0.686339i		−	0.206939i	−0.994633	−	0.103469i	$-0.967006\pi$
$11$		−	0.686339i		−	0.206939i	0.994633	−	0.103469i	$-0.0329944\pi$
$12$	1.56098	+	0.750564i	0.450616	+	0.216669i
$13$	−0.948581	+	0.948581i	−0.263089	+	0.263089i	−0.826308	−	0.563219i	$-0.809563\pi$
$13$	−0.948581	+	0.948581i	−0.263089	+	0.263089i	0.563219	+	0.826308i	$0.309563\pi$
$14$	0.655158			0.175098
$15$	3.66002	+	1.26659i	0.945013	+	0.327032i
$16$	−1.00000			−0.250000
$17$	3.31382	−	3.31382i	0.803720	−	0.803720i	−0.179954	−	0.983675i	$-0.557595\pi$
$17$	3.31382	−	3.31382i	0.803720	−	0.803720i	0.983675	+	0.179954i	$0.0575950\pi$
$18$	−2.98154	−	0.332283i	−0.702756	−	0.0783199i
$19$			0.717422i			0.164588i	0.996608	+	0.0822940i	$0.0262246\pi$
$19$			0.717422i			0.164588i	−0.996608	+	0.0822940i	$0.973775\pi$
$20$	−2.22129	+	0.256652i	−0.496696	+	0.0573891i
$21$	−1.07086	+	0.375438i	−0.233681	+	0.0819273i
$22$	−0.485315	−	0.485315i	−0.103469	−	0.103469i
$23$	−6.73337	−	6.73337i	−1.40400	−	1.40400i	−0.786815	−	0.617189i	$-0.788271\pi$
$23$	−6.73337	−	6.73337i	−1.40400	−	1.40400i	−0.617189	−	0.786815i	$-0.711729\pi$
$24$	1.63451	−	0.573050i	0.333642	−	0.116973i
$25$	−4.86826	+	1.14020i	−0.973652	+	0.228039i
$26$			1.34150i			0.263089i
$27$	5.06377	−	1.16545i	0.974522	−	0.224291i
$28$	0.463267	−	0.463267i	0.0875492	−	0.0875492i
$29$	−5.30779			−0.985631			−0.492816	−	0.870134i	$-0.664032\pi$
$29$	−5.30779			−0.985631			−0.492816	+	0.870134i	$0.664032\pi$
$30$	3.48364	−	1.69241i	0.636023	−	0.308990i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.07136	+	0.515141i	0.186500	+	0.0896745i
$34$		−	4.68646i		−	0.803720i
$35$	0.910151	−	1.14795i	0.153844	−	0.194039i
$36$	−2.34323	+	1.87331i	−0.390538	+	0.312218i
$37$	−5.56932	−	5.56932i	−0.915591	−	0.915591i	0.0811142	−	0.996705i	$-0.474152\pi$
$37$	−5.56932	−	5.56932i	−0.915591	−	0.915591i	−0.996705	+	0.0811142i	$0.974152\pi$
$38$	0.507294	+	0.507294i	0.0822940	+	0.0822940i
$39$	−0.768745	−	2.19269i	−0.123098	−	0.351111i
$40$	−1.38921	+	1.75217i	−0.219653	+	0.277042i
$41$		−	2.24156i		−	0.350073i	−0.984562	−	0.175037i	$-0.943996\pi$
$41$		−	2.24156i		−	0.350073i	0.984562	−	0.175037i	$-0.0560044\pi$
$42$	−0.491738	+	1.02269i	−0.0758768	+	0.157804i
$43$	4.06381	−	4.06381i	0.619725	−	0.619725i	−0.325736	−	0.945461i	$-0.605612\pi$
$43$	4.06381	−	4.06381i	0.619725	−	0.619725i	0.945461	+	0.325736i	$0.105612\pi$
$44$	−0.686339			−0.103469
$45$	−4.72420	+	4.76256i	−0.704242	+	0.709960i
$46$	−9.52242			−1.40400
$47$	8.61031	−	8.61031i	1.25594	−	1.25594i	0.302930	−	0.953013i	$-0.402035\pi$
$47$	8.61031	−	8.61031i	1.25594	−	1.25594i	0.953013	−	0.302930i	$-0.0979649\pi$
$48$	0.750564	−	1.56098i	0.108335	−	0.225308i
$49$		−	6.57077i		−	0.938681i
$50$	−2.63614	+	4.24862i	−0.372806	+	0.600846i
$51$	2.68557	+	7.66005i	0.376055	+	1.07262i
$52$	0.948581	+	0.948581i	0.131545	+	0.131545i
$53$	5.32320	+	5.32320i	0.731197	+	0.731197i	0.970857	−	0.239660i	$-0.0770359\pi$
$53$	5.32320	+	5.32320i	0.731197	+	0.731197i	−0.239660	+	0.970857i	$0.577036\pi$
$54$	2.75652	−	4.40472i	0.375115	−	0.599407i
$55$	−1.52456	+	0.176150i	−0.205571	+	0.0237521i
$56$		−	0.655158i		−	0.0875492i
$57$	−1.11988	−	0.538471i	−0.148332	−	0.0713222i
$58$	−3.75317	+	3.75317i	−0.492816	+	0.492816i
$59$	13.6137			1.77236			0.886179	−	0.463343i	$-0.153350\pi$
$59$	13.6137			1.77236			0.886179	+	0.463343i	$0.153350\pi$
$60$	1.26659	−	3.66002i	0.163516	−	0.472507i
$61$	−13.2492			−1.69639			−0.848196	−	0.529682i	$-0.822311\pi$
$61$	−13.2492			−1.69639			−0.848196	+	0.529682i	$0.822311\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	0.217698	−	1.95338i	0.0274274	−	0.246103i
$64$			1.00000i			0.125000i
$65$	2.35053	+	1.86362i	0.291547	+	0.231154i
$66$	1.12183	−	0.393306i	0.138087	−	0.0484127i
$67$	3.26537	+	3.26537i	0.398928	+	0.398928i	0.877855	−	0.478927i	$-0.158974\pi$
$67$	3.26537	+	3.26537i	0.398928	+	0.398928i	−0.478927	+	0.877855i	$0.658974\pi$
$68$	−3.31382	−	3.31382i	−0.401860	−	0.401860i
$69$	15.5645	−	5.45682i	1.87374	−	0.656924i
$70$	−0.168148	−	1.45530i	−0.0200975	−	0.173941i
$71$			6.49437i			0.770740i	0.922762	+	0.385370i	$0.125926\pi$
$71$			6.49437i			0.770740i	−0.922762	+	0.385370i	$0.874074\pi$
$72$	−0.332283	+	2.98154i	−0.0391600	+	0.351378i
$73$	1.62118	−	1.62118i	0.189745	−	0.189745i	−0.605841	−	0.795586i	$-0.707163\pi$
$73$	1.62118	−	1.62118i	0.189745	−	0.189745i	0.795586	+	0.605841i	$0.207163\pi$
$74$	−7.87621			−0.915591
$75$	1.87412	−	8.45504i	0.216404	−	0.976304i
$76$	0.717422			0.0822940
$77$	0.317958	−	0.317958i	0.0362347	−	0.0362347i
$78$	−2.09405	−	1.00688i	−0.237104	−	0.114007i
$79$			5.04224i			0.567296i	0.958928	+	0.283648i	$0.0915447\pi$
$79$			5.04224i			0.567296i	−0.958928	+	0.283648i	$0.908455\pi$
$80$	0.256652	+	2.22129i	0.0286946	+	0.248348i
$81$	−1.98143	+	8.77918i	−0.220159	+	0.975464i
$82$	−1.58502	−	1.58502i	−0.175037	−	0.175037i
$83$	−6.41694	−	6.41694i	−0.704350	−	0.704350i	0.260991	−	0.965341i	$-0.415951\pi$
$83$	−6.41694	−	6.41694i	−0.704350	−	0.704350i	−0.965341	+	0.260991i	$0.915951\pi$
$84$	0.375438	+	1.07086i	0.0409637	+	0.116840i
$85$	−8.21147	−	6.51047i	−0.890658	−	0.706159i
$86$		−	5.74710i		−	0.619725i
$87$	3.98383	−	8.28534i	0.427112	−	0.888282i
$88$	−0.485315	+	0.485315i	−0.0517347	+	0.0517347i
$89$	−4.84625			−0.513701			−0.256851	−	0.966451i	$-0.582685\pi$
$89$	−4.84625			−0.513701			−0.256851	+	0.966451i	$0.582685\pi$
$90$	0.0271212	+	6.70815i	0.00285883	+	0.707101i
$91$	−0.878892			−0.0921330
$92$	−6.73337	+	6.73337i	−0.702002	+	0.702002i
$93$	0.750564	−	1.56098i	0.0778298	−	0.161866i
$94$		−	12.1768i		−	1.25594i
$95$	1.59360	−	0.184128i	0.163500	−	0.0188911i
$96$	−0.573050	−	1.63451i	−0.0584867	−	0.166821i
$97$	−11.0744	−	11.0744i	−1.12444	−	1.12444i	−0.991066	−	0.133374i	$-0.957419\pi$
$97$	−11.0744	−	11.0744i	−1.12444	−	1.12444i	−0.133374	−	0.991066i	$-0.542581\pi$
$98$	−4.64623	−	4.64623i	−0.469341	−	0.469341i
$99$	−1.60825	+	1.28572i	−0.161635	+	0.129220i
$100$	1.14020	+	4.86826i	0.114020	+	0.486826i
$101$			8.31077i			0.826953i	0.910515	+	0.413476i	$0.135686\pi$
$101$			8.31077i			0.826953i	−0.910515	+	0.413476i	$0.864314\pi$
$102$	7.31546	+	3.51748i	0.724338	+	0.348283i
$103$	−7.13953	+	7.13953i	−0.703478	+	0.703478i	−0.965155	−	0.261677i	$-0.915724\pi$
$103$	−7.13953	+	7.13953i	−0.703478	+	0.703478i	0.261677	+	0.965155i	$0.415724\pi$
$104$	1.34150			0.131545
$105$	1.10880	+	2.28234i	0.108207	+	0.222733i
$106$	7.52814			0.731197
$107$	8.12668	−	8.12668i	0.785635	−	0.785635i	−0.195140	−	0.980775i	$-0.562516\pi$
$107$	8.12668	−	8.12668i	0.785635	−	0.785635i	0.980775	+	0.195140i	$0.0625161\pi$
$108$	−1.16545	−	5.06377i	−0.112146	−	0.487261i
$109$			11.8065i			1.13085i	0.824798	+	0.565427i	$0.191289\pi$
$109$			11.8065i			1.13085i	−0.824798	+	0.565427i	$0.808711\pi$
$110$	−0.953468	+	1.20258i	−0.0909096	+	0.114662i
$111$	12.8737	−	4.51346i	1.22192	−	0.428399i
$112$	−0.463267	−	0.463267i	−0.0437746	−	0.0437746i
$113$	−1.38059	−	1.38059i	−0.129875	−	0.129875i	0.639181	−	0.769056i	$-0.279273\pi$
$113$	−1.38059	−	1.38059i	−0.129875	−	0.129875i	−0.769056	+	0.639181i	$0.779273\pi$
$114$	−1.17263	+	0.411119i	−0.109827	+	0.0385048i
$115$	−13.2286	+	16.6849i	−1.23358	+	1.55587i
$116$			5.30779i			0.492816i
$117$	3.99973	+	0.445757i	0.369775	+	0.0412102i
$118$	9.62637	−	9.62637i	0.886179	−	0.886179i
$119$	3.07037			0.281460
$120$	−1.69241	−	3.48364i	−0.154495	−	0.318011i
$121$	10.5289			0.957176
$122$	−9.36863	+	9.36863i	−0.848196	+	0.848196i
$123$	3.49903	+	1.68244i	0.315497	+	0.151700i
$124$			1.00000i			0.0898027i
$125$	3.78216	+	10.5212i	0.338286	+	0.941043i
$126$	−1.22731	−	1.53518i	−0.109338	−	0.136765i
$127$	9.72658	+	9.72658i	0.863094	+	0.863094i	0.991696	−	0.128602i	$-0.0410490\pi$
$127$	9.72658	+	9.72658i	0.863094	+	0.863094i	−0.128602	+	0.991696i	$0.541049\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	3.29337	+	9.39367i	0.289965	+	0.827067i
$130$	2.97985	−	0.344298i	0.261350	−	0.0301969i
$131$			10.5434i			0.921185i	0.887612	+	0.460593i	$0.152363\pi$
