# Properties

 Label 370.2.g.b.43.1 Level $370$ Weight $2$ Character 370.43 Analytic conductor $2.954$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.g (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 43.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.43 Dual form 370.2.g.b.327.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +1.00000i q^{8} +3.00000i q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +1.00000i q^{8} +3.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +4.00000i q^{13} +(2.00000 + 2.00000i) q^{14} +1.00000 q^{16} -2.00000 q^{17} +3.00000 q^{18} +(2.00000 - 2.00000i) q^{19} +(2.00000 + 1.00000i) q^{20} +4.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +(2.00000 - 2.00000i) q^{28} +(-7.00000 - 7.00000i) q^{29} +(-4.00000 + 4.00000i) q^{31} -1.00000i q^{32} +2.00000i q^{34} +(6.00000 - 2.00000i) q^{35} -3.00000i q^{36} +(-6.00000 + 1.00000i) q^{37} +(-2.00000 - 2.00000i) q^{38} +(1.00000 - 2.00000i) q^{40} +4.00000i q^{43} +(3.00000 - 6.00000i) q^{45} +4.00000 q^{46} +(-2.00000 + 2.00000i) q^{47} -1.00000i q^{49} +(4.00000 - 3.00000i) q^{50} -4.00000i q^{52} +(-1.00000 - 1.00000i) q^{53} +(-2.00000 - 2.00000i) q^{56} +(-7.00000 + 7.00000i) q^{58} +(2.00000 - 2.00000i) q^{59} +(1.00000 - 1.00000i) q^{61} +(4.00000 + 4.00000i) q^{62} +(-6.00000 - 6.00000i) q^{63} -1.00000 q^{64} +(4.00000 - 8.00000i) q^{65} +2.00000 q^{68} +(-2.00000 - 6.00000i) q^{70} +12.0000 q^{71} -3.00000 q^{72} +(-5.00000 + 5.00000i) q^{73} +(1.00000 + 6.00000i) q^{74} +(-2.00000 + 2.00000i) q^{76} +(12.0000 - 12.0000i) q^{79} +(-2.00000 - 1.00000i) q^{80} -9.00000 q^{81} +(4.00000 + 4.00000i) q^{83} +(4.00000 + 2.00000i) q^{85} +4.00000 q^{86} +(-7.00000 - 7.00000i) q^{89} +(-6.00000 - 3.00000i) q^{90} +(-8.00000 - 8.00000i) q^{91} -4.00000i q^{92} +(2.00000 + 2.00000i) q^{94} +(-6.00000 + 2.00000i) q^{95} -12.0000 q^{97} -1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{4} - 4q^{5} - 4q^{7} + O(q^{10})$$ $$2q - 2q^{4} - 4q^{5} - 4q^{7} - 2q^{10} + 4q^{14} + 2q^{16} - 4q^{17} + 6q^{18} + 4q^{19} + 4q^{20} + 6q^{25} + 8q^{26} + 4q^{28} - 14q^{29} - 8q^{31} + 12q^{35} - 12q^{37} - 4q^{38} + 2q^{40} + 6q^{45} + 8q^{46} - 4q^{47} + 8q^{50} - 2q^{53} - 4q^{56} - 14q^{58} + 4q^{59} + 2q^{61} + 8q^{62} - 12q^{63} - 2q^{64} + 8q^{65} + 4q^{68} - 4q^{70} + 24q^{71} - 6q^{72} - 10q^{73} + 2q^{74} - 4q^{76} + 24q^{79} - 4q^{80} - 18q^{81} + 8q^{83} + 8q^{85} + 8q^{86} - 14q^{89} - 12q^{90} - 16q^{91} + 4q^{94} - 12q^{95} - 24q^{97} - 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$297$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$e\left(\frac{3}{4}\right)$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ −2.00000 1.00000i −0.894427 0.447214i
$$6$$ 0 0
$$7$$ −2.00000 + 2.00000i −0.755929 + 0.755929i −0.975579 0.219650i $$-0.929509\pi$$
0.219650 + 0.975579i $$0.429509\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 3.00000i 1.00000i
$$10$$ −1.00000 + 2.00000i −0.316228 + 0.632456i
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 4.00000i 1.10940i 0.832050 + 0.554700i $$0.187167\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 2.00000 + 2.00000i 0.534522 + 0.534522i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 3.00000 0.707107
$$19$$ 2.00000 2.00000i 0.458831 0.458831i −0.439440 0.898272i $$-0.644823\pi$$
0.898272 + 0.439440i $$0.144823\pi$$
$$20$$ 2.00000 + 1.00000i 0.447214 + 0.223607i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 4.00000i 0.834058i 0.908893 + 0.417029i $$0.136929\pi$$
−0.908893 + 0.417029i $$0.863071\pi$$
$$24$$ 0 0
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ 4.00000 0.784465
$$27$$ 0 0
$$28$$ 2.00000 2.00000i 0.377964 0.377964i
$$29$$ −7.00000 7.00000i −1.29987 1.29987i −0.928477 0.371391i $$-0.878881\pi$$
−0.371391 0.928477i $$-0.621119\pi$$
$$30$$ 0 0
$$31$$ −4.00000 + 4.00000i −0.718421 + 0.718421i −0.968282 0.249861i $$-0.919615\pi$$
0.249861 + 0.968282i $$0.419615\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 2.00000i 0.342997i
$$35$$ 6.00000 2.00000i 1.01419 0.338062i
$$36$$ 3.00000i 0.500000i
$$37$$ −6.00000 + 1.00000i −0.986394 + 0.164399i
$$38$$ −2.00000 2.00000i −0.324443 0.324443i
$$39$$ 0 0
$$40$$ 1.00000 2.00000i 0.158114 0.316228i
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 0 0
$$45$$ 3.00000 6.00000i 0.447214 0.894427i
$$46$$ 4.00000 0.589768
$$47$$ −2.00000 + 2.00000i −0.291730 + 0.291730i −0.837763 0.546033i $$-0.816137\pi$$
0.546033 + 0.837763i $$0.316137\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 0.142857i
$$50$$ 4.00000 3.00000i 0.565685 0.424264i
$$51$$ 0 0
$$52$$ 4.00000i 0.554700i
$$53$$ −1.00000 1.00000i −0.137361 0.137361i 0.635083 0.772444i $$-0.280966\pi$$
−0.772444 + 0.635083i $$0.780966\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −2.00000 2.00000i −0.267261 0.267261i
$$57$$ 0 0
$$58$$ −7.00000 + 7.00000i −0.919145 + 0.919145i
$$59$$ 2.00000 2.00000i 0.260378 0.260378i −0.564830 0.825208i $$-0.691058\pi$$
0.825208 + 0.564830i $$0.191058\pi$$
$$60$$ 0 0
$$61$$ 1.00000 1.00000i 0.128037 0.128037i −0.640184 0.768221i $$-0.721142\pi$$
0.768221 + 0.640184i $$0.221142\pi$$
$$62$$ 4.00000 + 4.00000i 0.508001 + 0.508001i
$$63$$ −6.00000 6.00000i −0.755929 0.755929i
$$64$$ −1.00000 −0.125000
$$65$$ 4.00000 8.00000i 0.496139 0.992278i
$$66$$ 0 0
$$67$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$68$$ 2.00000 0.242536
$$69$$ 0 0
$$70$$ −2.00000 6.00000i −0.239046 0.717137i
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ −3.00000 −0.353553
$$73$$ −5.00000 + 5.00000i −0.585206 + 0.585206i −0.936329 0.351123i $$-0.885800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 1.00000 + 6.00000i 0.116248 + 0.697486i
$$75$$ 0 0
$$76$$ −2.00000 + 2.00000i −0.229416 + 0.229416i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 12.0000 12.0000i 1.35011 1.35011i 0.464568 0.885537i $$-0.346210\pi$$
0.885537 0.464568i $$-0.153790\pi$$
$$80$$ −2.00000 1.00000i −0.223607 0.111803i
$$81$$ −9.00000 −1.00000
$$82$$ 0 0
$$83$$ 4.00000 + 4.00000i 0.439057 + 0.439057i 0.891695 0.452638i $$-0.149517\pi$$
−0.452638 + 0.891695i $$0.649517\pi$$
$$84$$ 0 0
$$85$$ 4.00000 + 2.00000i 0.433861 + 0.216930i
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −7.00000 7.00000i −0.741999 0.741999i 0.230964 0.972962i $$-0.425812\pi$$
−0.972962 + 0.230964i $$0.925812\pi$$
$$90$$ −6.00000 3.00000i −0.632456 0.316228i
$$91$$ −8.00000 8.00000i −0.838628 0.838628i
$$92$$ 4.00000i 0.417029i
$$93$$ 0 0
$$94$$ 2.00000 + 2.00000i 0.206284 + 0.206284i
$$95$$ −6.00000 + 2.00000i −0.615587 + 0.205196i
$$96$$ 0 0
$$97$$ −12.0000 −1.21842 −0.609208 0.793011i $$-0.708512\pi$$
−0.609208 + 0.793011i $$0.708512\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ −3.00000 4.00000i −0.300000 0.400000i
$$101$$ 10.0000i 0.995037i 0.867453 + 0.497519i $$0.165755\pi$$
−0.867453 + 0.497519i $$0.834245\pi$$
$$102$$ 0 0
$$103$$ −16.0000 −1.57653 −0.788263 0.615338i $$-0.789020\pi$$
−0.788263 + 0.615338i $$0.789020\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ 0 0
$$106$$ −1.00000 + 1.00000i −0.0971286 + 0.0971286i
$$107$$ 8.00000 8.00000i 0.773389 0.773389i −0.205308 0.978697i $$-0.565820\pi$$
0.978697 + 0.205308i $$0.0658197\pi$$
$$108$$ 0 0
$$109$$ −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i $$-0.815129\pi$$
0.548683 + 0.836031i $$0.315129\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.00000 + 2.00000i −0.188982 + 0.188982i
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 4.00000 8.00000i 0.373002 0.746004i
$$116$$ 7.00000 + 7.00000i 0.649934 + 0.649934i
$$117$$ −12.0000 −1.10940
$$118$$ −2.00000 2.00000i −0.184115 0.184115i
$$119$$ 4.00000 4.00000i 0.366679 0.366679i
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ −1.00000 1.00000i −0.0905357 0.0905357i
$$123$$ 0 0
$$124$$ 4.00000 4.00000i 0.359211 0.359211i
$$125$$ −2.00000 11.0000i −0.178885 0.983870i
$$126$$ −6.00000 + 6.00000i −0.534522 + 0.534522i
$$127$$ −2.00000 + 2.00000i −0.177471 + 0.177471i −0.790253 0.612781i $$-0.790051\pi$$
0.612781 + 0.790253i $$0.290051\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ −8.00000 4.00000i −0.701646 0.350823i
$$131$$ 6.00000 6.00000i 0.524222 0.524222i −0.394621 0.918844i $$-0.629124\pi$$
0.918844 + 0.394621i $$0.129124\pi$$
$$132$$ 0 0
$$133$$ 8.00000i 0.693688i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 2.00000i 0.171499i
$$137$$ −7.00000 + 7.00000i −0.598050 + 0.598050i −0.939793 0.341743i $$-0.888983\pi$$
0.341743 + 0.939793i $$0.388983\pi$$
$$138$$ 0 0
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ −6.00000 + 2.00000i −0.507093 + 0.169031i
$$141$$ 0 0
$$142$$ 12.0000i 1.00702i
$$143$$ 0 0
$$144$$ 3.00000i 0.250000i
$$145$$ 7.00000 + 21.0000i 0.581318 + 1.74396i
$$146$$ 5.00000 + 5.00000i 0.413803 + 0.413803i
$$147$$ 0 0
$$148$$ 6.00000 1.00000i 0.493197 0.0821995i