$131$			10.5434i			0.921185i	−0.887612	+	0.460593i	$0.847637\pi$
$132$	0.515141	−	1.07136i	0.0448373	−	0.0932499i
$133$	−0.332358	+	0.332358i	−0.0288191	+	0.0288191i
$134$	4.61793			0.398928
$135$	−3.88843	−	10.9490i	−0.334663	−	0.942338i
$136$	−4.68646			−0.401860
$137$	−5.99620	+	5.99620i	−0.512290	+	0.512290i	−0.915227	−	0.402938i	$-0.867989\pi$
$137$	−5.99620	+	5.99620i	−0.512290	+	0.512290i	0.402938	+	0.915227i	$0.367989\pi$
$138$	7.14718	−	14.8643i	0.608408	−	1.26533i
$139$		−	15.7454i		−	1.33551i	−0.744381	−	0.667755i	$-0.767256\pi$
$139$		−	15.7454i		−	1.33551i	0.744381	−	0.667755i	$-0.232744\pi$
$140$	−1.14795	−	0.910151i	−0.0970193	−	0.0769218i
$141$	6.97792	+	19.9031i	0.587647	+	1.67614i
$142$	4.59221	+	4.59221i	0.385370	+	0.385370i
$143$	0.651048	+	0.651048i	0.0544434	+	0.0544434i
$144$	1.87331	+	2.34323i	0.156109	+	0.195269i
$145$	1.36225	+	11.7901i	0.113129	+	0.979117i
$146$		−	2.29270i		−	0.189745i
$147$	10.2568	+	4.93178i	0.845969	+	0.406766i
$148$	−5.56932	+	5.56932i	−0.457795	+	0.457795i
$149$	12.8200			1.05026			0.525128	−	0.851023i	$-0.324018\pi$
$149$	12.8200			1.05026			0.525128	+	0.851023i	$0.324018\pi$
$150$	−4.65342	−	7.30382i	−0.379950	−	0.596354i
$151$	9.60890			0.781961			0.390981	−	0.920399i	$-0.372136\pi$
$151$	9.60890			0.781961			0.390981	+	0.920399i	$0.372136\pi$
$152$	0.507294	−	0.507294i	0.0411470	−	0.0411470i
$153$	−13.9729	−	1.55723i	−1.12964	−	0.125895i
$154$		−	0.449660i		−	0.0362347i
$155$	0.256652	+	2.22129i	0.0206148	+	0.178418i
$156$	−2.19269	+	0.768745i	−0.175555	+	0.0615488i
$157$	8.98320	+	8.98320i	0.716937	+	0.716937i	0.967977	−	0.251040i	$-0.0807724\pi$
$157$	8.98320	+	8.98320i	0.716937	+	0.716937i	−0.251040	+	0.967977i	$0.580772\pi$
$158$	3.56540	+	3.56540i	0.283648	+	0.283648i
$159$	−12.3048	+	4.31400i	−0.975833	+	0.342122i
$160$	1.75217	+	1.38921i	0.138521	+	0.109827i
$161$		−	6.23869i		−	0.491678i
$162$	4.80673	+	7.60890i	0.377652	+	0.597812i
$163$	2.69946	−	2.69946i	0.211438	−	0.211438i	−0.593440	−	0.804878i	$-0.702231\pi$
$163$	2.69946	−	2.69946i	0.211438	−	0.211438i	0.804878	+	0.593440i	$0.202231\pi$
$164$	−2.24156			−0.175037
$165$	0.869311	−	2.51201i	0.0676757	−	0.195560i
$166$	−9.07492			−0.704350
$167$	−0.510603	+	0.510603i	−0.0395116	+	0.0395116i	−0.726587	−	0.687075i	$-0.758894\pi$
$167$	−0.510603	+	0.510603i	−0.0395116	+	0.0395116i	0.687075	+	0.726587i	$0.258894\pi$
$168$	1.02269	+	0.491738i	0.0789021	+	0.0379384i
$169$			11.2004i			0.861568i
$170$	−10.4100	+	1.20279i	−0.798409	+	0.0922497i
$171$	1.68108	−	1.34395i	0.128556	−	0.102775i
$172$	−4.06381	−	4.06381i	−0.309863	−	0.309863i
$173$	−0.148177	−	0.148177i	−0.0112657	−	0.0112657i	0.701452	−	0.712717i	$-0.252536\pi$
$173$	−0.148177	−	0.148177i	−0.0112657	−	0.0112657i	−0.712717	+	0.701452i	$0.752536\pi$
$174$	−3.04163	−	8.67562i	−0.230585	−	0.657697i
$175$	−2.78352	−	1.72709i	−0.210414	−	0.130556i
$176$			0.686339i			0.0517347i
$177$	−10.2180	+	21.2508i	−0.768030	+	1.59730i
$178$	−3.42681	+	3.42681i	−0.256851	+	0.256851i
$179$	10.1213			0.756500			0.378250	−	0.925703i	$-0.376526\pi$
$179$	10.1213			0.756500			0.378250	+	0.925703i	$0.376526\pi$
$180$	4.76256	+	4.72420i	0.354980	+	0.352121i
$181$	8.47685			0.630080			0.315040	−	0.949078i	$-0.397982\pi$
$181$	8.47685			0.630080			0.315040	+	0.949078i	$0.397982\pi$
$182$	−0.621471	+	0.621471i	−0.0460665	+	0.0460665i
$183$	9.94440	−	20.6818i	0.735111	−	1.52884i
$184$			9.52242i			0.702002i
$185$	−10.9417	+	13.8005i	−0.804450	+	1.01463i
$186$	−0.573050	−	1.63451i	−0.0420181	−	0.119848i
$187$	−2.27441	−	2.27441i	−0.166321	−	0.166321i
$188$	−8.61031	−	8.61031i	−0.627971	−	0.627971i
$189$	2.88579	+	1.80596i	0.209910	+	0.131364i
$190$	0.996649	−	1.25705i	0.0723045	−	0.0911957i
$191$		−	17.9621i		−	1.29969i	−0.760065	−	0.649847i	$-0.774833\pi$
$191$		−	17.9621i		−	1.29969i	0.760065	−	0.649847i	$-0.225167\pi$
$192$	−1.56098	−	0.750564i	−0.112654	−	0.0541673i
$193$	3.62430	−	3.62430i	0.260883	−	0.260883i	−0.564530	−	0.825413i	$-0.690943\pi$
$193$	3.62430	−	3.62430i	0.260883	−	0.260883i	0.825413	+	0.564530i	$0.190943\pi$
$194$	−15.6616			−1.12444
$195$	−4.67329	+	2.27036i	−0.334661	+	0.162584i
$196$	−6.57077			−0.469341
$197$	6.89663	−	6.89663i	0.491365	−	0.491365i	−0.417371	−	0.908736i	$-0.637049\pi$
$197$	6.89663	−	6.89663i	0.491365	−	0.491365i	0.908736	+	0.417371i	$0.137049\pi$
$198$	−0.228059	+	2.04635i	−0.0162074	+	0.145428i
$199$			25.1164i			1.78045i	0.455520	+	0.890226i	$0.349453\pi$
$199$			25.1164i			1.78045i	−0.455520	+	0.890226i	$0.650547\pi$
$200$	4.24862	+	2.63614i	0.300423	+	0.186403i
$201$	−7.54803	+	2.64630i	−0.532397	+	0.186656i
$202$	5.87660	+	5.87660i	0.413476	+	0.413476i
$203$	−2.45892	−	2.45892i	−0.172582	−	0.172582i
$204$	7.66005	−	2.68557i	0.536310	−	0.188028i
$205$	−4.97916	+	0.575302i	−0.347760	+	0.0401808i
$206$			10.0968i			0.703478i
$207$	−3.16414	+	28.3915i	−0.219923	+	1.97334i
$208$	0.948581	−	0.948581i	0.0657723	−	0.0657723i
$209$	0.492395			0.0340596
$210$	2.39789	+	0.829818i	0.165470	+	0.0572629i
$211$	−2.03309			−0.139964			−0.0699820	−	0.997548i	$-0.522294\pi$
$211$	−2.03309			−0.139964			−0.0699820	+	0.997548i	$0.522294\pi$
$212$	5.32320	−	5.32320i	0.365599	−	0.365599i
$213$	−10.1376	−	4.87444i	−0.694615	−	0.333991i
$214$		−	11.4929i		−	0.785635i
$215$	−10.0699	−	7.98392i	−0.686761	−	0.544499i
$216$	−4.40472	−	2.75652i	−0.299703	−	0.187558i
$217$	−0.463267	−	0.463267i	−0.0314486	−	0.0314486i
$218$	8.34843	+	8.34843i	0.565427	+	0.565427i
$219$	1.31383	+	3.74743i	0.0887803	+	0.253228i
$220$	0.176150	+	1.52456i	0.0118760	+	0.102786i
$221$			6.28686i			0.422900i
$222$	5.91160	−	12.2946i	0.396760	−	0.825159i
$223$	−3.41333	+	3.41333i	−0.228573	+	0.228573i	−0.812096	−	0.583523i	$-0.801674\pi$
$223$	−3.41333	+	3.41333i	−0.228573	+	0.228573i	0.583523	+	0.812096i	$0.301674\pi$
$224$	−0.655158			−0.0437746
$225$	11.7915	+	9.27150i	0.786100	+	0.618100i
$226$	−1.95245			−0.129875
$227$	14.8307	−	14.8307i	0.984345	−	0.984345i	−0.0155340	−	0.999879i	$-0.504945\pi$
$227$	14.8307	−	14.8307i	0.984345	−	0.984345i	0.999879	+	0.0155340i	$0.00494483\pi$
$228$	−0.538471	+	1.11988i	−0.0356611	+	0.0741659i
$229$			8.52563i			0.563389i	0.959504	+	0.281695i	$0.0908965\pi$
$229$			8.52563i			0.563389i	−0.959504	+	0.281695i	$0.909104\pi$
$230$	2.44395	+	21.1521i	0.161149	+	1.39473i
$231$	0.257678	+	0.734973i	0.0169540	+	0.0483577i
$232$	3.75317	+	3.75317i	0.246408	+	0.246408i
$233$	−3.54971	−	3.54971i	−0.232549	−	0.232549i	0.581207	−	0.813756i	$-0.302581\pi$
$233$	−3.54971	−	3.54971i	−0.232549	−	0.232549i	−0.813756	+	0.581207i	$0.802581\pi$
$234$	3.14343	−	2.51304i	0.205493	−	0.164282i
$235$	−21.3359	−	16.9161i	−1.39180	−	1.10349i
$236$		−	13.6137i		−	0.886179i
$237$	−7.87083	−	3.78452i	−0.511265	−	0.245831i
$238$	2.17108	−	2.17108i	0.140730	−	0.140730i
$239$	−28.3403			−1.83318			−0.916592	−	0.399823i	$-0.869072\pi$
$239$	−28.3403			−1.83318			−0.916592	+	0.399823i	$0.869072\pi$
$240$	−3.66002	−	1.26659i	−0.236253	−	0.0817581i
$241$	−11.4414			−0.737007			−0.368503	−	0.929626i	$-0.620130\pi$
$241$	−11.4414			−0.737007			−0.368503	+	0.929626i	$0.620130\pi$
$242$	7.44508	−	7.44508i	0.478588	−	0.478588i
$243$	−12.2169	−	9.68230i	−0.783715	−	0.621120i
$244$			13.2492i			0.848196i
$245$	−14.5956	+	1.68640i	−0.932478	+	0.107740i
$246$	3.66385	−	1.28453i	0.233599	−	0.0818985i
$247$	−0.680533	−	0.680533i	−0.0433013	−	0.0433013i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	14.8330	−	5.20038i	0.940004	−	0.329561i
$250$	10.1140	+	4.76521i	0.639665	+	0.301378i
$251$		−	6.14267i		−	0.387722i	−0.981029	−	0.193861i	$-0.937899\pi$
$251$		−	6.14267i		−	0.387722i	0.981029	−	0.193861i	$-0.0621011\pi$
$252$	−1.95338	−	0.217698i	−0.123051	−	0.0137137i
$253$	−4.62137	+	4.62137i	−0.290543	+	0.290543i
$254$	13.7555			0.863094
$255$	16.3259	−	7.93140i	1.02237	−	0.496684i
$256$	1.00000			0.0625000
$257$	−0.177566	+	0.177566i	−0.0110763	+	0.0110763i	−0.712623	−	0.701547i	$-0.752493\pi$