$$149$$ 6.00000i 0.491539i 0.969328 + 0.245770i $$0.0790407\pi$$
−0.969328 + 0.245770i $$0.920959\pi$$
$$150$$ 0 0
$$151$$ 20.0000i 1.62758i 0.581161 + 0.813788i $$0.302599\pi$$
−0.581161 + 0.813788i $$0.697401\pi$$
$$152$$ 2.00000 + 2.00000i 0.162221 + 0.162221i
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 12.0000 4.00000i 0.963863 0.321288i
$$156$$ 0 0
$$157$$ −7.00000 + 7.00000i −0.558661 + 0.558661i −0.928926 0.370265i $$-0.879267\pi$$
0.370265 + 0.928926i $$0.379267\pi$$
$$158$$ −12.0000 12.0000i −0.954669 0.954669i
$$159$$ 0 0
$$160$$ −1.00000 + 2.00000i −0.0790569 + 0.158114i
$$161$$ −8.00000 8.00000i −0.630488 0.630488i
$$162$$ 9.00000i 0.707107i
$$163$$ 24.0000 1.87983 0.939913 0.341415i $$-0.110906\pi$$
0.939913 + 0.341415i $$0.110906\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 4.00000 4.00000i 0.310460 0.310460i
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ −3.00000 −0.230769
$$170$$ 2.00000 4.00000i 0.153393 0.306786i
$$171$$ 6.00000 + 6.00000i 0.458831 + 0.458831i
$$172$$ 4.00000i 0.304997i
$$173$$ 5.00000 5.00000i 0.380143 0.380143i −0.491011 0.871154i $$-0.663372\pi$$
0.871154 + 0.491011i $$0.163372\pi$$
$$174$$ 0 0
$$175$$ −14.0000 2.00000i −1.05830 0.151186i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −7.00000 + 7.00000i −0.524672 + 0.524672i
$$179$$ −2.00000 2.00000i −0.149487 0.149487i 0.628402 0.777889i $$-0.283709\pi$$
−0.777889 + 0.628402i $$0.783709\pi$$
$$180$$ −3.00000 + 6.00000i −0.223607 + 0.447214i
$$181$$ −8.00000 −0.594635 −0.297318 0.954779i $$-0.596092\pi$$
−0.297318 + 0.954779i $$0.596092\pi$$
$$182$$ −8.00000 + 8.00000i −0.592999 + 0.592999i
$$183$$ 0 0
$$184$$ −4.00000 −0.294884
$$185$$ 13.0000 + 4.00000i 0.955779 + 0.294086i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 2.00000 2.00000i 0.145865 0.145865i
$$189$$ 0 0
$$190$$ 2.00000 + 6.00000i 0.145095 + 0.435286i
$$191$$ 16.0000 + 16.0000i 1.15772 + 1.15772i 0.984965 + 0.172754i $$0.0552667\pi$$
0.172754 + 0.984965i $$0.444733\pi$$
$$192$$ 0 0
$$193$$ 14.0000i 1.00774i 0.863779 + 0.503871i $$0.168091\pi$$
−0.863779 + 0.503871i $$0.831909\pi$$
$$194$$ 12.0000i 0.861550i
$$195$$ 0 0
$$196$$ 1.00000i 0.0714286i
$$197$$ 3.00000 3.00000i 0.213741 0.213741i −0.592113 0.805855i $$-0.701706\pi$$
0.805855 + 0.592113i $$0.201706\pi$$
$$198$$ 0 0
$$199$$ 8.00000 + 8.00000i 0.567105 + 0.567105i 0.931316 0.364211i $$-0.118661\pi$$
−0.364211 + 0.931316i $$0.618661\pi$$
$$200$$ −4.00000 + 3.00000i −0.282843 + 0.212132i
$$201$$ 0 0
$$202$$ 10.0000 0.703598
$$203$$ 28.0000 1.96521
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 16.0000i 1.11477i
$$207$$ −12.0000 −0.834058
$$208$$ 4.00000i 0.277350i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 1.00000 + 1.00000i 0.0686803 + 0.0686803i
$$213$$ 0 0
$$214$$ −8.00000 8.00000i −0.546869 0.546869i
$$215$$ 4.00000 8.00000i 0.272798 0.545595i
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 3.00000 + 3.00000i 0.203186 + 0.203186i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 8.00000i 0.538138i
$$222$$ 0 0
$$223$$ −6.00000 6.00000i −0.401790 0.401790i 0.477074 0.878863i $$-0.341698\pi$$
−0.878863 + 0.477074i $$0.841698\pi$$
$$224$$ 2.00000 + 2.00000i 0.133631 + 0.133631i
$$225$$ −12.0000 + 9.00000i −0.800000 + 0.600000i
$$226$$ 14.0000i 0.931266i
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ 16.0000i 1.05731i 0.848837 + 0.528655i $$0.177303\pi$$
−0.848837 + 0.528655i $$0.822697\pi$$
$$230$$ −8.00000 4.00000i −0.527504 0.263752i
$$231$$ 0 0
$$232$$ 7.00000 7.00000i 0.459573 0.459573i
$$233$$ −5.00000 + 5.00000i −0.327561 + 0.327561i −0.851658 0.524097i $$-0.824403\pi$$
0.524097 + 0.851658i $$0.324403\pi$$
$$234$$ 12.0000i 0.784465i
$$235$$ 6.00000 2.00000i 0.391397 0.130466i
$$236$$ −2.00000 + 2.00000i −0.130189 + 0.130189i
$$237$$ 0 0
$$238$$ −4.00000 4.00000i −0.259281 0.259281i
$$239$$ −8.00000 + 8.00000i −0.517477 + 0.517477i −0.916807 0.399330i $$-0.869243\pi$$
0.399330 + 0.916807i $$0.369243\pi$$
$$240$$ 0 0
$$241$$ −19.0000 19.0000i −1.22390 1.22390i −0.966235 0.257663i $$-0.917048\pi$$
−0.257663 0.966235i $$-0.582952\pi$$
$$242$$ 11.0000i 0.707107i
$$243$$ 0 0
$$244$$ −1.00000 + 1.00000i −0.0640184 + 0.0640184i
$$245$$ −1.00000 + 2.00000i −0.0638877 + 0.127775i
$$246$$ 0 0
$$247$$ 8.00000 + 8.00000i 0.509028 + 0.509028i
$$248$$ −4.00000 4.00000i −0.254000 0.254000i
$$249$$ 0 0
$$250$$ −11.0000 + 2.00000i −0.695701 + 0.126491i
$$251$$ −14.0000 + 14.0000i −0.883672 + 0.883672i −0.993906 0.110234i $$-0.964840\pi$$
0.110234 + 0.993906i $$0.464840\pi$$
$$252$$ 6.00000 + 6.00000i 0.377964 + 0.377964i
$$253$$ 0 0
$$254$$ 2.00000 + 2.00000i 0.125491 + 0.125491i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 10.0000 14.0000i 0.621370 0.869918i
$$260$$ −4.00000 + 8.00000i −0.248069 + 0.496139i
$$261$$ 21.0000 21.0000i 1.29987 1.29987i
$$262$$ −6.00000 6.00000i −0.370681 0.370681i
$$263$$ −10.0000 + 10.0000i −0.616626 + 0.616626i −0.944664 0.328038i $$-0.893613\pi$$
0.328038 + 0.944664i $$0.393613\pi$$
$$264$$ 0 0
$$265$$ 1.00000 + 3.00000i 0.0614295 + 0.184289i
$$266$$ 8.00000 0.490511
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 14.0000i 0.853595i −0.904347 0.426798i $$-0.859642\pi$$
0.904347 0.426798i $$-0.140358\pi$$
$$270$$ 0 0
$$271$$ −28.0000 −1.70088 −0.850439 0.526073i $$-0.823664\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 7.00000 + 7.00000i 0.422885 + 0.422885i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 12.0000i 0.721010i 0.932757 + 0.360505i $$0.117396\pi$$
−0.932757 + 0.360505i $$0.882604\pi$$
$$278$$ 20.0000i 1.19952i
$$279$$ −12.0000 12.0000i −0.718421 0.718421i
$$280$$ 2.00000 + 6.00000i 0.119523 + 0.358569i
$$281$$ 1.00000 + 1.00000i 0.0596550 + 0.0596550i 0.736305 0.676650i $$-0.236569\pi$$
−0.676650 + 0.736305i $$0.736569\pi$$
$$282$$ 0 0
$$283$$ 24.0000 1.42665 0.713326 0.700832i $$-0.247188\pi$$
0.713326 + 0.700832i $$0.247188\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 3.00000 0.176777
$$289$$ −13.0000 −0.764706
$$290$$ 21.0000 7.00000i 1.23316 0.411054i
$$291$$ 0 0
$$292$$ 5.00000 5.00000i 0.292603 0.292603i
$$293$$ 9.00000 + 9.00000i 0.525786 + 0.525786i 0.919313 0.393527i $$-0.128745\pi$$
−0.393527 + 0.919313i $$0.628745\pi$$
$$294$$ 0 0
$$295$$ −6.00000 + 2.00000i −0.349334 + 0.116445i
$$296$$ −1.00000 6.00000i −0.0581238 0.348743i
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ −16.0000 −0.925304
$$300$$ 0 0
$$301$$ −8.00000 8.00000i −0.461112 0.461112i
$$302$$ 20.0000 1.15087
$$303$$ 0 0
$$304$$ 2.00000 2.00000i 0.114708 0.114708i
$$305$$ −3.00000 + 1.00000i −0.171780 + 0.0572598i
$$306$$ −6.00000 −0.342997
$$307$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −4.00000 12.0000i −0.227185 0.681554i
$$311$$ −4.00000 + 4.00000i −0.226819 + 0.226819i −0.811363 0.584543i $$-0.801274\pi$$
0.584543 + 0.811363i $$0.301274\pi$$
$$312$$ 0 0
$$313$$ 26.0000i 1.46961i −0.678280 0.734803i $$-0.737274\pi$$
0.678280 0.734803i $$-0.262726\pi$$
$$314$$ 7.00000 + 7.00000i 0.395033 + 0.395033i
$$315$$ 6.00000 + 18.0000i 0.338062 + 1.01419i
$$316$$ −12.0000 + 12.0000i −0.675053 + 0.675053i
$$317$$ −5.00000 5.00000i −0.280828 0.280828i 0.552611 0.833439i $$-0.313631\pi$$
−0.833439 + 0.552611i $$0.813631\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 2.00000 + 1.00000i 0.111803 + 0.0559017i
$$321$$ 0 0
$$322$$ −8.00000 + 8.00000i −0.445823 + 0.445823i
$$323$$ −4.00000 + 4.00000i −0.222566 + 0.222566i
$$324$$ 9.00000 0.500000
$$325$$ −16.0000 + 12.0000i −0.887520 + 0.665640i
$$326$$ 24.0000i 1.32924i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 8.00000i 0.441054i
$$330$$ 0 0
$$331$$ 6.00000 + 6.00000i 0.329790 + 0.329790i 0.852506 0.522717i $$-0.175081\pi$$
−0.522717 + 0.852506i $$0.675081\pi$$
$$332$$ −4.00000 4.00000i −0.219529 0.219529i
$$333$$ −3.00000 18.0000i −0.164399 0.986394i
$$334$$ 8.00000i 0.437741i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 15.0000 + 15.0000i 0.817102 + 0.817102i 0.985687 0.168585i $$-0.0539198\pi$$
−0.168585 + 0.985687i $$0.553920\pi$$
$$338$$ 3.00000i 0.163178i
$$339$$ 0 0
$$340$$ −4.00000 2.00000i −0.216930 0.108465i
$$341$$ 0 0
$$342$$ 6.00000 6.00000i 0.324443 0.324443i
$$343$$ −12.0000 12.0000i −0.647939 0.647939i
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ −5.00000 5.00000i −0.268802 0.268802i
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 0 0
$$349$$ 14.0000i 0.749403i −0.927146 0.374701i $$-0.877745\pi$$
0.927146 0.374701i $$-0.122255\pi$$
$$350$$ −2.00000 + 14.0000i −0.106904 + 0.748331i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −36.0000 −1.91609 −0.958043 0.286623i $$-0.907467\pi$$
−0.958043 + 0.286623i $$0.907467\pi$$
$$354$$ 0 0
$$355$$ −24.0000 12.0000i −1.27379 0.636894i
$$356$$ 7.00000 + 7.00000i 0.370999 + 0.370999i
$$357$$ 0 0
$$358$$ −2.00000 + 2.00000i −0.105703 + 0.105703i