$257$	−0.177566	+	0.177566i	−0.0110763	+	0.0110763i	0.701547	+	0.712623i	$0.252493\pi$
$258$	8.97110	+	4.31356i	0.558516	+	0.268551i
$259$		−	5.16016i		−	0.320637i
$260$	1.86362	−	2.35053i	0.115577	−	0.145774i
$261$	9.94312	+	12.4374i	0.615464	+	0.769853i
$262$	7.45534	+	7.45534i	0.460593	+	0.460593i
$263$	4.20717	+	4.20717i	0.259425	+	0.259425i	0.824820	−	0.565395i	$-0.191276\pi$
$263$	4.20717	+	4.20717i	0.259425	+	0.259425i	−0.565395	+	0.824820i	$0.691276\pi$
$264$	−0.393306	−	1.12183i	−0.0242063	−	0.0690436i
$265$	10.4582	−	13.1906i	0.642439	−	0.810290i
$266$			0.470025i			0.0288191i
$267$	3.63742	−	7.56489i	0.222606	−	0.462964i
$268$	3.26537	−	3.26537i	0.199464	−	0.199464i
$269$	8.77396			0.534958			0.267479	−	0.963564i	$-0.413809\pi$
$269$	8.77396			0.534958			0.267479	+	0.963564i	$0.413809\pi$
$270$	−10.4916	−	4.99256i	−0.638500	−	0.303837i
$271$	31.7217			1.92696			0.963479	−	0.267785i	$-0.0862918\pi$
$271$	31.7217			1.92696			0.963479	+	0.267785i	$0.0862918\pi$
$272$	−3.31382	+	3.31382i	−0.200930	+	0.200930i
$273$	0.659665	−	1.37193i	0.0399247	−	0.0830331i
$274$			8.47991i			0.512290i
$275$	0.782562	+	3.34127i	0.0471902	+	0.201486i
$276$	−5.45682	−	15.5645i	−0.328462	−	0.936870i
$277$	6.23498	+	6.23498i	0.374624	+	0.374624i	0.869158	−	0.494534i	$-0.164661\pi$
$277$	6.23498	+	6.23498i	0.374624	+	0.374624i	−0.494534	+	0.869158i	$0.664661\pi$
$278$	−11.1337	−	11.1337i	−0.667755	−	0.667755i
$279$	1.87331	+	2.34323i	0.112152	+	0.140285i
$280$	−1.45530	+	0.168148i	−0.0869706	+	0.0100487i
$281$		−	31.8373i		−	1.89925i	−0.313385	−	0.949626i	$-0.601463\pi$
$281$		−	31.8373i		−	1.89925i	0.313385	−	0.949626i	$-0.398537\pi$
$282$	19.0078	+	9.13948i	1.13190	+	0.544248i
$283$	−5.86955	+	5.86955i	−0.348908	+	0.348908i	−0.859703	−	0.510795i	$-0.829351\pi$
$283$	−5.86955	+	5.86955i	−0.348908	+	0.348908i	0.510795	+	0.859703i	$0.329351\pi$
$284$	6.49437			0.385370
$285$	−0.908681	+	2.62578i	−0.0538256	+	0.155538i
$286$	0.920721			0.0544434
$287$	1.03844	−	1.03844i	0.0612973	−	0.0612973i
$288$	2.98154	+	0.332283i	0.175689	+	0.0195800i
$289$		−	4.96286i		−	0.291933i
$290$	9.30014	+	7.37363i	0.546123	+	0.432994i
$291$	25.5991	−	8.97490i	1.50064	−	0.526118i
$292$	−1.62118	−	1.62118i	−0.0948724	−	0.0948724i
$293$	6.55723	+	6.55723i	0.383077	+	0.383077i	0.872210	−	0.489132i	$-0.162686\pi$
$293$	6.55723	+	6.55723i	0.383077	+	0.383077i	−0.489132	+	0.872210i	$0.662686\pi$
$294$	10.7400	−	3.76538i	0.626368	−	0.219601i
$295$	−3.49399	−	30.2401i	−0.203428	−	1.76064i
$296$			7.87621i			0.457795i
$297$	−0.799895	−	3.47546i	−0.0464146	−	0.201667i
$298$	9.06511	−	9.06511i	0.525128	−	0.525128i
$299$	12.7743			0.738756
$300$	−8.45504	−	1.87412i	−0.488152	−	0.108202i
$301$	3.76526			0.217026
$302$	6.79452	−	6.79452i	0.390981	−	0.390981i
$303$	−12.9729	−	6.23776i	−0.745276	−	0.358350i
$304$		−	0.717422i		−	0.0411470i
$305$	3.40045	+	29.4304i	0.194709	+	1.68518i
$306$	−10.9814	+	8.77918i	−0.627767	+	0.501872i
$307$	−11.5302	−	11.5302i	−0.658061	−	0.658061i	0.296860	−	0.954921i	$-0.404061\pi$
$307$	−11.5302	−	11.5302i	−0.658061	−	0.658061i	−0.954921	+	0.296860i	$0.904061\pi$
$308$	−0.317958	−	0.317958i	−0.0181173	−	0.0181173i
$309$	−5.78598	−	16.5033i	−0.329153	−	0.938841i
$310$	1.75217	+	1.38921i	0.0995166	+	0.0789018i
$311$		−	1.18924i		−	0.0674356i	−0.999431	−	0.0337178i	$-0.989265\pi$
$311$		−	1.18924i		−	0.0674356i	0.999431	−	0.0337178i	$-0.0107348\pi$
$312$	−1.00688	+	2.09405i	−0.0570033	+	0.118552i
$313$	3.97381	−	3.97381i	0.224613	−	0.224613i	−0.585825	−	0.810438i	$-0.699229\pi$
$313$	3.97381	−	3.97381i	0.224613	−	0.224613i	0.810438	+	0.585825i	$0.199229\pi$
$314$	12.7042			0.716937
$315$	−4.39490	+	0.0177687i	−0.247624	+	0.00100115i
$316$	5.04224			0.283648
$317$	11.8433	−	11.8433i	0.665187	−	0.665187i	−0.291411	−	0.956598i	$-0.594125\pi$
$317$	11.8433	−	11.8433i	0.665187	−	0.665187i	0.956598	+	0.291411i	$0.0941247\pi$
$318$	−5.65034	+	11.7513i	−0.316856	+	0.658978i
$319$			3.64294i			0.203965i
$320$	2.22129	−	0.256652i	0.124174	−	0.0143473i
$321$	6.58598	+	18.7852i	0.367593	+	1.04849i
$322$	−4.41142	−	4.41142i	−0.245839	−	0.245839i
$323$	2.37741	+	2.37741i	0.132283	+	0.132283i
$324$	8.77918	+	1.98143i	0.487732	+	0.110080i
$325$	3.53637	−	5.69951i	0.196163	−	0.316152i
$326$		−	3.81761i		−	0.211438i
$327$	−18.4296	−	8.86151i	−1.01916	−	0.490042i
$328$	−1.58502	+	1.58502i	−0.0875184	+	0.0875184i
$329$	7.97774			0.439827
$330$	−1.16157	−	2.39096i	−0.0639421	−	0.131618i
$331$	10.9436			0.601516			0.300758	−	0.953701i	$-0.402760\pi$
$331$	10.9436			0.601516			0.300758	+	0.953701i	$0.402760\pi$
$332$	−6.41694	+	6.41694i	−0.352175	+	0.352175i
$333$	−2.61713	+	23.4832i	−0.143418	+	1.28687i
$334$			0.722101i			0.0395116i
$335$	6.41526	−	8.09139i	0.350503	−	0.442080i
$336$	1.07086	−	0.375438i	0.0584202	−	0.0204818i
$337$	−18.2977	−	18.2977i	−0.996740	−	0.996740i	0.00325438	−	0.999995i	$-0.498964\pi$
$337$	−18.2977	−	18.2977i	−0.996740	−	0.996740i	−0.999995	+	0.00325438i	$0.998964\pi$
$338$	7.91987	+	7.91987i	0.430784	+	0.430784i
$339$	3.19129	−	1.11885i	0.173327	−	0.0607675i
$340$	−6.51047	+	8.21147i	−0.353080	+	0.445329i
$341$			0.686339i			0.0371673i
$342$	0.238387	−	2.13902i	0.0128905	−	0.115665i
$343$	6.28689	−	6.28689i	0.339460	−	0.339460i
$344$	−5.74710			−0.309863
$345$	−16.1158	−	33.1727i	−0.867647	−	1.78596i
$346$	−0.209554			−0.0112657
$347$	−3.22385	+	3.22385i	−0.173065	+	0.173065i	−0.788325	−	0.615259i	$-0.789051\pi$
$347$	−3.22385	+	3.22385i	−0.173065	+	0.173065i	0.615259	+	0.788325i	$0.289051\pi$
$348$	−8.28534	−	3.98383i	−0.444141	−	0.213556i
$349$			20.8718i			1.11724i	0.829423	+	0.558621i	$0.188669\pi$
$349$			20.8718i			1.11724i	−0.829423	+	0.558621i	$0.811331\pi$
$350$	−3.18948	+	0.747010i	−0.170485	+	0.0399293i
$351$	−3.69787	+	5.90892i	−0.197378	+	0.315395i
$352$	0.485315	+	0.485315i	0.0258674	+	0.0258674i
$353$	−15.3570	−	15.3570i	−0.817372	−	0.817372i	0.168354	−	0.985727i	$-0.446155\pi$
$353$	−15.3570	−	15.3570i	−0.817372	−	0.817372i	−0.985727	+	0.168354i	$0.946155\pi$
$354$	7.80135	+	22.2518i	0.414637	+	1.18267i
$355$	14.4259	−	1.66679i	0.765646	−	0.0884642i
$356$			4.84625i			0.256851i
$357$	−2.30451	+	4.79278i	−0.121967	+	0.253661i
$358$	7.15683	−	7.15683i	0.378250	−	0.378250i
$359$	−0.395177			−0.0208567			−0.0104283	−	0.999946i	$-0.503320\pi$
$359$	−0.395177			−0.0208567			−0.0104283	+	0.999946i	$0.503320\pi$
$360$	6.70815	−	0.0271212i	0.353551	−	0.00142941i
$361$	18.4853			0.972911
$362$	5.99404	−	5.99404i	0.315040	−	0.315040i
$363$	−7.90264	+	16.4354i	−0.414781	+	0.862637i
$364$			0.878892i			0.0460665i
$365$	−4.01719	−	3.18503i	−0.210269	−	0.166712i
$366$	−7.59248	−	21.6560i	−0.396865	−	1.13198i
$367$	−4.46468	−	4.46468i	−0.233054	−	0.233054i	0.580912	−	0.813966i	$-0.302696\pi$
$367$	−4.46468	−	4.46468i	−0.233054	−	0.233054i	−0.813966	+	0.580912i	$0.802696\pi$
$368$	6.73337	+	6.73337i	0.351001	+	0.351001i
$369$	−5.25249	+	4.19914i	−0.273434	+	0.218598i
$370$	2.02145	+	17.4953i	0.105090	+	0.909540i
$371$			4.93212i			0.256063i
$372$	−1.56098	−	0.750564i	−0.0809330	−	0.0389149i
$373$	16.8118	−	16.8118i	0.870480	−	0.870480i	−0.122044	−	0.992525i	$-0.538945\pi$
$373$	16.8118	−	16.8118i	0.870480	−	0.870480i	0.992525	+	0.122044i	$0.0389450\pi$
$374$	−3.21650			−0.166321
$375$	−19.2621	−	1.99295i	−0.994690	−	0.102915i
$376$	−12.1768			−0.627971
$377$	5.03487	−	5.03487i	0.259309	−	0.259309i
$378$	3.31757	−	0.763556i	0.170637	−	0.0392731i
$379$			16.8682i			0.866463i	0.901283	+	0.433232i	$0.142627\pi$
$379$			16.8682i			0.866463i	−0.901283	+	0.433232i	$0.857373\pi$
$380$	−0.184128	−	1.59360i	−0.00944556	−	0.0817501i
$381$	−22.4834	+	7.88256i	−1.15186	+	0.403836i
$382$	−12.7011	−	12.7011i	−0.649847	−	0.649847i
$383$	−5.75879	−	5.75879i	−0.294260	−	0.294260i	0.544500	−	0.838761i	$-0.316719\pi$
$383$	−5.75879	−	5.75879i	−0.294260	−	0.294260i	−0.838761	+	0.544500i	$0.816719\pi$
$384$	−1.63451	+	0.573050i	−0.0834106	+	0.0292433i
$385$	−0.787881	−	0.624672i	−0.0401541	−	0.0318362i
$386$		−	5.12553i		−	0.260883i