$$359$$ 24.0000i 1.26667i −0.773877 0.633336i $$-0.781685\pi$$
0.773877 0.633336i $$-0.218315\pi$$
$$360$$ 6.00000 + 3.00000i 0.316228 + 0.158114i
$$361$$ 11.0000i 0.578947i
$$362$$ 8.00000i 0.420471i
$$363$$ 0 0
$$364$$ 8.00000 + 8.00000i 0.419314 + 0.419314i
$$365$$ 15.0000 5.00000i 0.785136 0.261712i
$$366$$ 0 0
$$367$$ 18.0000 18.0000i 0.939592 0.939592i −0.0586842 0.998277i $$-0.518691\pi$$
0.998277 + 0.0586842i $$0.0186905\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ 0 0
$$370$$ 4.00000 13.0000i 0.207950 0.675838i
$$371$$ 4.00000 0.207670
$$372$$ 0 0
$$373$$ −25.0000 + 25.0000i −1.29445 + 1.29445i −0.362446 + 0.932005i $$0.618058\pi$$
−0.932005 + 0.362446i $$0.881942\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −2.00000 2.00000i −0.103142 0.103142i
$$377$$ 28.0000 28.0000i 1.44207 1.44207i
$$378$$ 0 0
$$379$$ 4.00000i 0.205466i −0.994709 0.102733i $$-0.967241\pi$$
0.994709 0.102733i $$-0.0327588\pi$$
$$380$$ 6.00000 2.00000i 0.307794 0.102598i
$$381$$ 0 0
$$382$$ 16.0000 16.0000i 0.818631 0.818631i
$$383$$ 36.0000i 1.83951i −0.392488 0.919757i $$-0.628386\pi$$
0.392488 0.919757i $$-0.371614\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 14.0000 0.712581
$$387$$ −12.0000 −0.609994
$$388$$ 12.0000 0.609208
$$389$$ 17.0000 17.0000i 0.861934 0.861934i −0.129628 0.991563i $$-0.541378\pi$$
0.991563 + 0.129628i $$0.0413785\pi$$
$$390$$ 0 0
$$391$$ 8.00000i 0.404577i
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ −3.00000 3.00000i −0.151138 0.151138i
$$395$$ −36.0000 + 12.0000i −1.81136 + 0.603786i
$$396$$ 0 0
$$397$$ 25.0000 + 25.0000i 1.25471 + 1.25471i 0.953583 + 0.301131i $$0.0973643\pi$$
0.301131 + 0.953583i $$0.402636\pi$$
$$398$$ 8.00000 8.00000i 0.401004 0.401004i
$$399$$ 0 0
$$400$$ 3.00000 + 4.00000i 0.150000 + 0.200000i
$$401$$ 1.00000 1.00000i 0.0499376 0.0499376i −0.681697 0.731635i $$-0.738758\pi$$
0.731635 + 0.681697i $$0.238758\pi$$
$$402$$ 0 0
$$403$$ −16.0000 16.0000i −0.797017 0.797017i
$$404$$ 10.0000i 0.497519i
$$405$$ 18.0000 + 9.00000i 0.894427 + 0.447214i
$$406$$ 28.0000i 1.38962i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 13.0000 + 13.0000i 0.642809 + 0.642809i 0.951245 0.308436i $$-0.0998057\pi$$
−0.308436 + 0.951245i $$0.599806\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 16.0000 0.788263
$$413$$ 8.00000i 0.393654i
$$414$$ 12.0000i 0.589768i
$$415$$ −4.00000 12.0000i −0.196352 0.589057i
$$416$$ 4.00000 0.196116
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 36.0000i 1.75872i 0.476162 + 0.879358i $$0.342028\pi$$
−0.476162 + 0.879358i $$0.657972\pi$$
$$420$$ 0 0
$$421$$ 11.0000 11.0000i 0.536107 0.536107i −0.386276 0.922383i $$-0.626239\pi$$
0.922383 + 0.386276i $$0.126239\pi$$
$$422$$ 8.00000i 0.389434i
$$423$$ −6.00000 6.00000i −0.291730 0.291730i
$$424$$ 1.00000 1.00000i 0.0485643 0.0485643i
$$425$$ −6.00000 8.00000i −0.291043 0.388057i
$$426$$ 0 0
$$427$$ 4.00000i 0.193574i
$$428$$ −8.00000 + 8.00000i −0.386695 + 0.386695i
$$429$$ 0 0
$$430$$ −8.00000 4.00000i −0.385794 0.192897i
$$431$$ −4.00000 + 4.00000i −0.192673 + 0.192673i −0.796850 0.604177i $$-0.793502\pi$$
0.604177 + 0.796850i $$0.293502\pi$$
$$432$$ 0 0
$$433$$ −21.0000 21.0000i −1.00920 1.00920i −0.999957 0.00923827i $$-0.997059\pi$$
−0.00923827 0.999957i $$-0.502941\pi$$
$$434$$ −16.0000 −0.768025
$$435$$ 0 0
$$436$$ 3.00000 3.00000i 0.143674 0.143674i
$$437$$ 8.00000 + 8.00000i 0.382692 + 0.382692i
$$438$$ 0 0
$$439$$ 8.00000 + 8.00000i 0.381819 + 0.381819i 0.871757 0.489938i $$-0.162981\pi$$
−0.489938 + 0.871757i $$0.662981\pi$$
$$440$$ 0 0
$$441$$ 3.00000 0.142857
$$442$$ −8.00000 −0.380521
$$443$$ 20.0000 20.0000i 0.950229 0.950229i −0.0485901 0.998819i $$-0.515473\pi$$
0.998819 + 0.0485901i $$0.0154728\pi$$
$$444$$ 0 0
$$445$$ 7.00000 + 21.0000i 0.331832 + 0.995495i
$$446$$ −6.00000 + 6.00000i −0.284108 + 0.284108i
$$447$$ 0 0
$$448$$ 2.00000 2.00000i 0.0944911 0.0944911i
$$449$$ −23.0000 + 23.0000i −1.08544 + 1.08544i −0.0894454 + 0.995992i $$0.528509\pi$$
−0.995992 + 0.0894454i $$0.971491\pi$$
$$450$$ 9.00000 + 12.0000i 0.424264 + 0.565685i
$$451$$ 0 0
$$452$$ −14.0000 −0.658505
$$453$$ 0 0
$$454$$ 12.0000i 0.563188i
$$455$$ 8.00000 + 24.0000i 0.375046 + 1.12514i
$$456$$ 0 0
$$457$$ 28.0000 1.30978 0.654892 0.755722i $$-0.272714\pi$$
0.654892 + 0.755722i $$0.272714\pi$$
$$458$$ 16.0000 0.747631
$$459$$ 0 0
$$460$$ −4.00000 + 8.00000i −0.186501 + 0.373002i
$$461$$ −19.0000 19.0000i −0.884918 0.884918i 0.109111 0.994030i $$-0.465200\pi$$
−0.994030 + 0.109111i $$0.965200\pi$$
$$462$$ 0 0
$$463$$ 4.00000i 0.185896i 0.995671 + 0.0929479i $$0.0296290\pi$$
−0.995671 + 0.0929479i $$0.970371\pi$$
$$464$$ −7.00000 7.00000i −0.324967 0.324967i
$$465$$ 0 0
$$466$$ 5.00000 + 5.00000i 0.231621 + 0.231621i
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ 12.0000 0.554700
$$469$$ 0 0
$$470$$ −2.00000 6.00000i −0.0922531 0.276759i
$$471$$ 0 0
$$472$$ 2.00000 + 2.00000i 0.0920575 + 0.0920575i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 14.0000 + 2.00000i 0.642364 + 0.0917663i
$$476$$ −4.00000 + 4.00000i −0.183340 + 0.183340i
$$477$$ 3.00000 3.00000i 0.137361 0.137361i
$$478$$ 8.00000 + 8.00000i 0.365911 + 0.365911i
$$479$$ −28.0000 + 28.0000i −1.27935 + 1.27935i −0.338322 + 0.941030i $$0.609859\pi$$
−0.941030 + 0.338322i $$0.890141\pi$$
$$480$$ 0 0
$$481$$ −4.00000 24.0000i −0.182384 1.09431i
$$482$$ −19.0000 + 19.0000i −0.865426 + 0.865426i
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 24.0000 + 12.0000i 1.08978 + 0.544892i
$$486$$ 0 0
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ 1.00000 + 1.00000i 0.0452679 + 0.0452679i
$$489$$ 0 0
$$490$$ 2.00000 + 1.00000i 0.0903508 + 0.0451754i
$$491$$ −8.00000 −0.361035 −0.180517 0.983572i $$-0.557777\pi$$
−0.180517 + 0.983572i $$0.557777\pi$$
$$492$$ 0 0
$$493$$ 14.0000 + 14.0000i 0.630528 + 0.630528i
$$494$$ 8.00000 8.00000i 0.359937 0.359937i
$$495$$ 0 0
$$496$$ −4.00000 + 4.00000i −0.179605 + 0.179605i
$$497$$ −24.0000 + 24.0000i −1.07655 + 1.07655i
$$498$$ 0 0
$$499$$ −2.00000 2.00000i −0.0895323 0.0895323i 0.660922 0.750454i $$-0.270165\pi$$
−0.750454 + 0.660922i $$0.770165\pi$$
$$500$$ 2.00000 + 11.0000i 0.0894427 + 0.491935i
$$501$$ 0 0
$$502$$ 14.0000 + 14.0000i 0.624851 + 0.624851i
$$503$$ 16.0000i 0.713405i −0.934218 0.356702i $$-0.883901\pi$$
0.934218 0.356702i $$-0.116099\pi$$
$$504$$ 6.00000 6.00000i 0.267261 0.267261i
$$505$$ 10.0000 20.0000i 0.444994 0.889988i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 2.00000 2.00000i 0.0887357 0.0887357i
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ 20.0000i 0.884748i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 18.0000i 0.793946i
$$515$$ 32.0000 + 16.0000i 1.41009 + 0.705044i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −14.0000 10.0000i −0.615125 0.439375i
$$519$$ 0 0
$$520$$ 8.00000 + 4.00000i 0.350823 + 0.175412i
$$521$$ 10.0000i 0.438108i −0.975713 0.219054i $$-0.929703\pi$$
0.975713 0.219054i $$-0.0702971\pi$$
$$522$$ −21.0000 21.0000i −0.919145 0.919145i
$$523$$ 24.0000i 1.04945i 0.851273 + 0.524723i $$0.175831\pi$$
−0.851273 + 0.524723i $$0.824169\pi$$
$$524$$ −6.00000 + 6.00000i −0.262111 + 0.262111i
$$525$$ 0 0
$$526$$ 10.0000 + 10.0000i 0.436021 + 0.436021i
$$527$$ 8.00000 8.00000i 0.348485 0.348485i
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 3.00000 1.00000i 0.130312 0.0434372i
$$531$$ 6.00000 + 6.00000i 0.260378 + 0.260378i
$$532$$ 8.00000i 0.346844i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −24.0000 + 8.00000i −1.03761 + 0.345870i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −14.0000 −0.603583
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 11.0000 + 11.0000i 0.472927 + 0.472927i 0.902861 0.429934i $$-0.141463\pi$$
−0.429934 + 0.902861i $$0.641463\pi$$
$$542$$ 28.0000i 1.20270i
$$543$$ 0 0
$$544$$ 2.00000i 0.0857493i
$$545$$ 9.00000 3.00000i 0.385518 0.128506i
$$546$$ 0 0
$$547$$ 8.00000i 0.342055i −0.985266 0.171028i $$-0.945291\pi$$
0.985266 0.171028i $$-0.0547087\pi$$
$$548$$ 7.00000 7.00000i 0.299025 0.299025i
$$549$$ 3.00000 + 3.00000i 0.128037 + 0.128037i
$$550$$ 0 0
$$551$$ −28.0000 −1.19284
$$552$$ 0 0
$$553$$ 48.0000i 2.04117i
$$554$$ 12.0000 0.509831
$$555$$ 0 0
$$556$$ −20.0000 −0.848189
$$557$$ 12.0000i 0.508456i 0.967144 + 0.254228i $$0.0818214\pi$$
−0.967144 + 0.254228i $$0.918179\pi$$
$$558$$ −12.0000 + 12.0000i −0.508001 + 0.508001i
$$559$$ −16.0000 −0.676728
$$560$$ 6.00000 2.00000i 0.253546 0.0845154i
$$561$$ 0 0
$$562$$ 1.00000 1.00000i 0.0421825 0.0421825i
$$563$$ 24.0000i 1.01148i 0.862686 + 0.505740i $$0.168780\pi$$
−0.862686 + 0.505740i $$0.831220\pi$$
$$564$$ 0 0
$$565$$ −28.0000 14.0000i −1.17797 0.588984i
$$566$$ 24.0000i 1.00880i
$$567$$ 18.0000 18.0000i 0.755929 0.755929i
$$568$$ 12.0000i 0.503509i
$$569$$ 3.00000 + 3.00000i 0.125767 + 0.125767i 0.767188 0.641422i $$-0.221655\pi$$