$387$	−17.1352	−	1.90966i	−0.871031	−	0.0970737i
$388$	−11.0744	+	11.0744i	−0.562220	+	0.562220i
$389$	−12.6237			−0.640049			−0.320024	−	0.947409i	$-0.603691\pi$
$389$	−12.6237			−0.640049			−0.320024	+	0.947409i	$0.603691\pi$
$390$	−1.69913	+	4.90990i	−0.0860387	+	0.248623i
$391$	−44.6264			−2.25685
$392$	−4.64623	+	4.64623i	−0.234670	+	0.234670i
$393$	−16.4581	−	7.91353i	−0.830201	−	0.399185i
$394$		−	9.75331i		−	0.491365i
$395$	11.2003	−	1.29410i	0.563547	−	0.0651133i
$396$	1.28572	+	1.60825i	0.0646101	+	0.0808175i
$397$	−23.9313	−	23.9313i	−1.20108	−	1.20108i	−0.973840	−	0.227237i	$-0.927031\pi$
$397$	−23.9313	−	23.9313i	−1.20108	−	1.20108i	−0.227237	−	0.973840i	$-0.572969\pi$
$398$	17.7599	+	17.7599i	0.890226	+	0.890226i
$399$	−0.269348	−	0.768259i	−0.0134843	−	0.0384611i
$400$	4.86826	−	1.14020i	0.243413	−	0.0570099i
$401$			15.9112i			0.794565i	0.917696	+	0.397283i	$0.130047\pi$
$401$			15.9112i			0.794565i	−0.917696	+	0.397283i	$0.869953\pi$
$402$	−3.46605	+	7.20848i	−0.172871	+	0.359527i
$403$	0.948581	−	0.948581i	0.0472522	−	0.0472522i
$404$	8.31077			0.413476
$405$	20.0096	+	2.14814i	0.994287	+	0.106742i
$406$	−3.47744			−0.172582
$407$	−3.82244	+	3.82244i	−0.189471	+	0.189471i
$408$	3.51748	−	7.31546i	0.174141	−	0.362169i
$409$		−	27.5233i		−	1.36094i	−0.732776	−	0.680470i	$-0.761776\pi$
$409$		−	27.5233i		−	1.36094i	0.732776	−	0.680470i	$-0.238224\pi$
$410$	−3.11400	+	3.92760i	−0.153790	+	0.193970i
$411$	−4.85941	−	13.8605i	−0.239697	−	0.683687i
$412$	7.13953	+	7.13953i	0.351739	+	0.351739i
$413$	6.30679	+	6.30679i	0.310337	+	0.310337i
$414$	17.8384	+	22.3132i	0.876711	+	1.09663i
$415$	−12.6070	+	15.9008i	−0.618851	+	0.780539i
$416$		−	1.34150i		−	0.0657723i
$417$	24.5783	+	11.8179i	1.20360	+	0.578727i
$418$	0.348176	−	0.348176i	0.0170298	−	0.0170298i
$419$	−5.91620			−0.289025			−0.144513	−	0.989503i	$-0.546161\pi$
$419$	−5.91620			−0.289025			−0.144513	+	0.989503i	$0.546161\pi$
$420$	2.28234	−	1.10880i	0.111367	−	0.0541037i
$421$	23.8359			1.16169			0.580844	−	0.814015i	$-0.302722\pi$
$421$	23.8359			1.16169			0.580844	+	0.814015i	$0.302722\pi$
$422$	−1.43761	+	1.43761i	−0.0699820	+	0.0699820i
$423$	−36.3057	−	4.04615i	−1.76524	−	0.196731i
$424$		−	7.52814i		−	0.365599i
$425$	−12.3541	+	19.9110i	−0.599264	+	0.965824i
$426$	−10.6151	+	3.72160i	−0.514303	+	0.180312i
$427$	−6.13794	−	6.13794i	−0.297036	−	0.297036i
$428$	−8.12668	−	8.12668i	−0.392818	−	0.392818i
$429$	−1.50493	+	0.527619i	−0.0726585	+	0.0254737i
$430$	−12.7660	+	1.47500i	−0.615630	+	0.0711310i
$431$		−	13.0846i		−	0.630262i	−0.949048	−	0.315131i	$-0.897952\pi$
$431$		−	13.0846i		−	0.630262i	0.949048	−	0.315131i	$-0.102048\pi$
$432$	−5.06377	+	1.16545i	−0.243631	+	0.0560729i
$433$	14.7617	−	14.7617i	0.709400	−	0.709400i	−0.257009	−	0.966409i	$-0.582737\pi$
$433$	14.7617	−	14.7617i	0.709400	−	0.709400i	0.966409	+	0.257009i	$0.0827370\pi$
$434$	−0.655158			−0.0314486
$435$	−19.4266	−	6.72280i	−0.931435	−	0.322333i
$436$	11.8065			0.565427
$437$	4.83067	−	4.83067i	0.231082	−	0.231082i
$438$	3.57885	+	1.72081i	0.171004	+	0.0822237i
$439$			1.14369i			0.0545854i	0.999627	+	0.0272927i	$0.00868861\pi$
$439$			1.14369i			0.0545854i	−0.999627	+	0.0272927i	$0.991311\pi$
$440$	1.20258	+	0.953468i	0.0573308	+	0.0454548i
$441$	−15.3968	+	12.3091i	−0.733181	+	0.586146i
$442$	4.44548	+	4.44548i	0.211450	+	0.211450i
$443$	−10.0785	−	10.0785i	−0.478846	−	0.478846i	0.425917	−	0.904762i	$-0.359952\pi$
$443$	−10.0785	−	10.0785i	−0.478846	−	0.478846i	−0.904762	+	0.425917i	$0.859952\pi$
$444$	−4.51346	−	12.8737i	−0.214199	−	0.610960i
$445$	1.24380	+	10.7649i	0.0589617	+	0.510306i
$446$			4.82717i			0.228573i
$447$	−9.62223	+	20.0117i	−0.455116	+	0.946523i
$448$	−0.463267	+	0.463267i	−0.0218873	+	0.0218873i
$449$	−4.22622			−0.199447			−0.0997237	−	0.995015i	$-0.531796\pi$
$449$	−4.22622			−0.199447			−0.0997237	+	0.995015i	$0.531796\pi$
$450$	14.8938	−	1.78190i	0.702100	−	0.0839998i
$451$	−1.53847			−0.0724438
$452$	−1.38059	+	1.38059i	−0.0649374	+	0.0649374i
$453$	−7.21209	+	14.9993i	−0.338854	+	0.704728i
$454$		−	20.9737i		−	0.984345i
$455$	0.225570	+	1.95228i	0.0105749	+	0.0915241i
$456$	0.411119	+	1.17263i	0.0192524	+	0.0549135i
$457$	−12.9219	−	12.9219i	−0.604460	−	0.604460i	0.337033	−	0.941493i	$-0.390577\pi$
$457$	−12.9219	−	12.9219i	−0.604460	−	0.604460i	−0.941493	+	0.337033i	$0.890577\pi$
$458$	6.02853	+	6.02853i	0.281695	+	0.281695i
$459$	12.9183	−	20.6425i	0.602976	−	0.963511i
$460$	16.6849	+	13.2286i	0.777937	+	0.616788i
$461$			16.9509i			0.789484i	0.918792	+	0.394742i	$0.129166\pi$
$461$			16.9509i			0.789484i	−0.918792	+	0.394742i	$0.870834\pi$
$462$	0.701910	+	0.337499i	0.0326558	+	0.0157019i
$463$	2.69782	−	2.69782i	0.125378	−	0.125378i	−0.641633	−	0.767012i	$-0.721743\pi$
$463$	2.69782	−	2.69782i	0.125378	−	0.125378i	0.767012	+	0.641633i	$0.221743\pi$
$464$	5.30779			0.246408
$465$	−3.66002	−	1.26659i	−0.169729	−	0.0587368i
$466$	−5.02005			−0.232549
$467$	−3.63625	+	3.63625i	−0.168266	+	0.168266i	−0.786217	−	0.617951i	$-0.787963\pi$
$467$	−3.63625	+	3.63625i	−0.168266	+	0.168266i	0.617951	+	0.786217i	$0.287963\pi$
$468$	0.445757	−	3.99973i	0.0206051	−	0.184887i
$469$			3.02547i			0.139703i
$470$	−27.0482	+	3.12521i	−1.24764	+	0.144155i
$471$	−20.7650	+	7.28012i	−0.956803	+	0.335450i
$472$	−9.62637	−	9.62637i	−0.443089	−	0.443089i
$473$	−2.78915	−	2.78915i	−0.128245	−	0.128245i
$474$	−8.24157	+	2.88945i	−0.378548	+	0.132717i
$475$	−0.818003	−	3.49260i	−0.0375325	−	0.160251i
$476$		−	3.07037i		−	0.140730i
$477$	2.50147	−	22.4454i	0.114535	−	1.02771i
$478$	−20.0397	+	20.0397i	−0.916592	+	0.916592i
$479$	−22.2433			−1.01632			−0.508160	−	0.861263i	$-0.669674\pi$
$479$	−22.2433			−1.01632			−0.508160	+	0.861263i	$0.669674\pi$
$480$	−3.48364	+	1.69241i	−0.159006	+	0.0772476i
$481$	10.5659			0.481764
$482$	−8.09031	+	8.09031i	−0.368503	+	0.368503i
$483$	9.73846	+	4.68253i	0.443115	+	0.213063i
$484$		−	10.5289i		−	0.478588i
$485$	−21.7573	+	27.4418i	−0.987947	+	1.24607i
$486$	−15.4851	+	1.79224i	−0.702418	+	0.0812976i
$487$	11.3085	+	11.3085i	0.512435	+	0.512435i	0.915272	−	0.402837i	$-0.131976\pi$
$487$	11.3085	+	11.3085i	0.512435	+	0.512435i	−0.402837	+	0.915272i	$0.631976\pi$
$488$	9.36863	+	9.36863i	0.424098	+	0.424098i
$489$	2.18768	+	6.23992i	0.0989305	+	0.282179i
$490$	−9.12817	+	11.5131i	−0.412369	+	0.520109i
$491$		−	9.73235i		−	0.439215i	−0.975588	−	0.219607i	$-0.929522\pi$
$491$		−	9.73235i		−	0.439215i	0.975588	−	0.219607i	$-0.0704776\pi$
$492$	1.68244	−	3.49903i	0.0758501	−	0.157749i
$493$	−17.5891	+	17.5891i	−0.792172	+	0.792172i
$494$	−0.962420			−0.0433013
$495$	3.26873	+	3.24240i	0.146918	+	0.145735i
$496$	1.00000			0.0449013
$497$	−3.00863	+	3.00863i	−0.134955	+	0.134955i
$498$	6.81130	−	14.1658i	0.305222	−	0.634783i
$499$		−	25.6861i		−	1.14987i	−0.818199	−	0.574935i	$-0.805027\pi$
$499$		−	25.6861i		−	1.14987i	0.818199	−	0.574935i	$-0.194973\pi$
$500$	10.5212	−	3.78216i	0.470522	−	0.169143i
$501$	−0.413800	−	1.18028i	−0.0184872	−	0.0527310i
$502$	−4.34352	−	4.34352i	−0.193861	−	0.193861i
$503$	27.2203	+	27.2203i	1.21369	+	1.21369i	0.969803	+	0.243891i	$0.0784240\pi$
$503$	27.2203	+	27.2203i	1.21369	+	1.21369i	0.243891	+	0.969803i	$0.421576\pi$
$504$	−1.53518	+	1.22731i	−0.0683826	+	0.0546689i
$505$	18.4606	−	2.13298i	0.821487	−	0.0949162i
$506$			6.53560i			0.290543i
$507$	−17.4836	−	8.40660i	−0.776472	−	0.373350i
$508$	9.72658	−	9.72658i	0.431547	−	0.431547i
$509$	−38.2288			−1.69446			−0.847231	−	0.531224i	$-0.821732\pi$
$509$	−38.2288			−1.69446			−0.847231	+	0.531224i	$0.821732\pi$
$510$	5.93582	−	17.1525i	0.262843	−	0.759526i
$511$	1.50208			0.0664480
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.836121	+	3.63286i	0.0369157	+	0.160395i
$514$			0.251116i			0.0110763i
$515$	17.6913	+	14.0266i	0.779573	+	0.618085i
$516$	9.39367	−	3.29337i	0.413533	−	0.144983i
$517$	−5.90959	−	5.90959i	−0.259903	−	0.259903i
$518$	−3.64879	−	3.64879i	−0.160318	−	0.160318i