−0.641422 + 0.767188i $$0.721655\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −16.0000 + 12.0000i −0.667246 + 0.500435i
$$576$$ 3.00000i 0.125000i
$$577$$ 18.0000 0.749350 0.374675 0.927156i $$-0.377754\pi$$
0.374675 + 0.927156i $$0.377754\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 0 0
$$580$$ −7.00000 21.0000i −0.290659 0.871978i
$$581$$ −16.0000 −0.663792
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −5.00000 5.00000i −0.206901 0.206901i
$$585$$ 24.0000 + 12.0000i 0.992278 + 0.496139i
$$586$$ 9.00000 9.00000i 0.371787 0.371787i
$$587$$ 28.0000i 1.15568i −0.816149 0.577842i $$-0.803895\pi$$
0.816149 0.577842i $$-0.196105\pi$$
$$588$$ 0 0
$$589$$ 16.0000i 0.659269i
$$590$$ 2.00000 + 6.00000i 0.0823387 + 0.247016i
$$591$$ 0 0
$$592$$ −6.00000 + 1.00000i −0.246598 + 0.0410997i
$$593$$ −1.00000 1.00000i −0.0410651 0.0410651i 0.686276 0.727341i $$-0.259244\pi$$
−0.727341 + 0.686276i $$0.759244\pi$$
$$594$$ 0 0
$$595$$ −12.0000 + 4.00000i −0.491952 + 0.163984i
$$596$$ 6.00000i 0.245770i
$$597$$ 0 0
$$598$$ 16.0000i 0.654289i
$$599$$ 36.0000i 1.47092i 0.677568 + 0.735460i $$0.263034\pi$$
−0.677568 + 0.735460i $$0.736966\pi$$
$$600$$ 0 0
$$601$$ 32.0000 1.30531 0.652654 0.757656i $$-0.273656\pi$$
0.652654 + 0.757656i $$0.273656\pi$$
$$602$$ −8.00000 + 8.00000i −0.326056 + 0.326056i
$$603$$ 0 0
$$604$$ 20.0000i 0.813788i
$$605$$ −22.0000 11.0000i −0.894427 0.447214i
$$606$$ 0 0
$$607$$ 12.0000i 0.487065i 0.969893 + 0.243532i $$0.0783062\pi$$
−0.969893 + 0.243532i $$0.921694\pi$$
$$608$$ −2.00000 2.00000i −0.0811107 0.0811107i
$$609$$ 0 0
$$610$$ 1.00000 + 3.00000i 0.0404888 + 0.121466i
$$611$$ −8.00000 8.00000i −0.323645 0.323645i
$$612$$ 6.00000i 0.242536i
$$613$$ −5.00000 + 5.00000i −0.201948 + 0.201948i −0.800834 0.598886i $$-0.795610\pi$$
0.598886 + 0.800834i $$0.295610\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 15.0000 + 15.0000i 0.603877 + 0.603877i 0.941339 0.337462i $$-0.109568\pi$$
−0.337462 + 0.941339i $$0.609568\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ −12.0000 + 4.00000i −0.481932 + 0.160644i
$$621$$ 0 0
$$622$$ 4.00000 + 4.00000i 0.160385 + 0.160385i
$$623$$ 28.0000 1.12180
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ −26.0000 −1.03917
$$627$$ 0 0
$$628$$ 7.00000 7.00000i 0.279330 0.279330i
$$629$$ 12.0000 2.00000i 0.478471 0.0797452i
$$630$$ 18.0000 6.00000i 0.717137 0.239046i
$$631$$ 16.0000 16.0000i 0.636950 0.636950i −0.312852 0.949802i $$-0.601284\pi$$
0.949802 + 0.312852i $$0.101284\pi$$
$$632$$ 12.0000 + 12.0000i 0.477334 + 0.477334i
$$633$$ 0 0
$$634$$ −5.00000 + 5.00000i −0.198575 + 0.198575i
$$635$$ 6.00000 2.00000i 0.238103 0.0793676i
$$636$$ 0 0
$$637$$ 4.00000 0.158486
$$638$$ 0 0
$$639$$ 36.0000i 1.42414i
$$640$$ 1.00000 2.00000i 0.0395285 0.0790569i
$$641$$ −48.0000 −1.89589 −0.947943 0.318440i $$-0.896841\pi$$
−0.947943 + 0.318440i $$0.896841\pi$$
$$642$$ 0 0
$$643$$ 44.0000 1.73519 0.867595 0.497271i $$-0.165665\pi$$
0.867595 + 0.497271i $$0.165665\pi$$
$$644$$ 8.00000 + 8.00000i 0.315244 + 0.315244i
$$645$$ 0 0
$$646$$ 4.00000 + 4.00000i 0.157378 + 0.157378i
$$647$$ 32.0000i 1.25805i 0.777385 + 0.629025i $$0.216546\pi$$
−0.777385 + 0.629025i $$0.783454\pi$$
$$648$$ 9.00000i 0.353553i
$$649$$ 0 0
$$650$$ 12.0000 + 16.0000i 0.470679 + 0.627572i
$$651$$ 0 0
$$652$$ −24.0000 −0.939913
$$653$$ 4.00000 0.156532 0.0782660 0.996933i $$-0.475062\pi$$
0.0782660 + 0.996933i $$0.475062\pi$$
$$654$$ 0 0
$$655$$ −18.0000 + 6.00000i −0.703318 + 0.234439i
$$656$$ 0 0
$$657$$ −15.0000 15.0000i −0.585206 0.585206i
$$658$$ −8.00000 −0.311872
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 0 0
$$661$$ 21.0000 21.0000i 0.816805 0.816805i −0.168838 0.985644i $$-0.554002\pi$$
0.985644 + 0.168838i $$0.0540016\pi$$
$$662$$ 6.00000 6.00000i 0.233197 0.233197i
$$663$$ 0 0
$$664$$ −4.00000 + 4.00000i −0.155230 + 0.155230i
$$665$$ 8.00000 16.0000i 0.310227 0.620453i
$$666$$ −18.0000 + 3.00000i −0.697486 + 0.116248i
$$667$$ 28.0000 28.0000i 1.08416 1.08416i
$$668$$ −8.00000 −0.309529
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 9.00000 + 9.00000i 0.346925 + 0.346925i 0.858963 0.512038i $$-0.171109\pi$$
−0.512038 + 0.858963i $$0.671109\pi$$
$$674$$ 15.0000 15.0000i 0.577778 0.577778i
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ −25.0000 25.0000i −0.960828 0.960828i 0.0384331 0.999261i $$-0.487763\pi$$