$519$	0.342517	−	0.120085i	0.0150348	−	0.00527113i
$520$	−0.344298	−	2.97985i	−0.0150985	−	0.130675i
$521$		−	28.0660i		−	1.22959i	−0.788685	−	0.614797i	$-0.789238\pi$
$521$		−	28.0660i		−	1.22959i	0.788685	−	0.614797i	$-0.210762\pi$
$522$	15.8254	+	1.76369i	0.692658	+	0.0771946i
$523$	6.68771	−	6.68771i	0.292433	−	0.292433i	−0.545608	−	0.838041i	$-0.683701\pi$
$523$	6.68771	−	6.68771i	0.292433	−	0.292433i	0.838041	+	0.545608i	$0.183701\pi$
$524$	10.5434			0.460593
$525$	4.78515	−	3.04872i	0.208841	−	0.133057i
$526$	5.94984			0.259425
$527$	−3.31382	+	3.31382i	−0.144352	+	0.144352i
$528$	−1.07136	−	0.515141i	−0.0466250	−	0.0224186i
$529$			67.6764i			2.94245i
$530$	−1.93211	−	16.7222i	−0.0839256	−	0.726365i
$531$	−25.5027	−	31.9001i	−1.10672	−	1.38435i
$532$	0.332358	+	0.332358i	0.0144095	+	0.0144095i
$533$	2.12631	+	2.12631i	0.0921005	+	0.0921005i
$534$	−2.77714	−	7.92122i	−0.120179	−	0.342785i
$535$	−20.1374	−	15.9660i	−0.870617	−	0.690269i
$536$		−	4.61793i		−	0.199464i
$537$	−7.59667	+	15.7991i	−0.327820	+	0.681782i
$538$	6.20412	−	6.20412i	0.267479	−	0.267479i
$539$	−4.50977			−0.194250
$540$	−10.9490	+	3.88843i	−0.471169	+	0.167332i
$541$	2.95969			0.127247			0.0636234	−	0.997974i	$-0.479734\pi$
$541$	2.95969			0.127247			0.0636234	+	0.997974i	$0.479734\pi$
$542$	22.4306	−	22.4306i	0.963479	−	0.963479i
$543$	−6.36242	+	13.2322i	−0.273038	+	0.567848i
$544$			4.68646i			0.200930i
$545$	26.2256	−	3.03015i	1.12338	−	0.129798i
$546$	−0.503649	−	1.43656i	−0.0215542	−	0.0614789i
$547$	32.3516	+	32.3516i	1.38325	+	1.38325i	0.838773	+	0.544481i	$0.183273\pi$
$547$	32.3516	+	32.3516i	1.38325	+	1.38325i	0.544481	+	0.838773i	$0.316727\pi$
$548$	5.99620	+	5.99620i	0.256145	+	0.256145i
$549$	24.8199	+	31.0460i	1.05929	+	1.32501i
$550$	2.91599	+	1.80928i	0.124338	+	0.0771481i
$551$		−	3.80792i		−	0.162223i
$552$	−14.8643	−	7.14718i	−0.632666	−	0.304204i
$553$	−2.33590	+	2.33590i	−0.0993326	+	0.0993326i
$554$	8.81759			0.374624
$555$	−13.3298	−	27.4379i	−0.565817	−	1.16467i
$556$	−15.7454			−0.667755
$557$	28.5350	−	28.5350i	1.20907	−	1.20907i	0.237736	−	0.971330i	$-0.423595\pi$
$557$	28.5350	−	28.5350i	1.20907	−	1.20907i	0.971330	−	0.237736i	$-0.0764052\pi$
$558$	2.98154	+	0.332283i	0.126219	+	0.0140667i
$559$			7.70971i			0.326086i
$560$	−0.910151	+	1.14795i	−0.0384609	+	0.0485097i
$561$	5.25739	−	1.84321i	0.221967	−	0.0778205i
$562$	−22.5123	−	22.5123i	−0.949626	−	0.949626i
$563$	−7.36558	−	7.36558i	−0.310422	−	0.310422i	0.534651	−	0.845073i	$-0.320443\pi$
$563$	−7.36558	−	7.36558i	−0.310422	−	0.310422i	−0.845073	+	0.534651i	$0.820443\pi$
$564$	19.9031	−	6.97792i	0.838072	−	0.293824i
$565$	−2.71235	+	3.42102i	−0.114110	+	0.143923i
$566$			8.30079i			0.348908i
$567$	−4.98503	+	3.14917i	−0.209352	+	0.132253i
$568$	4.59221	−	4.59221i	0.192685	−	0.192685i
$569$	11.8275			0.495835			0.247917	−	0.968781i	$-0.420254\pi$
$569$	11.8275			0.495835			0.247917	+	0.968781i	$0.420254\pi$
$570$	1.21417	+	2.49924i	0.0508561	+	0.104682i
$571$	22.3004			0.933242			0.466621	−	0.884457i	$-0.345471\pi$
$571$	22.3004			0.933242			0.466621	+	0.884457i	$0.345471\pi$
$572$	0.651048	−	0.651048i	0.0272217	−	0.0272217i
$573$	28.0385	+	13.4817i	1.17132	+	0.563207i
$574$		−	1.46858i		−	0.0612973i
$575$	40.4571	+	25.1024i	1.68718	+	1.04684i
$576$	2.34323	−	1.87331i	0.0976345	−	0.0780545i
$577$	−5.79926	−	5.79926i	−0.241426	−	0.241426i	0.576014	−	0.817440i	$-0.304607\pi$
$577$	−5.79926	−	5.79926i	−0.241426	−	0.241426i	−0.817440	+	0.576014i	$0.804607\pi$
$578$	−3.50928	−	3.50928i	−0.145967	−	0.145967i
$579$	2.93718	+	8.37771i	0.122065	+	0.348166i
$580$	11.7901	−	1.36225i	0.489559	−	0.0565645i
$581$		−	5.94551i		−	0.246661i
$582$	11.7551	−	24.4475i	0.487263	−	1.01338i
$583$	3.65351	−	3.65351i	0.151313	−	0.151313i
$584$	−2.29270			−0.0948724
$585$	−0.0363830	−	8.99896i	−0.00150425	−	0.372061i
$586$	9.27332			0.383077
$587$	18.3411	−	18.3411i	0.757018	−	0.757018i	−0.218760	−	0.975779i	$-0.570201\pi$
$587$	18.3411	−	18.3411i	0.757018	−	0.757018i	0.975779	+	0.218760i	$0.0702013\pi$
$588$	4.93178	−	10.2568i	0.203383	−	0.422984i
$589$		−	0.717422i		−	0.0295609i
$590$	−23.8536	−	18.9123i	−0.982036	−	0.778608i
$591$	5.58913	+	15.9419i	0.229906	+	0.655760i
$592$	5.56932	+	5.56932i	0.228898	+	0.228898i
$593$	−14.5489	−	14.5489i	−0.597454	−	0.597454i	0.342181	−	0.939634i	$-0.388835\pi$
$593$	−14.5489	−	14.5489i	−0.597454	−	0.597454i	−0.939634	+	0.342181i	$0.888835\pi$
$594$	−3.02313	−	1.89191i	−0.124041	−	0.0776260i
$595$	−0.788017	−	6.82018i	−0.0323055	−	0.279600i
$596$		−	12.8200i		−	0.525128i
$597$	−39.2061	−	18.8514i	−1.60460	−	0.771537i
$598$	9.03279	−	9.03279i	0.369378	−	0.369378i
$599$	−27.1824			−1.11064			−0.555320	−	0.831636i	$-0.687404\pi$
$599$	−27.1824			−1.11064			−0.555320	+	0.831636i	$0.687404\pi$
$600$	−7.30382	+	4.65342i	−0.298177	+	0.189975i
$601$	−17.4964			−0.713692			−0.356846	−	0.934163i	$-0.616148\pi$
$601$	−17.4964			−0.713692			−0.356846	+	0.934163i	$0.616148\pi$
$602$	2.66244	−	2.66244i	0.108513	−	0.108513i
$603$	1.53446	−	13.7685i	0.0624880	−	0.560698i
$604$		−	9.60890i		−	0.390981i
$605$	−2.70227	−	23.3878i	−0.109863	−	0.950850i
$606$	−13.5840	+	4.76249i	−0.551813	+	0.193463i
$607$	−31.6422	−	31.6422i	−1.28432	−	1.28432i	−0.938186	−	0.346132i	$-0.887495\pi$
$607$	−31.6422	−	31.6422i	−1.28432	−	1.28432i	−0.346132	−	0.938186i	$-0.612505\pi$
$608$	−0.507294	−	0.507294i	−0.0205735	−	0.0205735i
$609$	5.68390	−	1.99275i	0.230323	−	0.0807502i
$610$	23.2149	+	18.4060i	0.939945	+	0.745236i
$611$			16.3352i			0.660850i
$612$	−1.55723	+	13.9729i	−0.0629473	+	0.564819i
$613$	−24.8249	+	24.8249i	−1.00267	+	1.00267i	−0.00267113	+	0.999996i	$0.500850\pi$
$613$	−24.8249	+	24.8249i	−1.00267	+	1.00267i	−0.999996	+	0.00267113i	$0.999150\pi$
$614$	−16.3061			−0.658061
$615$	2.83915	−	8.20417i	0.114485	−	0.330824i
$616$	−0.449660			−0.0181173
$617$	1.75034	−	1.75034i	0.0704661	−	0.0704661i	−0.670995	−	0.741461i	$-0.734133\pi$
$617$	1.75034	−	1.75034i	0.0704661	−	0.0704661i	0.741461	+	0.670995i	$0.234133\pi$
$618$	−15.7609	−	7.57830i	−0.633997	−	0.304844i
$619$			21.7983i			0.876148i	0.898939	+	0.438074i	$0.144339\pi$
$619$			21.7983i			0.876148i	−0.898939	+	0.438074i	$0.855661\pi$
$620$	2.22129	−	0.256652i	0.0892092	−	0.0103074i
$621$	−41.9436	−	26.2488i	−1.68314	−	1.05333i
$622$	−0.840920	−	0.840920i	−0.0337178	−	0.0337178i
$623$	−2.24510	−	2.24510i	−0.0899482	−	0.0899482i
$624$	0.768745	+	2.19269i	0.0307744	+	0.0877777i
$625$	22.3999	−	11.1016i	0.895996	−	0.444062i
$626$		−	5.61982i		−	0.224613i
$627$	−0.369574	+	0.768617i	−0.0147593	+	0.0306956i
$628$	8.98320	−	8.98320i	0.358469	−	0.358469i
$629$	−36.9115			−1.47176
$630$	−3.09510	+	3.12023i	−0.123312	+	0.124313i
$631$	6.78885			0.270260			0.135130	−	0.990828i	$-0.456855\pi$
$631$	6.78885			0.270260			0.135130	+	0.990828i	$0.456855\pi$
$632$	3.56540	−	3.56540i	0.141824	−	0.141824i
$633$	1.52597	−	3.17362i	0.0606517	−	0.126140i
$634$		−	16.7490i		−	0.665187i
$635$	19.1092	−	24.1019i	0.758326	−	0.956454i
$636$	4.31400	+	12.3048i	0.171061	+	0.487917i
$637$	6.23291	+	6.23291i	0.246957	+	0.246957i
$638$	2.57595	+	2.57595i	0.101983	+	0.101983i
$639$	15.2178	−	12.1660i	0.602007	−	0.481278i
$640$	1.38921	−	1.75217i	0.0549133	−	0.0692606i
$641$		−	5.96675i		−	0.235672i	−0.993033	−	0.117836i	$-0.962404\pi$
$641$		−	5.96675i		−	0.235672i	0.993033	−	0.117836i	$-0.0375958\pi$
$642$	17.9401	+	8.62612i	0.708039	+	0.340446i
$643$	31.8138	−	31.8138i	1.25461	−	1.25461i	0.300986	−	0.953629i	$-0.402684\pi$
$643$	31.8138	−	31.8138i	1.25461	−	1.25461i	0.953629	−	0.300986i	$-0.0973156\pi$
$644$	−6.23869			−0.245839
$645$	20.0208	−	9.72644i	0.788319	−	0.382978i
$646$	3.36217			0.132283
$647$	−6.98781	+	6.98781i	−0.274719	+	0.274719i	−0.830997	−	0.556277i	$-0.812229\pi$
$647$	−6.98781	+	6.98781i	−0.274719	+	0.274719i	0.556277	+	0.830997i	$0.312229\pi$
$648$	7.60890	−	4.80673i	0.298906	−	0.188826i
$649$		−	9.34363i		−	0.366770i
$650$	−1.52957	−	6.53075i	−0.0599947	−	0.256157i
$651$	1.07086	−	0.375438i	0.0419703	−	0.0147146i
$652$	−2.69946	−	2.69946i	−0.105719	−	0.105719i
$653$	2.34568	+	2.34568i	0.0917935	+	0.0917935i	0.751512	−	0.659719i	$-0.229325\pi$
$653$	2.34568	+	2.34568i	0.0917935	+	0.0917935i	−0.659719	+	0.751512i	$0.729325\pi$
$654$	−19.2978	+	6.76569i	−0.754602	+	0.264560i
$655$	23.4201	−	2.70600i	0.915097	−	0.105732i
$656$			2.24156i			0.0875184i
$657$	−6.83577	−	0.761824i	−0.266689	−	0.0297216i
$658$	5.64111	−	5.64111i	0.219914	−	0.219914i
$659$	20.0540			0.781194			0.390597	−	0.920562i	$-0.372269\pi$
$659$	20.0540			0.781194			0.390597	+	0.920562i	$0.372269\pi$
$660$	−2.51201	−	0.869311i	−0.0977800	−	0.0338379i
$661$	−32.5459			−1.26589			−0.632945	−	0.774197i	$-0.718154\pi$
$661$	−32.5459			−1.26589			−0.632945	+	0.774197i	$0.718154\pi$
$662$	7.73831	−	7.73831i	0.300758	−	0.300758i
$663$	−9.81366	−	4.71869i	−0.381131	−	0.183259i
$664$			9.07492i			0.352175i
$665$	0.823564	+	0.652963i	0.0319364	+	0.0253208i
$666$	14.7546	+	18.4557i	0.571728	+	0.715146i
$667$	35.7393	+	35.7393i	1.38383	+	1.38383i
$668$	0.510603	+	0.510603i	0.0197558	+	0.0197558i
$669$	−2.76621	−	7.89005i	−0.106948	−	0.305047i
$670$	−1.18520	−	10.2578i	−0.0457883	−	0.396292i
$671$			9.09347i			0.351050i
$672$	0.491738	−	1.02269i	0.0189692	−	0.0394510i
$673$	−8.33983	+	8.33983i	−0.321477	+	0.321477i	−0.849334	−	0.527857i	$-0.822996\pi$
$673$	−8.33983	+	8.33983i	−0.321477	+	0.321477i	0.527857	+	0.849334i	$0.322996\pi$
$674$	−25.8769			−0.996740
$675$	−23.3229	+	11.4474i	−0.897698	+	0.440611i
$676$	11.2004			0.430784
$677$	−4.13429	+	4.13429i	−0.158894	+	0.158894i	−0.782076	−	0.623183i	$-0.785839\pi$
$677$	−4.13429	+	4.13429i	−0.158894	+	0.158894i	0.623183	+	0.782076i	$0.285839\pi$
$678$	1.46543	−	3.04773i	0.0562797	−	0.117047i
$679$		−	10.2608i		−	0.393775i
$680$	1.20279	+	10.4100i	0.0461248	+	0.399204i
$681$	12.0190	+	34.2817i	0.460569	+	1.31368i
$682$	0.485315	+	0.485315i	0.0185837	+	0.0185837i
$683$	20.7876	+	20.7876i	0.795414	+	0.795414i	0.982369	−	0.186955i	$-0.0598617\pi$
$683$	20.7876	+	20.7876i	0.795414	+	0.795414i	−0.186955	+	0.982369i	$0.559862\pi$
$684$	−1.34395	−	1.68108i	−0.0513873	−	0.0642778i
$685$	14.8582	+	11.7804i	0.567704	+	0.450105i
$686$		−	8.89100i		−	0.339460i
$687$	−13.3083	−	6.39902i	−0.507744	−	0.244138i
$688$	−4.06381	+	4.06381i	−0.154931	+	0.154931i
$689$	−10.0990			−0.384740
$690$	−34.8522	−	12.0610i	−1.32680	−	0.459155i
$691$	−14.9688			−0.569439			−0.284719	−	0.958611i	$-0.591900\pi$
$691$	−14.9688			−0.569439			−0.284719	+	0.958611i	$0.591900\pi$
$692$	−0.148177	+	0.148177i	−0.00563284	+	0.00563284i
$693$	−1.34068	−	0.149415i	−0.0509283	−	0.00567579i
$694$			4.55921i			0.173065i
$695$	−34.9751	+	4.04109i	−1.32668	+	0.153287i
$696$	−8.67562	+	3.04163i	−0.328848	+	0.115293i
$697$	−7.42815	−	7.42815i	−0.281361	−	0.281361i
$698$	14.7586	+	14.7586i	0.558621	+	0.558621i
$699$	8.20531	−	2.87674i	0.310353	−	0.108808i
$700$	−1.72709	+	2.78352i	−0.0652778	+	0.105207i
$701$			42.5799i			1.60822i	0.594480	+	0.804110i	$0.297358\pi$
$701$			42.5799i			1.60822i	−0.594480	+	0.804110i	$0.702642\pi$
$702$	1.56345	+	6.79302i	0.0590086	+	0.256386i
$703$	3.99555	−	3.99555i	0.150695	−	0.150695i
$704$	0.686339			0.0258674
$705$	42.4197	−	20.6082i	1.59762	−	0.776148i
$706$	−21.7181			−0.817372
$707$	−3.85010	+	3.85010i	−0.144798	+	0.144798i
$708$	21.2508	+	10.2180i	0.798652	+	0.384015i
$709$		−	3.88177i		−	0.145783i	−0.997340	−	0.0728914i	$-0.976777\pi$
$709$		−	3.88177i		−	0.145783i	0.997340	−	0.0728914i	$-0.0232226\pi$
$710$	9.02204	−	11.3792i	0.338591	−	0.427055i
$711$	11.8151	−	9.44567i	0.443101	−	0.354240i
$712$	3.42681	+	3.42681i	0.128425	+	0.128425i
$713$	6.73337	+	6.73337i	0.252167	+	0.252167i
$714$	1.75947	+	5.01854i	0.0658467	+	0.187814i
$715$	1.27907	−	1.61326i	0.0478347	−	0.0603325i
$716$		−	10.1213i		−	0.378250i
$717$	21.2712	−	44.2387i	0.794389	−	1.65212i
$718$	−0.279433	+	0.279433i	−0.0104283	+	0.0104283i
$719$	−30.7012			−1.14496			−0.572480	−	0.819919i	$-0.694019\pi$
$719$	−30.7012			−1.14496			−0.572480	+	0.819919i	$0.694019\pi$
$720$	4.72420	−	4.76256i	0.176061	−	0.177490i
$721$	−6.61501			−0.246356
$722$	13.0711	−	13.0711i	0.486455	−	0.486455i
$723$	8.58752	−	17.8598i	0.319373	−	0.664214i
$724$		−	8.47685i		−	0.315040i
$725$	25.8397	−	6.05193i	0.959662	−	0.224763i
$726$	6.03361	+	17.2096i	0.223928	+	0.638709i
$727$	34.4676	+	34.4676i	1.27833	+	1.27833i	0.941600	+	0.336733i	$0.109322\pi$
$727$	34.4676	+	34.4676i	1.27833	+	1.27833i	0.336733	+	0.941600i	$0.390678\pi$
$728$	0.621471	+	0.621471i	0.0230332	+	0.0230332i
$729$	24.2834	−	11.8032i	0.899387	−	0.437154i
$730$	−5.09274	+	0.588425i	−0.188491	+	0.0217786i
$731$		−	26.9335i		−	0.996172i
$732$	−20.6818	−	9.94440i	−0.764421	−	0.367556i
$733$	−1.60124	+	1.60124i	−0.0591432	+	0.0591432i	−0.736060	−	0.676917i	$-0.763316\pi$
$733$	−1.60124	+	1.60124i	−0.0591432	+	0.0591432i	0.676917	+	0.736060i	$0.263316\pi$
$734$	−6.31401			−0.233054
$735$	8.32248	−	24.0491i	0.306979	−	0.887066i
$736$	9.52242			0.351001
$737$	2.24115	−	2.24115i	0.0825537	−	0.0825537i
$738$	−0.744834	+	6.68331i	−0.0274177	+	0.246016i
$739$		−	17.6270i		−	0.648421i	−0.945985	−	0.324210i	$-0.894901\pi$
$739$		−	17.6270i		−	0.648421i	0.945985	−	0.324210i	$-0.105099\pi$
$740$	13.8005	+	10.9417i	0.507315	+	0.402225i
$741$	1.57308	−	0.551514i	0.0577886	−	0.0202604i
$742$	3.48753	+	3.48753i	0.128031	+	0.128031i
$743$	19.6205	+	19.6205i	0.719807	+	0.719807i	0.968565	−	0.248759i	$-0.0800227\pi$
$743$	19.6205	+	19.6205i	0.719807	+	0.719807i	−0.248759	+	0.968565i	$0.580023\pi$
$744$	−1.63451	+	0.573050i	−0.0599239	+	0.0210090i
$745$	−3.29028	−	28.4769i	−0.120547	−	1.04331i
$746$		−	23.7754i		−	0.870480i
$747$	−3.01544	+	27.0572i	−0.110329	+	0.989973i
$748$	−2.27441	+	2.27441i	−0.0831605	+	0.0831605i
$749$	7.52964			0.275127
$750$	−15.0296	+	12.2111i	−0.548803	+	0.445887i
$751$	26.8047			0.978117			0.489059	−	0.872251i	$-0.337340\pi$
$751$	26.8047			0.978117			0.489059	+	0.872251i	$0.337340\pi$
$752$	−8.61031	+	8.61031i	−0.313986	+	0.313986i
$753$	9.58858	+	4.61047i	0.349427	+	0.168015i
$754$		−	7.12038i		−	0.259309i
$755$	−2.46614	−	21.3442i	−0.0897522	−	0.776794i
$756$	1.80596	−	2.88579i	0.0656821	−	0.104955i
$757$	24.9923	+	24.9923i	0.908362	+	0.908362i	0.996140	−	0.0877777i	$-0.0279765\pi$
$757$	24.9923	+	24.9923i	0.908362	+	0.908362i	−0.0877777	+	0.996140i	$0.527977\pi$
$758$	11.9276	+	11.9276i	0.433232	+	0.433232i
$759$	−3.74523	−	10.6825i	−0.135943	−	0.387750i
$760$	−1.25705	−	0.996649i	−0.0455978	−	0.0361523i
$761$		−	31.7383i		−	1.15051i	−0.817974	−	0.575255i	$-0.804903\pi$
$761$		−	31.7383i		−	1.15051i	0.817974	−	0.575255i	$-0.195097\pi$
$762$	−10.3243	+	21.4720i	−0.374012	+	0.777847i
$763$	−5.46954	+	5.46954i	−0.198011	+	0.198011i
$764$	−17.9621			−0.649847
$765$	0.127102	+	31.4374i	0.00459540	+	1.13662i
$766$	−8.14416			−0.294260
$767$	−12.9137	+	12.9137i	−0.466288	+	0.466288i
$768$	−0.750564	+	1.56098i	−0.0270836	+	0.0563270i
$769$		−	16.2635i		−	0.586478i	−0.956039	−	0.293239i	$-0.905267\pi$
$769$		−	16.2635i		−	0.586478i	0.956039	−	0.293239i	$-0.0947332\pi$
$770$	−0.998826	+	0.115406i	−0.0359952	+	0.00415895i
$771$	−0.143902	−	0.410451i	−0.00518251	−	0.0147820i
$772$	−3.62430	−	3.62430i	−0.130441	−	0.130441i
$773$	−12.2067	−	12.2067i	−0.439043	−	0.439043i	0.452647	−	0.891690i	$-0.350480\pi$
$773$	−12.2067	−	12.2067i	−0.439043	−	0.439043i	−0.891690	+	0.452647i	$0.850480\pi$
$774$	−13.4668	+	10.7661i	−0.484053	+	0.386979i
$775$	4.86826	−	1.14020i	0.174873	−	0.0409571i
$776$			15.6616i			0.562220i
$777$	8.05490	+	3.87303i	0.288968	+	0.138944i
$778$	−8.92633	+	8.92633i	−0.320024	+	0.320024i
$779$	1.60815			0.0576179
$780$	2.27036	+	4.67329i	0.0812920	+	0.167331i
$781$	4.45734			0.159496
$782$	−31.5556	+	31.5556i	−1.12843	+	1.12843i
$783$	−26.8774	+	6.18597i	−0.960520	+	0.221069i
$784$			6.57077i			0.234670i
$785$	17.6487	−	22.2598i	0.629910	−	0.794488i
$786$	−17.2333	+	6.04192i	−0.614693	+	0.215508i