−0.999261 + 0.0384331i $$0.987763\pi$$
$$678$$ 0 0
$$679$$ 24.0000 24.0000i 0.921035 0.921035i
$$680$$ −2.00000 + 4.00000i −0.0766965 + 0.153393i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 36.0000i 1.37750i −0.724998 0.688751i $$-0.758159\pi$$
0.724998 0.688751i $$-0.241841\pi$$
$$684$$ −6.00000 6.00000i −0.229416 0.229416i
$$685$$ 21.0000 7.00000i 0.802369 0.267456i
$$686$$ −12.0000 + 12.0000i −0.458162 + 0.458162i
$$687$$ 0 0
$$688$$ 4.00000i 0.152499i
$$689$$ 4.00000 4.00000i 0.152388 0.152388i
$$690$$ 0 0
$$691$$ 20.0000i 0.760836i 0.924815 + 0.380418i $$0.124220\pi$$
−0.924815 + 0.380418i $$0.875780\pi$$
$$692$$ −5.00000 + 5.00000i −0.190071 + 0.190071i
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ −40.0000 20.0000i −1.51729 0.758643i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −14.0000 −0.529908
$$699$$ 0 0
$$700$$ 14.0000 + 2.00000i 0.529150 + 0.0755929i
$$701$$ 31.0000 + 31.0000i 1.17085 + 1.17085i 0.982006 + 0.188847i $$0.0604752\pi$$
0.188847 + 0.982006i $$0.439525\pi$$
$$702$$ 0 0
$$703$$ −10.0000 + 14.0000i −0.377157 + 0.528020i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 36.0000i 1.35488i
$$707$$ −20.0000 20.0000i −0.752177 0.752177i
$$708$$ 0 0
$$709$$ 27.0000 27.0000i 1.01401 1.01401i 0.0141058 0.999901i $$-0.495510\pi$$
0.999901 0.0141058i $$-0.00449016\pi$$
$$710$$ −12.0000 + 24.0000i −0.450352 + 0.900704i
$$711$$ 36.0000 + 36.0000i 1.35011 + 1.35011i
$$712$$ 7.00000 7.00000i 0.262336 0.262336i
$$713$$ −16.0000 16.0000i −0.599205 0.599205i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 2.00000 + 2.00000i 0.0747435 + 0.0747435i
$$717$$ 0 0
$$718$$ −24.0000 −0.895672
$$719$$ 4.00000i 0.149175i −0.997214 0.0745874i $$-0.976236\pi$$
0.997214 0.0745874i $$-0.0237640\pi$$
$$720$$ 3.00000 6.00000i 0.111803 0.223607i
$$721$$ 32.0000 32.0000i 1.19174 1.19174i
$$722$$ 11.0000 0.409378
$$723$$ 0 0
$$724$$ 8.00000 0.297318
$$725$$ 7.00000 49.0000i 0.259973 1.81981i
$$726$$ 0 0
$$727$$ 28.0000i 1.03846i −0.854634 0.519231i $$-0.826218\pi$$
0.854634 0.519231i $$-0.173782\pi$$
$$728$$ 8.00000 8.00000i 0.296500 0.296500i
$$729$$ 27.0000i 1.00000i
$$730$$ −5.00000 15.0000i −0.185058 0.555175i
$$731$$ 8.00000i 0.295891i
$$732$$ 0 0
$$733$$ 15.0000 15.0000i 0.554038 0.554038i −0.373566 0.927604i $$-0.621865\pi$$
0.927604 + 0.373566i $$0.121865\pi$$
$$734$$ −18.0000 18.0000i −0.664392 0.664392i
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ −13.0000 4.00000i −0.477890 0.147043i
$$741$$ 0 0
$$742$$ 4.00000i 0.146845i
$$743$$ 10.0000 10.0000i 0.366864 0.366864i −0.499468 0.866332i $$-0.666471\pi$$
0.866332 + 0.499468i $$0.166471\pi$$
$$744$$ 0 0
$$745$$ 6.00000 12.0000i 0.219823 0.439646i
$$746$$ 25.0000 + 25.0000i 0.915315 + 0.915315i
$$747$$ −12.0000 + 12.0000i −0.439057 + 0.439057i
$$748$$ 0 0
$$749$$ 32.0000i 1.16925i
$$750$$ 0 0
$$751$$ 40.0000i 1.45962i 0.683650 + 0.729810i $$0.260392\pi$$
−0.683650 + 0.729810i $$0.739608\pi$$
$$752$$ −2.00000 + 2.00000i −0.0729325 + 0.0729325i
$$753$$ 0 0
$$754$$ −28.0000 28.0000i −1.01970 1.01970i
$$755$$ 20.0000 40.0000i 0.727875 1.45575i
$$756$$ 0 0
$$757$$ 28.0000 1.01768 0.508839 0.860862i $$-0.330075\pi$$
0.508839 + 0.860862i $$0.330075\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ −2.00000 6.00000i −0.0725476 0.217643i
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 12.0000i 0.434429i
$$764$$ −16.0000 16.0000i −0.578860 0.578860i
$$765$$ −6.00000 + 12.0000i −0.216930 + 0.433861i
$$766$$ −36.0000 −1.30073
$$767$$ 8.00000 + 8.00000i 0.288863 + 0.288863i
$$768$$ 0 0
$$769$$ 3.00000 + 3.00000i 0.108183 + 0.108183i 0.759126 0.650943i $$-0.225627\pi$$
−0.650943 + 0.759126i $$0.725627\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 14.0000i 0.503871i
$$773$$ −21.0000 21.0000i −0.755318 0.755318i 0.220149 0.975466i $$-0.429346\pi$$
−0.975466 + 0.220149i $$0.929346\pi$$
$$774$$ 12.0000i 0.431331i
$$775$$ −28.0000 4.00000i −1.00579 0.143684i
$$776$$ 12.0000i 0.430775i
$$777$$ 0 0
$$778$$ −17.0000 17.0000i −0.609480 0.609480i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −8.00000 −0.286079
$$783$$ 0 0
$$784$$ 1.00000i 0.0357143i
$$785$$ 21.0000 7.00000i 0.749522 0.249841i
$$786$$ 0 0
$$787$$ −12.0000 + 12.0000i −0.427754 + 0.427754i −0.887863 0.460109i $$-0.847810\pi$$
0.460109 + 0.887863i $$0.347810\pi$$
$$788$$ −3.00000 + 3.00000i −0.106871 + 0.106871i
$$789$$ 0 0
$$790$$ 12.0000 + 36.0000i 0.426941 + 1.28082i