$787$	33.4982	+	33.4982i	1.19408	+	1.19408i	0.975910	+	0.218172i	$0.0700095\pi$
$787$	33.4982	+	33.4982i	1.19408	+	1.19408i	0.218172	+	0.975910i	$0.429991\pi$
$788$	−6.89663	−	6.89663i	−0.245682	−	0.245682i
$789$	−9.72506	+	3.40956i	−0.346221	+	0.121383i
$790$	7.00472	−	8.83486i	0.249217	−	0.314330i
$791$		−	1.27916i		−	0.0454817i
$792$	2.04635	+	0.228059i	0.0727138	+	0.00810372i
$793$	12.5680	−	12.5680i	0.446302	−	0.446302i
$794$	−33.8439			−1.20108
$795$	12.7407	+	26.2253i	0.451866	+	0.930116i
$796$	25.1164			0.890226
$797$	−31.3906	+	31.3906i	−1.11191	+	1.11191i	−0.119020	+	0.992892i	$0.537975\pi$
$797$	−31.3906	+	31.3906i	−1.11191	+	1.11191i	−0.992892	+	0.119020i	$0.962025\pi$
$798$	−0.733699	−	0.352784i	−0.0259727	−	0.0124884i
$799$		−	57.0661i		−	2.01885i
$800$	2.63614	−	4.24862i	0.0932016	−	0.150211i
$801$	9.07851	+	11.3559i	0.320773	+	0.401240i
$802$	11.2509	+	11.2509i	0.397283	+	0.397283i
$803$	−1.11268	−	1.11268i	−0.0392656	−	0.0392656i
$804$	2.64630	+	7.54803i	0.0933279	+	0.266199i
$805$	−13.8579	+	1.60117i	−0.488428	+	0.0564339i
$806$		−	1.34150i		−	0.0472522i
$807$	−6.58541	+	13.6960i	−0.231818	+	0.482121i
$808$	5.87660	−	5.87660i	0.206738	−	0.206738i
$809$	−44.6155			−1.56860			−0.784299	−	0.620383i	$-0.786977\pi$
$809$	−44.6155			−1.56860			−0.784299	+	0.620383i	$0.786977\pi$
$810$	15.6679	−	12.6300i	0.550514	−	0.443772i
$811$	5.86989			0.206120			0.103060	−	0.994675i	$-0.467137\pi$
$811$	5.86989			0.206120			0.103060	+	0.994675i	$0.467137\pi$
$812$	−2.45892	+	2.45892i	−0.0862912	+	0.0862912i
$813$	−23.8092	+	49.5169i	−0.835024	+	1.73663i
$814$			5.40575i			0.189471i
$815$	−6.68911	−	5.30346i	−0.234309	−	0.185772i
$816$	−2.68557	−	7.66005i	−0.0940138	−	0.268155i
$817$	2.91547	+	2.91547i	0.101999	+	0.101999i
$818$	−19.4619	−	19.4619i	−0.680470	−	0.680470i
$819$	1.64644	+	2.05945i	0.0575311	+	0.0719628i
$820$	0.575302	+	4.97916i	0.0200904	+	0.173880i
$821$		−	22.5131i		−	0.785712i	−0.919600	−	0.392856i	$-0.871487\pi$
$821$		−	22.5131i		−	0.785712i	0.919600	−	0.392856i	$-0.128513\pi$
$822$	−13.2370	−	6.36471i	−0.461692	−	0.221995i
$823$	12.9399	−	12.9399i	0.451058	−	0.451058i	−0.444647	−	0.895706i	$-0.646671\pi$
$823$	12.9399	−	12.9399i	0.451058	−	0.451058i	0.895706	+	0.444647i	$0.146671\pi$
$824$	10.0968			0.351739
$825$	−5.80302	−	1.28628i	−0.202035	−	0.0447824i
$826$	8.91915			0.310337
$827$	−15.3307	+	15.3307i	−0.533100	+	0.533100i	−0.921494	−	0.388394i	$-0.873030\pi$
$827$	−15.3307	+	15.3307i	−0.533100	+	0.533100i	0.388394	+	0.921494i	$0.373030\pi$
$828$	28.3915	+	3.16414i	0.986672	+	0.109961i
$829$			24.3562i			0.845927i	0.906147	+	0.422963i	$0.139010\pi$
$829$			24.3562i			0.845927i	−0.906147	+	0.422963i	$0.860990\pi$
$830$	2.32910	+	20.1580i	0.0808441	+	0.699695i
$831$	−14.4124	+	5.05292i	−0.499961	+	0.175284i
$832$	−0.948581	−	0.948581i	−0.0328861	−	0.0328861i
$833$	−21.7744	−	21.7744i	−0.754437	−	0.754437i
$834$	25.7360	−	9.02291i	0.891165	−	0.312438i
$835$	1.26524	+	1.00315i	0.0437856	+	0.0347154i
$836$		−	0.492395i		−	0.0170298i
$837$	−5.06377	+	1.16545i	−0.175029	+	0.0402839i
$838$	−4.18338	+	4.18338i	−0.144513	+	0.144513i
$839$	−17.8027			−0.614618			−0.307309	−	0.951610i	$-0.599428\pi$
$839$	−17.8027			−0.614618			−0.307309	+	0.951610i	$0.599428\pi$
$840$	0.829818	−	2.39789i	0.0286314	−	0.0827351i
$841$	−0.827391			−0.0285307
$842$	16.8545	−	16.8545i	0.580844	−	0.580844i
$843$	49.6973	+	23.8959i	1.71167	+	0.823018i
$844$			2.03309i			0.0699820i
$845$	24.8793	−	2.87460i	0.855874	−	0.0988893i
$846$	−28.5331	+	22.8109i	−0.980987	+	0.784256i
$847$	4.87771	+	4.87771i	0.167600	+	0.167600i
$848$	−5.32320	−	5.32320i	−0.182799	−	0.182799i
$849$	−4.75677	−	13.5677i	−0.163252	−	0.465642i
$850$	5.34348	+	22.8149i	0.183280	+	0.782544i
$851$			75.0005i			2.57099i
$852$	−4.87444	+	10.1376i	−0.166996	+	0.347308i
$853$	26.5212	−	26.5212i	0.908070	−	0.908070i	−0.0880462	−	0.996116i	$-0.528062\pi$
$853$	26.5212	−	26.5212i	0.908070	−	0.908070i	0.996116	+	0.0880462i	$0.0280623\pi$
$854$	−8.68035			−0.297036
$855$	−3.41676	−	3.38925i	−0.116851	−	0.115910i
$856$	−11.4929			−0.392818
$857$	27.2041	−	27.2041i	0.929274	−	0.929274i	−0.0683847	−	0.997659i	$-0.521785\pi$
$857$	27.2041	−	27.2041i	0.929274	−	0.929274i	0.997659	+	0.0683847i	$0.0217845\pi$
$858$	−0.691060	+	1.43723i	−0.0235924	+	0.0490661i
$859$			56.2682i			1.91985i	0.280263	+	0.959923i	$0.409578\pi$
$859$			56.2682i			1.91985i	−0.280263	+	0.959923i	$0.590422\pi$
$860$	−7.98392	+	10.0699i	−0.272249	+	0.343380i
$861$	0.841569	+	2.40040i	0.0286806	+	0.0818055i
$862$	−9.25219	−	9.25219i	−0.315131	−	0.315131i
$863$	−6.47041	−	6.47041i	−0.220255	−	0.220255i	0.588351	−	0.808606i	$-0.299777\pi$
$863$	−6.47041	−	6.47041i	−0.220255	−	0.220255i	−0.808606	+	0.588351i	$0.799777\pi$
$864$	−2.75652	+	4.40472i	−0.0937788	+	0.149852i
$865$	−0.291114	+	0.367173i	−0.00989816	+	0.0124843i
$866$		−	20.8761i		−	0.709400i
$867$	7.74693	+	3.72495i	0.263099	+	0.126506i
$868$	−0.463267	+	0.463267i	−0.0157243	+	0.0157243i
$869$	3.46068			0.117396
$870$	−18.4904	+	8.98295i	−0.626884	+	0.304551i
$871$	−6.19493			−0.209907
$872$	8.34843	−	8.34843i	0.282714	−	0.282714i
$873$	−5.20410	+	46.6958i	−0.176132	+	1.58041i
$874$		−	6.83159i		−	0.231082i
$875$	−3.12197	+	6.62626i	−0.105542	+	0.224009i
$876$	3.74743	−	1.31383i	0.126614	−	0.0443902i
$877$	1.30751	+	1.30751i	0.0441516	+	0.0441516i	0.728838	−	0.684686i	$-0.240061\pi$
$877$	1.30751	+	1.30751i	0.0441516	+	0.0441516i	−0.684686	+	0.728838i	$0.740061\pi$
$878$	0.808712	+	0.808712i	0.0272927	+	0.0272927i
$879$	−15.1573	+	5.31408i	−0.511243	+	0.179239i
$880$	1.52456	−	0.176150i	0.0513928	−	0.00593802i
$881$		−	26.4643i		−	0.891606i	−0.895131	−	0.445803i	$-0.852918\pi$
$881$		−	26.4643i		−	0.891606i	0.895131	−	0.445803i	$-0.147082\pi$
$882$	−2.18336	+	19.5910i	−0.0735174	+	0.659664i
$883$	−27.6992	+	27.6992i	−0.932153	+	0.932153i	−0.997840	−	0.0656872i	$-0.979076\pi$
$883$	−27.6992	+	27.6992i	−0.932153	+	0.932153i	0.0656872	+	0.997840i	$0.479076\pi$
$884$	6.28686			0.211450
$885$	49.8266	+	17.2430i	1.67490	+	0.579619i
$886$	−14.2532			−0.478846
$887$	32.9104	−	32.9104i	1.10502	−	1.10502i	0.111228	−	0.993795i	$-0.464522\pi$
$887$	32.9104	−	32.9104i	1.10502	−	1.10502i	0.993795	−	0.111228i	$-0.0354783\pi$
$888$	−12.2946	−	5.91160i	−0.412580	−	0.198380i
$889$			9.01200i			0.302253i
$890$	8.49145	+	6.73245i	0.284634	+	0.225672i
$891$	6.02549	+	1.35993i	0.201861	+	0.0455595i
$892$	3.41333	+	3.41333i	0.114287	+	0.114287i
$893$	6.17723	+	6.17723i	0.206713	+	0.206713i
$894$	7.34650	+	20.9544i	0.245704	+	0.700819i
$895$	−2.59765	−	22.4823i	−0.0868298	−	0.751500i
$896$			0.655158i			0.0218873i
$897$	−9.58792	+	19.9404i	−0.320131	+	0.665790i
$898$	−2.98839	+	2.98839i	−0.0997237	+	0.0997237i
$899$	5.30779			0.177025
$900$	9.27150	−	11.7915i	0.309050	−	0.393050i
$901$	35.2803			1.17536
$902$	−1.08786	+	1.08786i	−0.0362219	+	0.0362219i
$903$	−2.82607	+	5.87749i	−0.0940456	+	0.195590i
$904$			1.95245i			0.0649374i
$905$	−2.17560	−	18.8296i	−0.0723195	−	0.625916i
$906$	5.50638	+	15.7058i	0.182937	+	0.521791i
$907$	9.28296	+	9.28296i	0.308236	+	0.308236i	0.844225	−	0.535989i	$-0.180061\pi$
$907$	9.28296	+	9.28296i	0.308236	+	0.308236i	−0.535989	+	0.844225i	$0.680061\pi$
$908$	−14.8307	−	14.8307i	−0.492173	−	0.492173i
$909$	19.4740	−	15.5686i	0.645913	−	0.516379i
$910$	1.53997	+	1.22097i	0.0510495	+	0.0404746i
$911$		−	39.4500i		−	1.30704i	−0.756910	−	0.653519i	$-0.773292\pi$
$911$		−	39.4500i		−	1.30704i	0.756910	−	0.653519i	$-0.226708\pi$
$912$	1.11988	+	0.538471i	0.0370830	+	0.0178306i
$913$	−4.40419	+	4.40419i	−0.145757	+	0.145757i
$914$	−18.2743			−0.604460
$915$	−48.4925	−	16.7814i	−1.60311	−	0.554775i
$916$	8.52563			0.281695
$917$	−4.88443	+	4.88443i	−0.161298	+	0.161298i
$918$	−5.46184	−	23.7311i	−0.180268	−	0.783243i
$919$			14.1821i			0.467825i	0.972258	+	0.233913i	$0.0751530\pi$
$919$			14.1821i			0.467825i	−0.972258	+	0.233913i	$0.924847\pi$
$920$	21.1521	−	2.44395i	0.697363	−	0.0805746i
$921$	26.6525	−	9.34422i	0.878228	−	0.307902i
$922$	11.9861	+	11.9861i	0.394742	+	0.394742i
$923$	−6.16044	−	6.16044i	−0.202773	−	0.202773i
$924$	0.734973	−	0.257678i	0.0241788	−	0.00847698i
$925$	33.4630	+	20.7628i	1.10026	+	0.682676i
$926$		−	3.81529i		−	0.125378i
$927$	30.1041	+	3.35500i	0.988747	+	0.110193i
$928$	3.75317	−	3.75317i	0.123204	−	0.123204i
$929$	36.6614			1.20282			0.601411	−	0.798940i	$-0.294606\pi$
$929$	36.6614			1.20282			0.601411	+	0.798940i	$0.294606\pi$
$930$	−3.48364	+	1.69241i	−0.114233	+	0.0554963i
$931$	4.71401			0.154496
$932$	−3.54971	+	3.54971i	−0.116275	+	0.116275i
$933$	1.85638	+	0.892601i	0.0607751	+	0.0292224i
$934$			5.14244i			0.168266i
$935$	−4.46838	+	5.63585i	−0.146132	+	0.184312i
$936$	−2.51304	−	3.14343i	−0.0821412	−	0.102746i
$937$	23.7672	+	23.7672i	0.776442	+	0.776442i	0.979224	−	0.202782i	$-0.0649984\pi$
$937$	23.7672	+	23.7672i	0.776442	+	0.776442i	−0.202782	+	0.979224i	$0.564998\pi$
$938$	2.13933	+	2.13933i	0.0698517	+	0.0698517i
$939$	3.22044	+	9.18564i	0.105095	+	0.299762i
$940$	−16.9161	+	21.3359i	−0.551744	+	0.695899i
$941$		−	3.60473i		−	0.117511i	−0.998272	−	0.0587555i	$-0.981287\pi$
$941$		−	3.60473i		−	0.117511i	0.998272	−	0.0587555i	$-0.0187132\pi$
$942$	−9.53528	+	19.8309i	−0.310676	+	0.646126i
$943$	−15.0933	+	15.0933i	−0.491504	+	0.491504i
$944$	−13.6137			−0.443089
$945$	3.27091	−	6.87368i	0.106403	−	0.223601i
$946$	−3.94445			−0.128245
$947$	−1.26244	+	1.26244i	−0.0410238	+	0.0410238i	−0.727321	−	0.686297i	$-0.759235\pi$
$947$	−1.26244	+	1.26244i	−0.0410238	+	0.0410238i	0.686297	+	0.727321i	$0.259235\pi$
$948$	−3.78452	+	7.87083i	−0.122916	+	0.255633i
$949$			3.07564i			0.0998396i
$950$	−3.04805	−	1.89122i	−0.0988920	−	0.0613594i
$951$	9.59800	+	27.3763i	0.311237	+	0.887738i
$952$	−2.17108	−	2.17108i	−0.0703651	−	0.0703651i
$953$	16.6023	+	16.6023i	0.537801	+	0.537801i	0.922883	−	0.385081i	$-0.125827\pi$
$953$	16.6023	+	16.6023i	0.537801	+	0.537801i	−0.385081	+	0.922883i	$0.625827\pi$
$954$	−14.1025	−	17.6401i	−0.456586	−	0.571120i
$955$	−39.8991	+	4.61002i	−1.29110	+	0.149177i
$956$			28.3403i			0.916592i
$957$	−5.68655	−	2.73426i	−0.183820	−	0.0883860i
$958$	−15.7284	+	15.7284i	−0.508160	+	0.508160i
$959$	−5.55568			−0.179402
$960$	−1.26659	+	3.66002i	−0.0408791	+	0.118127i
$961$	1.00000			0.0322581
$962$	7.47122	−	7.47122i	0.240882	−	0.240882i
$963$	−34.2664	−	3.81888i	−1.10422	−	0.123062i
$964$			11.4414i			0.368503i
$965$	−8.98080	−	7.12043i	−0.289102	−	0.229215i
$966$	10.1972	−	3.57508i	0.328089	−	0.115026i
$967$	−31.0614	−	31.0614i	−0.998869	−	0.998869i	0.00113086	−	0.999999i	$-0.499640\pi$
$967$	−31.0614	−	31.0614i	−0.998869	−	0.998869i	−0.999999	+	0.00113086i	$0.999640\pi$
$968$	−7.44508	−	7.44508i	−0.239294	−	0.239294i
$969$	−5.49549	+	1.92669i	−0.176540	+	0.0618942i
$970$	4.01959	+	34.7890i	0.129061	+	1.11701i
$971$			46.0432i			1.47760i	0.673927	+	0.738798i	$0.264606\pi$
$971$			46.0432i			1.47760i	−0.673927	+	0.738798i	$0.735394\pi$
$972$	−9.68230	+	12.2169i	−0.310560	+	0.391858i
$973$	7.29433	−	7.29433i	0.233845	−	0.233845i
$974$	15.9926			0.512435
$975$	6.24254	+	9.79804i	0.199921	+	0.313789i
$976$	13.2492			0.424098
$977$	−1.17822	+	1.17822i	−0.0376947	+	0.0376947i	−0.725703	−	0.688008i	$-0.758485\pi$
$977$	−1.17822	+	1.17822i	−0.0376947	+	0.0376947i	0.688008	+	0.725703i	$0.258485\pi$
$978$	5.95921	+	2.86536i	0.190555	+	0.0916242i
$979$			3.32617i			0.106305i
$980$	1.68640	+	14.5956i	0.0538701	+	0.466239i
$981$	27.6652	−	22.1172i	0.883283	−	0.706146i
$982$	−6.88181	−	6.88181i	−0.219607	−	0.219607i
$983$	36.6630	+	36.6630i	1.16937	+	1.16937i	0.982358	+	0.187009i	$0.0598795\pi$
$983$	36.6630	+	36.6630i	1.16937	+	1.16937i	0.187009	+	0.982358i	$0.440121\pi$
$984$	−1.28453	−	3.66385i	−0.0409492	−	0.116799i
$985$	−17.0895	−	13.5494i	−0.544515	−	0.431719i
$986$			24.8747i			0.792172i
$987$	−5.98780	+	12.4531i	−0.190594	+	0.396386i
$988$	−0.680533	+	0.680533i	−0.0216507	+	0.0216507i
$989$	−54.7263			−1.74019
$990$	4.60406	−	0.0186143i	0.146327	−	0.000591603i
$991$	−7.00667			−0.222574			−0.111287	−	0.993788i	$-0.535497\pi$
$991$	−7.00667			−0.222574			−0.111287	+	0.993788i	$0.535497\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−8.21388	+	17.0828i	−0.260660	+	0.542105i
$994$			4.25484i			0.134955i
$995$	55.7907	−	6.44616i	1.76868	−	0.204357i
$996$	−5.20038	−	14.8330i	−0.164780	−	0.470002i
$997$	0.154730	+	0.154730i	0.00490034	+	0.00490034i	0.709553	−	0.704652i	$-0.248897\pi$
$997$	0.154730	+	0.154730i	0.00490034	+	0.00490034i	−0.704652	+	0.709553i	$0.748897\pi$
$998$	−18.1628	−	18.1628i	−0.574935	−	0.574935i
$999$	−34.6925	−	21.7110i	−1.09762	−	0.686904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.14	yes	40
3.2	odd	2	inner	930.2.j.h.497.2	✓	40
5.3	odd	4	inner	930.2.j.h.683.2	yes	40
15.8	even	4	inner	930.2.j.h.683.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.2	✓	40	3.2	odd	2	inner
930.2.j.h.497.14	yes	40	1.1	even	1	trivial
930.2.j.h.683.2	yes	40	5.3	odd	4	inner
930.2.j.h.683.14	yes	40	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.750564 + 1.56098i) q^{3} -1.00000i q^{4} +(-0.256652 - 2.22129i) q^{5} +(0.573050 + 1.63451i) q^{6} +(0.463267 + 0.463267i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.87331 - 2.34323i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.750564 + 1.56098i) q^{3} -1.00000i q^{4} +(-0.256652 - 2.22129i) q^{5} +(0.573050 + 1.63451i) q^{6} +(0.463267 + 0.463267i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.87331 - 2.34323i) q^{9} +(-1.75217 - 1.38921i) q^{10} -0.686339i q^{11} +(1.56098 + 0.750564i) q^{12} +(-0.948581 + 0.948581i) q^{13} +0.655158 q^{14} +(3.66002 + 1.26659i) q^{15} -1.00000 q^{16} +(3.31382 - 3.31382i) q^{17} +(-2.98154 - 0.332283i) q^{18} +0.717422i q^{19} +(-2.22129 + 0.256652i) q^{20} +(-1.07086 + 0.375438i) q^{21} +(-0.485315 - 0.485315i) q^{22} +(-6.73337 - 6.73337i) q^{23} +(1.63451 - 0.573050i) q^{24} +(-4.86826 + 1.14020i) q^{25} +1.34150i q^{26} +(5.06377 - 1.16545i) q^{27} +(0.463267 - 0.463267i) q^{28} -5.30779 q^{29} +(3.48364 - 1.69241i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.07136 + 0.515141i) q^{33} -4.68646i q^{34} +(0.910151 - 1.14795i) q^{35} +(-2.34323 + 1.87331i) q^{36} +(-5.56932 - 5.56932i) q^{37} +(0.507294 + 0.507294i) q^{38} +(-0.768745 - 2.19269i) q^{39} +(-1.38921 + 1.75217i) q^{40} -2.24156i q^{41} +(-0.491738 + 1.02269i) q^{42} +(4.06381 - 4.06381i) q^{43} -0.686339 q^{44} +(-4.72420 + 4.76256i) q^{45} -9.52242 q^{46} +(8.61031 - 8.61031i) q^{47} +(0.750564 - 1.56098i) q^{48} -6.57077i q^{49} +(-2.63614 + 4.24862i) q^{50} +(2.68557 + 7.66005i) q^{51} +(0.948581 + 0.948581i) q^{52} +(5.32320 + 5.32320i) q^{53} +(2.75652 - 4.40472i) q^{54} +(-1.52456 + 0.176150i) q^{55} -0.655158i q^{56} +(-1.11988 - 0.538471i) q^{57} +(-3.75317 + 3.75317i) q^{58} +13.6137 q^{59} +(1.26659 - 3.66002i) q^{60} -13.2492 q^{61} +(-0.707107 + 0.707107i) q^{62} +(0.217698 - 1.95338i) q^{63} +1.00000i q^{64} +(2.35053 + 1.86362i) q^{65} +(1.12183 - 0.393306i) q^{66} +(3.26537 + 3.26537i) q^{67} +(-3.31382 - 3.31382i) q^{68} +(15.5645 - 5.45682i) q^{69} +(-0.168148 - 1.45530i) q^{70} +6.49437i q^{71} +(-0.332283 + 2.98154i) q^{72} +(1.62118 - 1.62118i) q^{73} -7.87621 q^{74} +(1.87412 - 8.45504i) q^{75} +0.717422 q^{76} +(0.317958 - 0.317958i) q^{77} +(-2.09405 - 1.00688i) q^{78} +5.04224i q^{79} +(0.256652 + 2.22129i) q^{80} +(-1.98143 + 8.77918i) q^{81} +(-1.58502 - 1.58502i) q^{82} +(-6.41694 - 6.41694i) q^{83} +(0.375438 + 1.07086i) q^{84} +(-8.21147 - 6.51047i) q^{85} -5.74710i q^{86} +(3.98383 - 8.28534i) q^{87} +(-0.485315 + 0.485315i) q^{88} -4.84625 q^{89} +(0.0271212 + 6.70815i) q^{90} -0.878892 q^{91} +(-6.73337 + 6.73337i) q^{92} +(0.750564 - 1.56098i) q^{93} -12.1768i q^{94} +(1.59360 - 0.184128i) q^{95} +(-0.573050 - 1.63451i) q^{96} +(-11.0744 - 11.0744i) q^{97} +(-4.64623 - 4.64623i) q^{98} +(-1.60825 + 1.28572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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